JPH09107370A - Simulation method and simulator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain the simulator that evaluates frequency of incidence of a low incidence probability in a system whose state is transited in a probable way at a high speed by providing each of simulation model setting means, initial state setting means, calculation of transition probability and calculation of incidence probability means. SOLUTION: An input section 49 receives various information. An environment setting section 50 sets various parameters based on characteristic information of the system received via the input section 49, models the network system being an evaluation object to set a proper traffic model. Furthermore, when information required to set an initial state and an intermediate state of the system is entered, a simulation environment corresponding to each state is set. An evaluation section 51 is a simulation engine and sends the information obtained as a result to a processing section 53. An output section 54 outputs a statistic variable obtained by the processing section 53 by using a CRT or a printer or the like.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a simulation method and a simulator for evaluating the performance of a system, for example, a packet or cell which is one of the performance indicators of a communication system such as a packet communication network or an ATM communication network. The present invention relates to a simulation method and a simulator for evaluating the occurrence frequency of an event having a low occurrence probability such as the occurrence frequency of a discarded state.

[0002]

2. Description of the Related Art Packet communication networks and ATM (Asynchronous
Tranfer Mode (Asynchronous Transfer Mode) One of the performance indicators of communication networks is the packet or cell loss rate. The specifications are written as 10-10 or less. Regarding delay dispersion (CDV, Cell DelayVariation), CDV <250 μsec (10 −10 quantil)
There is also a specification notation e). In this way, not only the average characteristics of the entire cell but also the average characteristics of very rare occurrence events (rare events, hereinafter called rare events) such as packet and cell discards are targeted for cell characteristic evaluation. To do. When designing a system, it is necessary to perform quality evaluation because it is necessary to design to meet these specifications. For quality evaluation, for example, the analysis method is difficult to apply to general network analysis. Therefore, in reality, the approximation analysis method and the Monte Carlo simulation method are used.

As an analysis method, various approximation methods have been proposed, but there are restrictions on approximation accuracy, applicable range, etc., and sufficient examination is required before use. Also,
Depending on the analysis target, it is necessary to secure enormous states and state transitions on a computer. In this case, there are practical restrictions such as the memory of the computer. In addition, it cannot be said in general that the analysis method can obtain an answer faster than the simulation.

The Monte Carlo simulation method is straightforward and easy to obtain accurate results. However, in order to make an evaluation of 10-10, in the simulation, 1011-1
012 events need to occur. Depending on the content of the event, it is difficult to obtain a result within a practical time even with a current computer or a computer several years later. In reality, the evaluation of 10-5 will be full.

Although a method of actually making an experimental evaluation device and performing simulation can be considered instead of a simulation by software, it is not easy to create a prototype, and the generality and expandability of evaluation contents are lacking. .

Based on these points, it is generally difficult to evaluate a rare event such as cell discard.

[0007] However, as the actual system specifications require the severe evaluation and design of rare events as described above, it is clear that "rare event evaluation technology" as a product design technology is actually required. is there. The following items should be considered in the method.

(1) High speed ... High speed is required so that an event such as 10-15 can be evaluated. (2) Versatility ...
To be able to provide a unified tool that can support diverse systems. (3) Ease of use: It is desirable that the overhead is as small as possible during use. At the very least, it should be easy to use for designer level people.

Recently, attempts have been made to execute a simulation of rare events at high speed. There, basically, an idea called IS (Importance Sampling) is adopted. This is a method of distorting (biasing) system parameters (including traffic parameters) so as to increase the frequency of occurrence of rare events. This method has some difficult problems such as optimization problem and calculation of transition probability matrix, and various solving methods have been studied.

Next, a conventional simulation method will be described with reference to the drawings.

In the queue model shown here, the distribution of event (transaction) arrival times and the distribution of service times are general distributions, the number of windows is 1, and the allowable queue length is K (G / G). / 1 / K).

Consider the steady state of a single queue of length K in FIG. Arrival rate λ, service rate μ (λ <
In the case of μ), generally, as shown in FIG. 22B, the distribution of the queue length (Q) becomes less frequent as the length thereof becomes longer, and becomes a rare event. Here, if it is desired to simulate the cell discard rate, in FIG. 22B, it is necessary to count the events (events) where Q> K.

In the conventional Monte Carlo simulation, the image shown in FIG. 22B was faithfully simulated.

On the other hand, the IS considers the following.
That is, as shown in FIG. 23B, the distribution of the queue Q is forcibly distorted so that the frequency of Q> K becomes much higher. As a method of distorting, for example, FIG.
As shown in (a), it is possible to change the ratio of the arrival rate and the service rate.

As a result, the time-series fluctuation locus of the queue length (Q) during the simulation is as shown in FIG. That is, with respect to the trajectory of the distortion queue (dashed line), the frequency of Q> K is much higher than that of the original trajectory (solid line). If the result obtained here can be converted back into the frequency information before distortion by some method, the result can be obtained at high speed using the distortion distribution. Actually, if the weighting of the probability density relationship according to the distortion is appropriately calculated, the originally intended statistic can be calculated.

[0016]

As described above, the degree of distortion in the IS method should be set so that an accurate result (like a normal Monte Carlo method) can be obtained with the shortest calculation time. It is better for the calculation time to have a smaller number of steps algorithmically, but it is also necessary to shorten the execution time of each step, and as a whole, the sum of (unit step processing time) × (number of steps) is the minimum. It can be said that it is the most efficient to do. Further, in this sense, the strain of the system for realizing the shortest time simulation is slow if evaluated for the first time after the simulation is completed. In other words, it is desirable that a new distortion can be found in a short time before the simulation starts, but even if that is not possible, at least while performing the simulation,
An algorithm that converges to the optimum distortion is required.

As an example, the document "Importance Samp
ling for Stochastic Simulations "by Glyn et al. Manag
ement Science Vol.35 No.11 pp.1367-1392 Nov.1986
) Describes that the distortion is adjusted so as to minimize the variance of the statistic to be obtained (Variance Reduction).

As another example, the document “Statistical
Optimization of Dynamic Impor- tance Sampling Para
meters for Efficient Simulation of Communication N
et-works ”(Devetsikiotis et al. IEEE / ACM Trans.N
etworking Vol.1 No.3 pp.293-305 Jun.1993), it is not possible to know the true variance of statistics, so a method using an unbiased variance estimator of the true variance is proposed. .

These methods basically result in a solution of an optimization problem that seeks to minimize the variance (or its estimated amount). In practice, it is necessary to provide some heuristics or to evaluate the local solution in order to avoid the local optimal solution (see "Simulation of
Digital Communication Systems Using a Stochastica-
lly Optimized Importance Sampling Technique '' Al-Q
aq et al. Proceeding of GLOBECOM pp.1718-1722 1993,
`` Stochastically Gradient Technique for the Effi
cient Simulation of High-Speed Networks Using Impo
rtance Sampling '' Al-Qaq et al. Proceeding of GLOBE
COM pp.751-756 1993). However, the method for obtaining the optimum solution has problems such as stability and convergence, and although it is originally intended to speed up the simulation, it may take a paradoxical result that it takes time to obtain the optimum solution.

Also, while gradually changing the distortion, create a "table" of variances (estimates of them) and put in a "search" for the optimum solution, where the distortion is determined and a full-scale IS simulation is performed. The idea of starting was also proposed (reference "Ef
ficient Estimation of CellBlocking Probability for
ATM System "Wang et al. IEEE / ACM Trans.Networking
See Vol.1 No.2 pp.230-235 Apr.1993).

However, even in this case, there is no guarantee that the optimum solution obtained by carrying out a small-scale simulation is the optimum solution in a full-scale simulation.

On the other hand, paying attention to the dynamic structure of the set of trajectories, the Hamiltonian of the system is actually
ian), and the idea of trying to find the maximum likelihood locus from the process of minimizing it has also been proposed (Reference “A Qu
ick Simulation Method forExcessive Backlogs in Net
works of Queues "Parekh et al. IEEE Trans. Autom.Con
torol Vol.34 No.1 pp54-66 Jan.1989). Here, it is assumed that it is necessary to explicitly find the shape of Hamiltonian. This may be possible with a very simple network, queuing, but is generally very difficult.

As is generally true of the conventional IS method, the weighting of the probability density function for distortion correction must be known. For this, it is necessary to devise to reduce the calculation time by following a certain modeling. This is also a difficult problem in general.

As described above, although there is theoretically a form of the IS method, there are many essential problems when it is applied to actual problems.

Therefore, an object of the present invention is to provide a simulation method capable of quickly evaluating the occurrence frequency of a state having a low occurrence probability in a system in which the states transition probabilistically, and a simulator using the simulation method.

[0026]

A simulation method according to the present invention (claim 1) is a simulation method for evaluating the occurrence frequency of a desired state in a system in which states transition probabilistically. A first step of setting a simulation model of the system based on the characteristic information of the system; and a step of setting the state of the simulation model set in the first step to an initial state of the system based on given conditions. Step 2 and at least one intermediate state through which the state transition sequence from the initial state set in this second step to the desired state passes, are set based on the given conditions. Frequency of transition to a state, frequency of transition from the intermediate state to the next intermediate state, transition from the intermediate state to the desired state Frequency is obtained stepwise, and the third step of calculating the inter-state transition probability from the frequency of transition between these states and the inter-state transition probability calculated in this third step are multiplied. By providing the fourth step of calculating the occurrence probability of the desired state, the occurrence frequency of the state having a low occurrence probability can be evaluated at high speed.

The simulation method (claim 2) of the present invention is a packet transfer system for transferring a packet via at least one buffer memory for temporarily storing an input packet, wherein the packet in the buffer memory is A simulation method for evaluating a frequency of occurrence of a state of being discarded, comprising a first step of setting a simulation model of the system based on given characteristic information of the system, and a first step. A second step of setting the state of the set simulation model to the initial state of the system based on the amount of packets accumulated in the given buffer memory, and from the initial state set in the second step to the above Gives an intermediate state that exists in the process of transitioning to the state where the packet is discarded At least one is set based on the amount of packets accumulated in the buffer memory, the frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, the intermediate state to the The third step of calculating the frequency of transition to the state in which the packet is discarded in stages, and calculating the transition probability between states from the frequency of transition between these states, and the respective steps calculated in this third step And a fourth step of calculating the occurrence probability of the state in which the packet is discarded by multiplying the transition probability between states, thereby increasing the occurrence frequency of a state with a low original occurrence probability such as a packet discard rate. Can be evaluated.

Further, the simulation method of the present invention (claim 3) is a packet transfer system for transferring a packet via a plurality of buffer memories for temporarily storing an input packet, wherein any one of the plurality of buffer memories is provided. Is a simulation method for evaluating the occurrence frequency of occurrence of a state in which the delay time when the packet arrives is equal to or more than a predetermined value, the simulation of the system based on the given characteristic information of the system. A first step of setting a model, and the state of the simulation model set in the first step is set to an initial state of the system based on a delay time when the packet arrives at the buffer memory. From the second step and the initial state set in this second step, When the packet arrives at the buffer memory, an intermediate state existing in the process of transiting to a state where the delay time when the packet arrives at one of the buffer memories becomes equal to or more than a predetermined value. At least one is set based on the delay time, the frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, the packet from the intermediate state to any of the plurality of buffer memories The frequency of transition to a state in which the delay time when arrives is equal to or greater than a predetermined value is obtained in stages, and the transition probability between states is statistically calculated from the frequency of transition between these states. And the probability of transition between states calculated in the third step, and the delay when the packet arrives at any one of the plurality of buffer memories. A fourth step of calculating the occurrence probability of a state in which time is equal to or greater than a predetermined value, and the occurrence frequency of a state with a low original occurrence probability such as CDV (cell delay time fluctuation) is rapidly evaluated. it can.

A simulation method (claim 1) of the present invention is a simulation method for evaluating the occurrence frequency of a desired state in a system in which the states transition probabilistically, and the method is based on the characteristic information of the system. A simulation model of the system is set, the state of the simulation model is set to the initial state of the system, and at least one intermediate state through which a state transition sequence from the initial state to the desired state passes is set, and The frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, the frequency of transition from the intermediate state to the desired state are obtained stepwise, and transitions are made between these states. Based on the product of the transition probabilities between states calculated from the frequency, by calculating the occurrence probability of the desired state, The occurrence frequency of the stomach state can be evaluated at a high speed.

Further, the simulation method (claim 2) of the present invention is a packet transfer system for transferring a packet via at least one buffer memory for temporarily storing an input packet, wherein the packet in the buffer memory is A simulation method for evaluating a frequency of occurrence of a discarded state, wherein a simulation model of the communication system is set based on characteristic information of the communication system, and the state of the simulation model is stored in the buffer memory. Present in the process of setting the initial state of the communication system based on the amount of accumulated packets and transitioning from the initial state determined based on the amount of packets accumulated in the buffer memory to the state where the packets are discarded. Set at least one intermediate state to From the intermediate state to the next intermediate state, the frequency from the intermediate state to the state where the packet is discarded, and the transition between these states. By calculating the occurrence probability of the state in which the packet is discarded, based on the product of the transition probabilities between states calculated from the frequency of
It is possible to quickly evaluate the occurrence frequency of a state with a low probability of occurrence, such as the packet discard rate.

Further, the simulation method (claim 3) of the present invention is a packet transfer system for transferring a packet via a plurality of buffer memories for temporarily storing an input packet, wherein any one of the plurality of buffer memories is provided. Is a simulation method for evaluating the occurrence frequency of occurrence of a state in which the delay time when the packet arrives is equal to or more than a predetermined value, the simulation of the system based on the characteristic information of the packet transfer system. A model is set, the state of the simulation model is set to the initial state of the system based on the delay time when the packet arrives at the buffer memory, and the delay time when the packet arrives at the buffer memory is set. Of the plurality of buffer memories from the initial state determined based on Set up at least one intermediate state delay time when the packet arrives on whether the deviation is present in the process of transition to a state where a predetermined value or more,
Frequency of transition from the initial state to the intermediate state, frequency of transition from the intermediate state to the next intermediate state, delay time when the packet arrives from the intermediate state to one of the plurality of buffer memories is predetermined. Determine the frequency of transition to a state that is greater than or equal to the specified value in stages, and then use one of the buffer memories based on the product of the transition probabilities between states calculated from the frequency of transition between these states. By calculating the occurrence probability of a state in which the delay time when the packet arrives is a predetermined value or more, the occurrence frequency of a state with a low original occurrence probability such as CDV (cell delay time fluctuation) can be evaluated at high speed. .

The simulator of the present invention (claim 5)
Is a simulator that evaluates the occurrence frequency of a desired state in a system in which the states transition probabilistically, and model setting means for setting a simulation model of the system based on the given feature information of the system. ,
Setting means for setting the state of the simulation model set by the model setting means to the initial state of the system based on given conditions, and a state transition sequence from the initial state set by the setting means to the desired state At least one intermediate state is set based on a given condition, the frequency of transition from the initial state to the intermediate state,
The frequency of transition from the intermediate state to the next intermediate state, the frequency of transition from the intermediate state to the desired state are obtained stepwise, and the transition probability between states is calculated from the frequency of transition between these states. By including the first calculation means and the second calculation means for calculating the occurrence probability of the desired state by multiplying the transition probabilities between states calculated by the first calculation means, The occurrence frequency of a state with a low probability can be evaluated quickly.

The simulator of the present invention (claim 6)
Is a simulator for evaluating a frequency of occurrence of a state in which a packet in the buffer memory is discarded in a packet transfer system that transfers the packet via at least one buffer memory that temporarily stores the input packet. Model setting means for setting a simulation model of the communication system based on the given characteristic information of the communication system, and the buffer memory provided with the state of the simulation model set by the model setting means. The setting means for setting the initial state of the communication system based on the amount of packets accumulated in the communication system, and the intermediate state existing in the process of transition from the initial state set by the setting means to the state where the packet is discarded. Less based on the amount of packets stored in the buffer memory 1 is also set, and the frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, and the frequency of transition from the intermediate state to the state where the packet is discarded are stepwise. Then, the packet is discarded by multiplying the first calculation means for calculating the inter-state transition probability from the frequency of transition between the respective states and the inter-state transition probability calculated by the first calculation means. By providing the second calculation means for calculating the occurrence probability of the state, the occurrence frequency of the state having a low original occurrence probability such as the packet discard rate can be evaluated at high speed.

A simulator of the present invention (claim 7)
In a packet transfer system that transfers a packet through a plurality of buffer memories that temporarily store an input packet, a delay time when the packet arrives at any one of the plurality of buffer memories is predetermined. A simulator for evaluating the occurrence frequency of occurrence of a value equal to or more than a value, the model setting means for setting a simulation model of the system based on the given characteristic information of the packet transfer system, and the model setting means. Setting means for setting the state of the simulation model set in 1. to the initial state of the system based on the delay time when the packet arrives at the buffer memory, and from the initial state set by the setting means, Delay time when the packet arrives at any of the multiple buffer memories At least one intermediate state existing in the process of transitioning to a state that is equal to or greater than a predetermined value is set based on the delay time when the packet arrives at the buffer memory, and transitions from the initial state to the intermediate state. Frequency, frequency of transition from the intermediate state to the next intermediate state, transition from the intermediate state to a state in which a delay time when the packet arrives at any of the plurality of buffer memories is a predetermined value or more First calculation means for statistically calculating the inter-state transition probability from the frequency of transition between these states by stepwise obtaining the frequency, and each inter-state transition probability calculated by the first calculation means Second calculating means for calculating a probability of occurrence of a state in which the delay time when the packet arrives at any of the plurality of buffer memories is equal to or more than a predetermined value by multiplying by The By providing, the occurrence frequency of the low state of the original probability such CDV (Cell Delay time fluctuation) can be evaluated at high speed.

Further, the simulator of the present invention is a simulator for evaluating the occurrence frequency of a desired state in a system in which states are probabilistically transitioned, and a simulation model of the system is calculated based on the characteristic information of the system. The model setting means for setting, the first setting means for setting the state of the simulation model set by the model setting means to the initial state of the system, and the state of the simulation model set by the model setting means,
A frequency for transition to an intermediate state existing in the process of transitioning from the initial state set by the first setting means to the desired state is calculated, and a transition probability between states is statistically calculated based on the frequency. The first statistical processing means, the second setting means for setting the state of the simulation model set by the model setting means to the intermediate state, and the state of the simulation model set by the model setting means are the second state.
Second statistical processing means for calculating the frequency of transition from the intermediate state set by the setting means to the desired state, and statistically calculating the transition probability between states based on the frequency;
By providing the occurrence probability calculation means for multiplying the transition probabilities between states calculated by the second statistical processing means to calculate the occurrence probability of the desired state, the occurrence frequency of a state with a low occurrence probability is increased. Can be evaluated.

Further, in the simulator of the present invention, in the communication system in which the state transition can be judged by the packet amount in the buffer memory for temporarily accumulating the input packet, the state in which the packet in the buffer memory is discarded occurs. A simulator for evaluating the occurrence frequency of
The model setting means for setting a simulation model based on the characteristic information of the system, and the state of the simulation model set by the model setting means based on the amount of packets accumulated in the buffer memory. Of the simulation model set by the model setting means and a state of the simulation model set by the model setting means transits from the initial state set by the first setting means to a state in which the packet is discarded. A first statistic that exists in the process and determines the frequency of transition to an intermediate state determined based on the amount of packets accumulated in the buffer memory, and statistically calculates the transition probability between states based on the frequency. Processing means and second setting means for setting the state of the simulation model set by the model setting means to the desired intermediate state The state of the simulation model set by the model setting means exists in the process of transition from the intermediate state set by the second setting means to the state where the call is discarded, and is stored in the buffer memory. Set by the second statistical processing means for calculating the frequency of transition to the intermediate state determined based on the packet amount, and statistically calculating the transition probability between states based on the frequency, and the model setting means. The state of the simulation model is the second
The transition frequency from the intermediate state set by the setting means to the state in which the packet is discarded, which is determined based on the packet amount accumulated in the buffer memory, is obtained, and the transition between states is performed based on the frequency. Occurrence of a state in which the packet is discarded by multiplying the third statistical processing means for statistically calculating the probability and the inter-state transition probability calculated by the first, second, and third statistical processing means. By including the occurrence probability calculating means for calculating the probability, it is possible to quickly evaluate the occurrence frequency of a state with a low occurrence probability such as a state in which a packet is discarded.

Further, in the simulator of the present invention, in the communication system in which the state transition can be judged by the packet amount in the buffer memory for temporarily storing the input packet, the state in which the packet in the buffer memory is discarded occurs. A simulator for evaluating the occurrence frequency of
The model setting means for setting a simulation model based on the characteristic information of the system, and the state of the simulation model set by the model setting means based on the amount of packets accumulated in the buffer memory. Of the simulation model set by the model setting means and a state of the simulation model set by the model setting means transits from the initial state set by the first setting means to a state in which the packet is discarded. A first statistic that exists in the process and determines the frequency of transition to an intermediate state determined based on the amount of packets accumulated in the buffer memory, and statistically calculates the transition probability between states based on the frequency. A processing means and a second for setting the state of the simulation model set by the model setting means to the intermediate state
And the state of the simulation model set by the model setting means is judged from the intermediate state set by the second setting means on the basis of the packet amount accumulated in the buffer memory. Second statistical processing means for obtaining a frequency of transition to a state in which a packet is discarded and statistically calculating an inter-state transition probability based on the frequency.
By providing an occurrence probability calculation unit that multiplies the transition probabilities between states calculated by the first and second statistical processing units and calculates the occurrence probability of the state in which the packet is discarded, for example, a packet It is possible to quickly evaluate the occurrence frequency of a state with a low occurrence probability, such as a state in which the is discarded.

[0038]

BEST MODE FOR CARRYING OUT THE INVENTION Before describing the embodiments of the present invention, the principle of the present invention will be described. The simulation method according to the present invention is different from the evaluation method such as the conventional IS method that brings in a distribution completely different from the original distribution of the queue length, and is a rare event based on the distribution of the queue length itself. The simulation is performed. In other words, paying attention to the fact that the fluctuation locus of the queue length on the time axis passes through an intermediate state with a higher occurrence frequency before reaching the state in which the rare event of interest occurs, the frequency of occurrence of that intermediate state ( Probability P {En}) and the frequency of occurrence of the target event (conditional probability P {Em | En}) on the premise that the intermediate state has been achieved by Monte Carlo simulation, and the target rare event occurs. The frequency (probability P {Em}) is calculated by multiplying them by the product (P {En} · P
It is obtained as {Em | En}).

Next, the principle of the present invention will be described by taking a simple queue model as an example. The queuing model shown in FIG. 2 (a) has a distribution of arrival times of events (transactions) and a distribution of service times of general distributions,
The number of windows is 1, and the allowable queue length is K (G /
G / 1 / K). When the arrival rate is λ and the service rate is μ (λ <μ), generally, as shown in FIG. 2B, the distribution of the queue length (Q) becomes less frequent as the length becomes longer. It is a rare event. Here, if it is desired to simulate the cell discard rate, in the case of FIG. 2B, Q> K
We must count the number of events.

FIG. 2C shows a time-series fluctuation locus of the queue length (Q). As is clear from FIG. 2C, before Q> K, Q = K '(0 <
It has passed the state of K '<K). Furthermore, the event that the queue length Q becomes longer than the allowable queue length K ({Q>
The relationship between the event that becomes K}) and the event that the queue length Q becomes longer than the queue length K ′ (the event that {Q> K ′}) is

(Equation 1)

It will also be clear that this can be expressed as

Therefore, first, the frequency of the state where Q> K 'is obtained by simulation. This ends in a short time. Next, the frequency of the state of Q> K starting from the state of Q = K ', that is, Q> K under the condition of Q>K'.
The probability of K is obtained by simulation.

Since only the locus under the condition of Q> K 'is targeted, the probability of occurrence of the event of Q> K becomes high. After all, the occurrence probability of the target state of Q> K is expressed by the product of the probability of the event of Q> K ′ and the conditional probability of Q> K under the condition of Q> K ′. By the way, here, it is considered that the cell discard event RE is set and the occurrence probability P {RE} thereof is obtained. This case will be described with reference to the schematic procedure of the simulation method of the present invention shown in FIG.

For example, when the packet discard characteristic of the packet queuing network is to be obtained, first, the intermediate state S is set (step S1). For example, the intermediate state is set as a combination of numbers within the capacity of the queue buffer.

Next, the occurrence probability P {S} of the intermediate state is evaluated by Monte Carlo simulation (step S
2). This is required in a shorter simulation time than directly simulating P {RE}.

With the intermediate state S as the initial state, the probability P {RE | S} of the desired state is newly obtained by simulation (step S3). Here, the intermediate state {S}
It is intended to obtain the occurrence probability of the target state {RE} under the condition of. Therefore, when the trajectory of the system starting from the initial state of {S} passes through {S} again and returns to the original state, the results up to that point are used for statistical processing, and the intermediate state {S} is newly set. Perform the simulation again as the initial state. This can improve the efficiency of simulation.

Probability P {RE | S} obtained as a result of the above
And the packet loss rate P {RE} in the network of the environment set in step S1 is obtained from the product of P {S} (step S4).

As described above, according to the present invention, basically, the probability of occurrence of a rare event is obtained by calculating the conditional probability. Since the procedure of introducing distortion into the original distribution adopted in the conventional IS method is not included here, a complicated result conversion (probability weight calculation) procedure or the like can be omitted.

Further, the simulation method of the present invention will be described based on a mathematical model. That is, it is assumed that the probability of the event Em = {x | x> xm} is to be obtained for the trajectory x (t) that follows the Markov process as shown in FIG. Here, the trajectory x (t) corresponds to the length of the queue in the description of FIG.

When xm> xn, the event En = {x | x>
xn} is also defined. That is, the relationship between Em and En is

(Equation 2)

Is as follows.

A (n, i) is

(Equation 3)

Shows one section (at most countable number)
A (m, i) is

(Equation 4)

One section (at most countable number) is given as follows.
Each section {A (m, i)} i is relatively prime. That is,

(Equation 5)

Is as follows.

{A (m, i)} i, {A (n, j)} j
For the subscript of

(Equation 6)

Those that have an inclusive relationship like this are common. Therefore, A (m, i) = φ may be satisfied.

In addition, the measure μ is introduced as the “length (residence time)” of each section. Then, the probability P of occurrence of event Em
{Em} is

(Equation 7)

It can be expressed as

In these equations (1) to (3), the right side is assumed to converge. Then, the formula (3) is further modified.

[0061]

(Equation 8)

Equation (6) is the occurrence probability P of the target event.
To obtain {Em}, from the initial state of the system to the target state Em
Occurrence probability of the state En that must pass through on the way to
It is shown that the conditional occurrence probability of the event Em that is conditional on the En state can be obtained, and P {Em} can be obtained in the form of their product. Further, according to the equation (5), the method of taking the intermediate state En is arbitrary as long as it is between Em and the initial state {0}. I understand.

Generally, P {Em | En} depends on the initial value. Regarding how to set the initial value, it is necessary to know the probability density of the locus x (t) passing on X = {x (t) | x (t) = xn} per unit time. For example, P
During the simulation for obtaining {En}, each A (n,
For i), the position (point on X) at the first time is stored. The position of this first En is taken as the initial value of the simulation of P {Em | En}. Also, by definition P
In the simulation of {E | En}, if the locus has come out of En, one trial may be aborted there, or the period during which it has come out may be ignored.

The generated intermediate state can be considered as a state in which the locus crosses the intermediate state. However, in an actual system, the locus does not fill the state space uniformly at all. As a trajectory until an event occurs, a set of trajectories in a fairly limited range contributes to the event occurrence. Hereinafter, the locus with a large contribution will be called the maximum likelihood locus of the event.

The maximum likelihood locus is not always a "one" locus. It may be a set of trajectories. For example, FIG.
As shown in (a), consider a network in which two queues are connected in parallel (M / M / 1 / K with λ <μ (random arrival, exponential distribution service, one window, allowable queue length K)). . Here, the probability distribution p in which the length of each queue is n
(N) is defined as ρ (average traffic density) = λ / μ,
It is described by p (n) = ρn (1-ρ). The call drop rate in each queue (eg, drop rate CLR in an ATM network) is equal to the probability that the length is K, so CLR is
= P (K) = [rho] K (1- [rho]). Since the discard event in this network is to be discarded in at least one of the two queues, the maximum likelihood locus here is that one queue is discard and the other queue is the average length. The trajectory seems plausible. Then, in the state space as shown in FIG. 4B, the locus L1 becomes the maximum likelihood locus. However, since the system is symmetric with respect to the two queues, the symmetric locus of L1 as shown by the locus L2 is also the maximum likelihood locus. Therefore, in this system, two maximum likelihood trajectories are considered. In this way, generally, a maximum likelihood trajectory set consisting of a plurality of maximum likelihood trajectories associated with the symmetry of the system can be considered. Since the elements of this set are symmetrical (equivalent), it is not necessary to be aware of which set each element was in the actual simulation. In the example of FIG. 4, the state En = {(n1, n2) | n1> K, or,
If n2> K} is recognized, the maximum likelihood locus is L
1, L2 are extracted with equal probability.

Up to this point, the intermediate state is, for example, En =
It has been described as {x | x> xn}. However, there is a caveat in the actual simulation, such as a queuing network, because it is a discrete system. Therefore, with reference to FIG. 5, an intermediate state in the case of a simple single queue will be described.

As shown in FIG. 5A, the queue has
Occasionally, multiple cells for the same outgoing route are input at one time. At this time, the number of cells in the queue jumps a plurality of steps at a time. For example, 8 cells at a time
In the case of the simultaneous input, as shown in FIG. 5B, not only state i + 1 but also i + in the next cell cycle from state i
There is a possibility of transition to 2, i + 3, ... i + 8.

If the intermediate state En is {i +
If only 1} is set, the jump transition as shown in FIG. 5B cannot be detected. Therefore, it is necessary to predict possible state transitions in advance and set intermediate states so that they can substantially be covered. For example, FIG.
If there is an input from 8 ports as in (a), En
= {I + 1, i + 2, ..., i + 8}. Actually, it may not be necessary up to this point. This is because the transition probability to the state where the difference in the number of cells is small is higher. In this way, when the intermediate state is appropriately defined by a set of a plurality of states, the transition destination is detected as En for any state transition. This is the same except for the case of a single queue, and the setting for detecting an intermediate state in a general queuing network includes a set having a cell number range as an element.

Based on the above points, points to be noted in each step of the flowchart shown in FIG. 1 will be summarized.

First, in setting the intermediate state in step S1, a set of variables that describe the system as the intermediate state is set. For example, the following variables can be considered.

Time-Number of cells in queue (length of queue) -Each cell's outgoing route information, characteristic information of individual cell such as priority class-State of cell source (for example, burst traffic is generated) Active source (AC)
T) or one of two states such as inactive (INACT)) Here, a source traffic model will be described.
The burst source is IBP (Interrupted Be)
rnoulli Process). The state transition diagram of the source model is shown in FIG.

As a simple source for generating burst traffic, in a simple model that generates burst traffic from state transitions of two states (active (ACT) and inactive (INACT)) Whether it is in the state of is one piece of information that determines the state of the system.

Consider the equilibrium state in the source model shown in FIG.

Here, α is the probability (occurrence rate) of generating a cell (call) in the ACT state, p is the probability of being ACT again at the next time in the ACT state, and q is INA.
It is the probability of being INACT again at the next time when in the state of CT.

Steady state probability distribution P of ACT and INACT
A and PI can be expressed by the following equations.

[0076]

(Equation 9)

The burst length distribution PA (L) can be expressed by the following equation.

[0078]

(Equation 10)

The average burst length EA {L} can be expressed by the following equation.

[0080]

[Equation 11]

The idle period distribution PI (L) can be expressed by the following equation.

[0082]

(Equation 12)

The average idle length EI {L} can be expressed by the following equation.

[0084]

(Equation 13)

The average load ρ can be expressed by the following equation.

[0086]

[Equation 14]

Here, if α = 1 and the average burst length L and the load ρ, p and q are given by the following equations.

[0088]

(Equation 15)

Thus, in the case of burst traffic,
If an intermediate state is described, it will be represented by p, q, and ρ, for example.

In the end, the intermediate state is enough information to restart the attempt.

In the evaluation of the occurrence probability of the intermediate state in step S2 of FIG. 1, it is sufficient to evaluate the occurrence of the intermediate state by using one simulation locus having a relatively short time.

The sufficient simulation time here can be defined as satisfying one of the following criteria, for example.

1. The lower limit of the number of times of rush into the intermediate state is set in advance, and the number of times of rush beyond that is achieved.

2. As a period in the intermediate state, the confidence interval is estimated from the mean and the unbiased variance, and a certain multiple or more of that interval is achieved.

In the simulation from the intermediate state in step S3 of FIG. 1, the simulation may be executed under the condition of En and the frequency of events of Em may be evaluated.

The initial value (state parameter) of En is determined as follows, for example. In the simulation used when the occurrence probability of the intermediate state is obtained, the state is recorded each time the trajectory enters the intermediate state, and these states are set as the initial values of the simulation from the intermediate state.

Next, the evaluation of the simulation result in step S4 of FIG. 1 will be described. As shown in FIG. 7, it is assumed that numbers (i = 1, 2, ..., N) are assigned to the target system and all incoming cells in the target time period. For each cell, Xi = {0,
1} and {0: pass, 1: discard) are associated with each other. As a “cell state” constituted by it, X =
Consider {X1, X2, ..., XN}.

State X of entered cells as a population (Ω)
Consider the full set of. The details are as follows. Simulations such as cell loss rate are based on stochastic Monte Carlo
Simulation (Monte Carlo Simu
nation). Since the probability parameter is included in the simulation condition, even if the simulation is performed under the same condition, the number of input cells and the state X thereof change for each simulation. Therefore, assuming that all sets of cell states obtained by each simulation under certain conditions are considered, "virtually" the population Ω
think of. And the result of each simulation is
Interpret as a "sample" from this population. Then, “determining the discard rate by simulation” is interpreted as a problem of trying to “estimate” the characteristic of the population (in this case, the characteristic of cell discard rate) from some samples of the population.

In this population Ω, an event in which cell discard occurs occurs is A. From now on, we often use the assumption that cell discard is a rare event.

A population is a set of states (vectors).

When arranged in a matrix form {X11, X12, ..., X1N} {X21, X22, ..., X2N}: {0, 1} are arranged two-dimensionally. Here, in each state in the population, X =
It is considered that the events that 1 occur have the same probability distribution. That is, the occurrence probability of {x = 1} can be said to be a characteristic of the population.

First, as a simulation result evaluation method, a non-correlated event evaluation method, that is, an evaluation method assuming that there is no correlation between events (states) {Xi} will be described.

The event in which X = 1 occurs is the parameter P (A)
Of Bernoulli distribution. P
(A) is a parameter indicating the characteristics of the population.

Further, here, the simplest probability that X = 1 occurs is the Bernoulli distribution of the parameter P (A). P
(A) is a parameter indicating the characteristics of the population. Consider estimating the parameter P (A) from a sample (simulation).

In this case, assuming that the total number of states in the population is N, the unbiased effective estimator is

(Equation 16)

Note that the statistical value such as the average and variance of a random variable from here is identified by adding a ^ to the upper portion of the true value such that the true value is σ.

Consider a situation in which the binomial distribution can be approximated by a normal distribution, that is, it can be considered that both N · P (A) and N · (1-P (A)) are 5 or more.

At this time, the point estimator

[Equation 17]

Is approximately the mean P (A) and the variance P (A)
It is considered to have a normal distribution of (1-P (A)) / N. From this, the 95% confidence interval of the cell discard probability P (A) is as follows.

[0110]

(Equation 18)

The above is the case where it is assumed that the events {Xi} are not correlated with each other. However, considering events such as cell discard, if discarding actually occurs,
It is not random at all, but will occur in bursts. In this case, the events should be considered correlated. Therefore, in the above decorrelation evaluation, variance,
Or the confidence interval is evaluated narrowly.

Therefore, a method of evaluating reliability in consideration of correlation between events will be described next.

First, as a premise, it is assumed that "there is a correlation between the events but the correlated event section is not so wide". This means that there is no correlation between very distant events, so in real stochastic processes this assumption is realistic.

First, the evaluation of the occurrence probability P {En} of the intermediate state will be described.

Basically, when the result is obtained by one simulation, for a series of events of the result,
A hierarchical statistical process called the batch method is performed instead of taking the average uniformly. That is, the sequence of events {Xi │
The entire i = 1 to N} is divided into kb bundles of length n (batch: BATCH). Here, N = kb * n holds. The probability of occurrence in each bundle is estimated by the following equation.

[0116]

[Equation 19]

If n is longer than the event correlation length,
The {X'j} may be considered uncorrelated with each other. Therefore, the overall event occurrence probability is

(Equation 20)

It is estimated that This is an unbiased estimator of the event occurrence probability.

Here, the variance is

(Equation 21)

Is obtained. Therefore, the 1-α confidence interval is

(Equation 22)

Is obtained. Here, t (n, 1-α / 2) is the 1-α / 2 upper limit of the t-distribution with n degrees of freedom.

Further, the statistical processing for obtaining the occurrence probability P {Em | En} of the conditional state Em with the intermediate state En as the initial state will be described.

Obtaining the conditional probability P {Em | En} means, as described with reference to FIG. 3, an interval sequence {A (n, i)} i.
Is to obtain the occurrence probability of the event Em for
Events are independent between each section of the section sequence {A (n, i)} i. Therefore, each section is considered a regeneration cycle and the regenerative method is used. That is, using the number of event occurrences Yi in each section and the section length Ti,

(Equation 23)

In addition,

(Equation 24)

Then, the occurrence probability is estimated. The estimated amount of variance is given by

[0126]

(Equation 25)

Here, the confidence interval is regeneration.
Assuming there are enough cycles,

(Equation 26)

Given as Here, z1-α / 2 is
It is the 1-α / 2 upper limit value of the normal distribution N (0,1).

The method of evaluating reliability in consideration of the correlation between events has been described above. Thus, the transition frequency between the states obtained as a result of the simulation in steps S2 and S3 of FIG. Based on the above, it is possible to statistically calculate the transition probabilities between states (intermediate state occurrence probability P {S}, conditional probability P {RE | S}).

Next, the confidence interval of the product of random variables will be considered.

Function of two random variables (rv) z = f
(X, y) is also r. v. It is. The evaluation of the variance σz 2 of z is calculated as follows from the error propagation rule when the variances σx 2 and σy 2 of x and y are relatively small.

[0132]

[Equation 27]

When z = x · y,

[Equation 28]

As the 95% confidence interval of z,

(Equation 29)

It can be evaluated as

From the above, the cell discard rate P {RE} obtained as a result of performing the simulation according to the flowchart of FIG. 1 with the cell discard as the evaluation target event is obtained by comparing the occurrence probability P {S} of the intermediate state with that of FIG. Is obtained as the product of the probabilities P {RE | S} of the target state when each intermediate state S is set as the initial state in step S3 of the above, P {S} is x, P {RE | S } As y (9)
If applied to the equation (10), the cell loss rate P {RE}
It can be seen that the confidence interval of is easily obtained.

Next, embodiments of the present invention will be described with reference to the drawings.

(First Embodiment) FIG. 8 is a block diagram showing the structure of the simulator according to the first embodiment. In FIG. 8, the simulator according to the present embodiment is
The input unit 49, the environment setting unit 50, the evaluation unit 51, the state storage unit 52, the statistical processing unit 53, and the evaluation result output unit 54 are included.

The input section 49 is for inputting the system characteristic information necessary for modeling the system to be simulated, the system initial state characteristic information, the target state characteristic information, the intermediate state characteristic information and the like. Of
For example, it is composed of various input devices such as a keyboard, a mouse, and a touch panel. The system characteristic information includes, for example, network topology, queue buffer capacity, number of output ports, packet or cell arrival rate λ, service rate μ, and type of traffic such as burst or random.

The environment setting unit 50 sets various parameters inside the simulator based on the system feature information input through the input unit 49, models the network system to be evaluated, and creates an appropriate traffic model. When the information necessary for setting the initial state and the intermediate state of the system is input through the input unit 49 while setting, the parameter values in the simulator correspond to the respective states of the set traffic model. The simulation environment is set. .

The evaluation unit 51 is a simulation engine, and performs a Monte Carlo simulation while setting a desired state for the traffic model set by the environment setting unit 50 based on the information stored in the state storage unit 52. Is designed to run. That is, a simulation for evaluating the occurrence probability of the intermediate state from the initial state is performed, information that describes the intermediate state is extracted as necessary, and stored in the state storage unit 52.
A simulation is performed to evaluate the occurrence probability of the target state when the intermediate state set based on the information stored in the state storage unit 52 is set as the initial state. Information on the state change obtained as a result of these simulations is stored in the statistical processing unit
Sent to 3.

The statistical processing section 53 accumulates the information on the state change obtained as a result of the simulation by the evaluation section 51, and calculates various statistical quantities based on the accumulated information. That is, the probability of occurrence of an intermediate state, the probability of occurrence of a target state with the intermediate state as the initial state, the confidence interval of each probability of occurrence, etc. are calculated, and the results are stored in a memory provided and evaluated as necessary. The result is output to the output unit 54.

In the evaluation result output unit 54, the statistical processing unit 53
The statistic obtained in step 1 is displayed on a CRT display device or printed on a printer.

The state storage section 52 may be any storage element capable of writing and reading data, such as a RAM or a hard disk. The data structure of the information stored in the state storage unit 52 may be an appropriate file. Further, an arrangement, a link, etc. may be defined and stored as necessary.

Data may be compressed and stored for the purpose of reducing the storage capacity. In that case, for example, means for performing compression / non-compression processing is provided in the front and rear stages of the state storage unit 52.

Furthermore, the state storage unit 52 is replaced by the environment setting unit 5.
The initial state {MSi} for obtaining the conditional probability P {MSi + 1 | MSi} is provided to 0, and the state information at the time of entering the intermediate state {MSi + 1} by performing simulation by the evaluation unit 51 is provided. When performing an operation such as memorizing (for example, when the simulator automatically sets the intermediate state),
The state storage unit 52 may require a kind of two-port storage configuration.

FIG. 9 shows the state storage unit 52 in the case of 2 ports.
2 shows a specific example of the configuration of FIG.

FIG. 9A shows the storage means MSx for writing.
Then, read-out storage means MSy is prepared, and data is transferred from MSx to MSy each time the information in the intermediate state is read.

FIG. 9B shows two storage areas MSα and M.
A switch configuration is shown in which Sβ is provided in parallel, and when writing to one, the other is used for reading.

In FIGS. 9A and 9B, the information itself in the intermediate state is not separately stored in two separate storage areas, and the actual state of the information is stored in a common memory. A pointer indicating the memory address may be held separately for two systems as shown in FIG.

FIG. 10 is a flow chart showing a specific example of the evaluation processing operation by the simulator having the configuration shown in FIG.

First, when the information necessary for modeling the system to be evaluated is input via the input unit 49, the environment setting unit 50 models the system (step S10). That is, that is, each parameter in the simulator is set to the simulation model corresponding to the evaluation target system.

Next, the state {MSi} i and its number k are set. That is, when the information necessary for setting the initial state and the intermediate state of the system is input via the input unit 49, the parameter values in the simulator are set in step S.
It corresponds to each state of the traffic model set in 10. Then, information such as parameter values necessary for setting each state is stored in the state storage unit 52 (step S1).
2). At this time, the data may be compressed and then stored for the purpose of reducing the storage capacity.

Next, the state identifier is initialized (i = 0) (step S13), and the process proceeds to step S14.

In step S14, the evaluation section 51 first reads the initial state information stored in the state storage section 52. If the information is compressed, it is also subjected to non-compression processing and then the information is also stored. Then, the parameters in the simulator are set to the initial state {MS0}. Then, a simulation is performed to obtain the conditional probability of the next intermediate state {MS1} from the initial state {MS0}, and the statistical processing unit 53 obtains the conditional probability P {MS1 | MS0} and its confidence interval. Further, if necessary, the state at the time of entering {MS1} is recorded in the state storage unit 52. The data may be stored after being compressed. Next, i is incremented (step S15), and the occurrence probability evaluation of the intermediate state is repeated.

As described above, the information of the state {MSi} stored in the state storage unit 52 is read out, and when the information is compressed, the non-compression process is performed, and then {M
The parameters inside the simulator are set to the state of Si}, and the conditional probability of the state {MSi + 1} is obtained. That is, the evaluation unit 51 executes a simulation, and the statistical processing unit 53 obtains P {MSi + 1 | MSi} and its confidence interval, and at that time, when entering into {MSi + 1}, if necessary. The operation of recording the state in the state storage unit 52 is performed.

When the process of steps S14 to S15 is repeated a required number of times and i = k-1 is obtained in step S16, the process proceeds to step S17, and the probability P {MSk} to be finally obtained in the statistical processing unit 53. Is a product of conditional probabilities (chain). Further, the confidence interval of the probability is calculated and output to the evaluation result output unit 54.

(Second Embodiment) A method of setting a reference parameter for defining an intermediate state, which has not been specifically described in the first embodiment, will be described. Regarding the setting here, for example, the user inputs the intermediate state feature information in step S11 of FIG. 10 and is stored in the state storage unit 52 in advance before the process of step S14 is executed. Alternatively, the intermediate state characteristic information in step S11 may be omitted and the system may automatically set the simulation information in step S14. At this time, the state storage unit 52 preferably has a 2-port configuration as shown in FIG.

In any case, in the case of the queuing model, the cell length of the queue within the cell buffer capacity of the queue is set as the basic setting criterion of the intermediate state, that is, the threshold value of the intermediate state. Would be the easiest.

Further, the intermediate state of one queue is defined as a cell length section having a cell number width within the maximum number of cells that may arrive at the same time from the input ports of each queue, and a plurality of wait states are defined. As the intermediate state of the entire system of the queuing network composed of queues, the intermediate state can be set as a set of this cell length section. By setting the interval, it is possible to monitor all the states in the intermediate state of the state trajectory.

Further, there are the following methods for setting the cell length threshold value or the cell length section.

1. A constant value or interval is set as an intermediate state regardless of the cell capacity of each queue. The intermediate state can be easily set. However, when the actual cell capacity of the queue is smaller than the threshold setting for this intermediate state, the actual cell capacity is set. As the section width, the above-mentioned maximum simultaneous arrival cell number may be adopted in each queue.

2. A threshold is set at a certain percentage of the cell points of each queue. This is also relatively easy to set.

[0164] 3. It is also possible to set the threshold value by the ratio of the average input / output traffic of each queue. Obtaining each average traffic is relatively easy by using the declared parameters or by measuring for a certain period of time.

(Third Embodiment) In the Monte Carlo simulation from the initial state of the system to the target state, the number of intermediate states is not limited to one. For example, in a two-dimensional state space as shown in FIG. 11, for example, in a system made up of two queues Q1 and Q2, the respective capacities are K1 and K2.
In case of 2, the origin is the initial state and [0, K1] ×
Two intermediate states MS1, MS2 in the domain of [0, K2]
Set. The state transition probability P {MS1 | MS0} from the initial state (origin) MS0 to the intermediate state MS1 and the state transition probability P {MS from the intermediate state MS1 to the intermediate state MS2, respectively.
2 | MS1}, and intermediate state MS2 to target state MS
The state transition probability P {MS3 | MS2} to 3 is obtained, and the probability P of the target state is obtained by multiplying the conditional probabilities
{MS3} can be obtained. That is, P {MS3} = P {MS3 | MS2} .P {MS2 | M
S1} .P {MS1 | MS0}.

Specifically, in the flowchart shown in FIG. 10, the states corresponding to the identifiers i = 1 and 2 are the intermediate states MS1 and MS2.

Even when a plurality of intermediate states are set, the probability of the target state can be obtained as the product of the conditional probabilities between the states. The system applied to this embodiment is basically a Markov process. This is because the locus may follow the maximum likelihood locus. The Markov property will be described in detail.

A system according to the Markov process is generally Xn + 1 = f (Xn; ξn), where ξn is multiplied by a random variable (11).

However, also in the following cases (when there are a plurality of intermediate states Xn, Xn-1, ..., Xn-m), it is possible to reduce to the Markov process.

Xn + 1 = f (Xn, Xn-1, ..., Xn-m; ξn), where ξn is a random variable (12), that is, Yn = {Xn, Xn-1, ..., Xn-m}. (12) is redefined as a state, the following equation is obtained.

Yn + 1 = f (Yn; ξn), where ξn is a random variable (13) This is the Markov process represented by equation (11).

Therefore, the probability of the target state is obtained as a product of conditional probabilities between states, and the conditional probabilities between states are defined as x, y, ... For example, in the above (20).
It can be seen that the confidence interval of the probability of the target state can be easily obtained by applying the equations (21).

(Fourth Embodiment) In the above-described first to third embodiments, Monte Carlo simulation is performed between the states such as the initial state to the intermediate state, the intermediate state to the intermediate state, and the intermediate state to the target final state. I applied it, but I
The S method may be applied.

Specifically, in step S14 of FIG. 10, simulation is performed by the IS method.

(Fifth Embodiment) Here, first to third
Using the simulation method described in the embodiment of
The case of evaluating an actual system will be described. The confidence intervals were evaluated using a model with no correlation between events.

First, the case where the quality of the single-stage common buffer switch is evaluated will be described.

Specifically, the discard characteristic of the ATM common buffer switch is simulated. FIG. 12 shows a simulation model of the common buffer switch. In FIG. 12, the common buffer switch is
The cells arriving from 8 input lines are multiplexed and written in a common buffer. Within the buffer, the transfer order of cells is managed for each 8 output lines, and the cells in the buffer are output to the output line according to the destination. Is being sent.

First, an example of random traffic will be shown. As a source model, the load (Offered loa)
d) Random traffic with ρ = 0.8 was used.

FIG. 13 shows a simulation for each capacity while changing the capacity of the common buffer. The simulations here are the results obtained within 1 hour on a workstation of the AS4000 series. At the same time, the conventional direct simulation method (points marked with ◯), the measured values reported (points marked with □), the results of the analytical limit formula based on the conventionally known M / D / 1 model (limits of Chernoff) Also describe.

From FIG. 13, in any case, if the buffer capacity increases, the cell discard probability decreases, and
It can be seen that the value (point indicated by ●) of the evaluation result by the simulation method of the present invention is almost equal to the actually measured value. That is, according to the simulation method of the present invention, it can be understood that the evaluation of the low discard probability can be executed accurately and in a short time as compared with the actually measured value.

Further, similar to FIG. 13, FIG. 14 shows the result of simulation performed for each capacity of each common buffer in the case of burst traffic. If there is a burst, there will be no effective analysis method. The results also show values close to the measured values. The execution time was almost the same as the case of random traffic.

FIG. 15 collectively shows the cell discard probability including the process of calculating the occurrence probability of the intermediate state in this case.

It should be noted that the intermediate state here is one intermediate state in consideration of the possibility that a plurality of cells may be simultaneously input through the eight input lines as described with reference to FIG. Suppose a state contains four steps. That is, when the capacity of the common buffer is 600 cell buffers, the cell amount as one intermediate state threshold is {297, 298,
299, 300}.

In FIG. 15, the capacity of the common buffer is 6
In the case of an amount of 00 cell buffers, looking at the diagram in the horizontal direction, first, the occurrence probability of the intermediate state is (9.47 ± 0.22) × 10.
It turns out that it is -2. Looking further at the figure horizontally,
The probability of a cell discard event occurring when this intermediate state is set as the initial state, that is, the value of the conditional probability is (2.1
It can be seen that it is ± 0.1) × 10 −3. By multiplying these two values, the cell discard probability P {cell discard} is (2.0 ±
0.1) × 10 −4.

The setting of the intermediate state here is, for example, attractive in that the intermediate state used in the simulation when the capacity of the common buffer is 600 cell buffers can be used as it is in the simulation of 700 cell states or more. Let's do it. In addition, even if it is unknown at what probability the event will occur, it is possible to restart it from the middle of the simulation by setting it in the intermediate state of the breaks for the time being and improving the calculation efficiency.

Next, the case where the quality evaluation of the multistage switch (Delta network) is performed will be described.

Specifically, the discard characteristic of the two-stage cross delta network is simulated. A network model is shown in FIG. Each stage has an input buffer and an output buffer, and the size of each queue is 8 cells. Flow control is applied directly from each queue to the previous queue. Therefore, cell discard only occurs at the entry of the input buffer.

The sources are connected with random uniform traffic with a load of 0.4, one for each input link.

Under these conditions, analysis is extremely difficult.
As a result of the simulation, a comparison with the conventional method is shown. The 95% confidence interval is used here.

In the conventional method, the model is simulated as it is. as a result,

[Equation 30]

Was obtained.

In the simulation by the simulation method of the present invention, an intermediate state consisting of three steps {{4}, {5}, {6}} is used.

Here, the notation {{4}} indicates that the number of cells in at least one queue is 4 and the rest is 4 or less. As a result, all inrushes into the intermediate state (En) were surface {{4}}. The occurrence probability p {En} of the intermediate state is

(Equation 31)

It was

Upon restarting from this intermediate state ({{4}}), the event of cell discard was simulated and the following results were obtained.

[0196]

(Equation 32)

After all, the total discard probability is

[Equation 33]

Therefore, both simulation results agree with each other within the 95% confidence interval.

Next, the cell discard characteristic of the output buffer switch is simulated.

FIG. 17 shows a simulation model of the output buffer. That is, there are eight input cell streams in one buffer, and the total traffic amount ρ = 0.72 for these eight IBP traffic sources,
FIG. 18 shows the simulation result in a situation where the average burst length is used as a parameter for multiplexing.

In this simulation, the simulation result according to the present invention and the simulation result according to the conventional method are compared only at the last point when the average burst length (BL) is 5, the buffer length 64. Here, a set of {40, 41, 42} is adopted as the intermediate state. The results were in agreement within the 64% confidence interval.

(Effects of First to Fifth Embodiments) As described above, according to the first to fifth embodiments,
In a system in which the states transition stochastically, one or more intermediate states are set between the initial state and the final state in which a rare event of interest occurs, and the probability of transition between these states, that is, the conditional probability Perform a simulation to statistically obtain, the occurrence probability of the final state that the rare event of interest occurs can be obtained by the product of the conditional probability statistically obtained by this simulation,
Unlike the conventional IS method, it is possible to evaluate the occurrence probability of rare events more quickly and accurately.

(Sixth Embodiment) Here, an actual simulation execution method in the simulation method of the present invention, specifically, a sequential simulation execution method in the evaluation section 51 of FIG. 8 will be described.

The sequential simulation means that, for example, in a system synchronized with a certain system clock, the state of the system changes according to the clock,
This is a method of simulating the system state successively according to the clock.

Description will be made with reference to the conceptual diagram of the processing operation of the sequential simulation shown in FIG.

In order to obtain the state of the system at a certain time t, it is generally necessary to know the state at the time t and the state at the time t-1 immediately before the time t. In that sense,
In FIG. 9, it is represented as a simulation (t, state (t-1)). As a result of this sequential simulation, the information of the state change is sent to the statistical processing unit 53 to accumulate the statistical information, and finally the necessary statistical amount is estimated based on the statistical information.

By rotating the routine for time t from a certain initial state in time series, it is possible to completely grasp the time series transition of the system state. This method is used for the simulation of the occurrence probability of the intermediate state and the simulation of the target occurrence probability with the condition of the intermediate state (step S14 in the flowchart of FIG. 10). In this case, the minimum time unit of system state transition may be set to the simulation time step.

(Seventh Embodiment) Here, another execution method of the actual simulation in the simulation method of the present invention, specifically, an event-driven simulation execution method in the evaluation section 51 of FIG. 8 will be described.

This execution method is to execute a simulation each time an event occurs, and the simulation is not executed in synchronization with the clock.

Description will be made with reference to the conceptual diagram of the processing operation of the event driven simulation shown in FIG.

The simulation knows the event e (t, c) of the content c that occurs at a certain time t, and simulates only the state that may change due to the occurrence event. In that sense, the simulation (t,
e (t, c)). If the state changes, the variation, that is, the occurrence time t e of the new event e and its content c e can be known by simulation.

Event e (te, ce) enters queue Q, but the position of the entry is te, and the event {ei (ti, ci}) i already entered in queue Q is
The occurrence times {ti} i of the above are compared with each other, and they are determined to be arranged in the order of the occurrence time.

When there are a plurality of events having the same occurrence time, those events are regarded as one event together, and the content c is rewritten as the merged content.

When the simulation (t, e (t, c)) is completed and a new event e (te, ce) is entered, the statistical processing section 53 is notified of the new statistical information obtained by the simulation. The statistical processing unit 53 accumulates statistical information. Then, from the new queue Q, the first event e1
(T1, c1) is picked up and the simulation (t1, (t1, c1)) at the time t1 is executed.
The rest is the repetition of this flow. At the end of the simulation, the statistical processing unit 53 estimates the statistical amount from the accumulated statistical processing information.

As an example of an event, for example, considering the case where cell characteristics are evaluated, there is a model in which a cell source generates cells according to a certain probability distribution, and from that model, the next cell is There is a method of knowing the time t at which it occurs. In this case, it can be expressed as e (t, cell generation from cell source).

Compared with the sequential simulation method described in the sixth embodiment, this event-driven simulation method simulates a time when there is no possibility of state change or a state where there is no possibility of change of state. Since it does not have to be performed, there is an advantage that the simulation time can be shortened.

(Eighth Embodiment) Here, a case will be described in which the simulation method of the present invention is used for connection admission control (CAC) in an ATM network.

At the time of a call request, the CAC notifies the network (specifically, the ATM switch) of a new call property, destination, used band, required quality, etc., and the network judges whether the request can be satisfied. Then, if the setting is possible, a call setting procedure is performed, and the transmitting / receiving terminal is notified of that fact.

In this embodiment, the simulation method of the present invention is used to evaluate the call quality and the required quality.

Conventionally, as a performance index of CAC, there is the number of times of CAC that can be processed in a unit time, and it is necessary to shorten one CAC procedure time. On the other hand, effective utilization of limited network resources, for example, bandwidth is also important as a performance index of CAC. However, since this generally complicates the contents of CAC processing, it is an index contrary to the time reduction.

Further, conventionally, in order to realize high speed of CAC, an evaluation formula proved to be on the safe side is calculated, or a table showing the quality for a combination of calls is prepared in advance and the table is searched. Was performing CAC.

However, with the method using the evaluation formula, it is very difficult to model the actual call characteristics in detail and prepare an efficient analysis formula. In addition, the method using the call combination table also requires a huge number of combinations, and
It is necessary to have a method that can retrieve the evaluation value on the safe side using a finite element table. Again, this is generally difficult to do efficiently.

Therefore, an efficient CAC is realized if the quality of the call accepted by the simulation can be predicted at high speed by using the nature of the call with the actual connection request and the nature of the call already accommodated. You can do it. However, in the past, there was a problem of simulation time, and there was no practical method.

When the simulation method of the present invention is applied to CAC, a rare event can be simulated in a much shorter time than in the conventional method, so that it is possible to accurately predict the quality of a call for which a setting request is made in a short time. Will be.

For example, the probability of occurrence of the above-mentioned intermediate state is measured using the information of the traffic state of the network, and the evaluation simulation of the rarer event is performed under the condition of the intermediate state, and the rare event is evaluated at high speed. It can be carried out.

FIG. 21 shows a CAC or network parameter setting device (hereinafter referred to as a call admission control device) according to the present embodiment to which the simulation method of the present invention is applied.
3 is a functional block diagram of FIG.

In FIG. 21, the call admission control device holds a parameter management unit 81 which holds and manages parameters indicating call characteristics in accordance with call setting request information from the network, model management for modeling call sources and services. A rare event evaluation unit 83 that performs a simulation of a rare event by the simulation method of the present invention based on the stochastic model information from the unit 82 and the model management unit 82, and estimates the occurrence probability of the rare event, and receives a call based on the evaluation result. CAC for the procedure
It is composed of a procedure unit 84.

The parameter management unit 81 holds the characteristics of the call in the form of parameters. The parameter is determined as a value obtained by mapping the call to the model prepared by the model management unit 82. The actual parameters themselves may be notified by call setup request information from the call connection request terminal, or the parameter management unit 81 may perform some mapping processing.

As a model prepared and managed by the model management unit 82, for example, a model recommended by ITU-T (International Telecommunication Union / Telecommunications Standardization Division), which is a standardization organization, or ATM Forum may be adopted.

The rare event evaluation unit 83 is a simulation engine, and the simulation method of the present invention, that is, the setting and management of the intermediate state, the simulation evaluation of the occurrence probability of the intermediate state, and the rare event for the purpose of making the intermediate state a condition. The occurrence probability of is evaluated, and the rare event is evaluated from the conditional probability calculation. This evaluation result is referred to as the CAC procedure section 84.
Notify.

The CAC procedure unit 84 determines whether or not to accept the call based on the notified result, notifies the terminal to that effect, and sets parameters necessary for call connection in the network.

In the call admission control device having such a configuration, first, the parameter management unit 81 sets up a call based on the traffic model managed by the model management unit 82 according to the call setting request information from the network. The requested network is modeled, and based on the traffic model, the rare event evaluation unit 83 sets the intermediate state,
Management, simulation evaluation of occurrence probability of intermediate state, evaluation of occurrence probability of target rare event on condition of intermediate state, evaluation of rare event from conditional probability calculation, C
The AC procedure unit 84 determines whether or not to accept the call based on the evaluation result, and performs a predetermined procedure necessary for call connection to the network, so that a setting request can be made accurately in a short time. It is possible to predict the quality of the received call, and thus to efficiently use the network resource. All evaluations may follow the simulation method of the present invention.

(Ninth Embodiment) Next, as a ninth embodiment, cell delay dispersion (Cell Delay) of ATM or the like will be described.
A method for evaluating a rare event for y Variation (CDV) will be described. In CDV, it is defined as a specification for controlling the probability that the time (delay time) that a cell spends in the system is within a certain set value. For example, CDV <250 μsec (10-10 quant
ile) and the like.

In order to evaluate this specification, attention is paid to the cell delay time (τ). If the probability that τ exceeds the set value of CDV is obtained by simulation, the probability that the difference between the two delay times exceeds the set value of CDV is smaller than that, and this is the basis for estimating the specifications of CDV on the safe side.

Specifically, in order to evaluate the delay time, the time when a packet enters the system is stored as a time stamp for each cell, and the difference from the time outside the system is detected for each cell. To do.

Therefore, in order to evaluate the probability that a cell having a relatively long residence time is present using the present invention, a simulation means having a state of a certain cell residence time as an initial value, and a system of cells in each system A means to obtain the stay time and "0"
And a set upper limit value for CDV, for example, 250 μsec in the above case, a means for setting a state that becomes an appropriate value or more as an intermediate state, and a system of at least one cell in the system. A storage means is provided for obtaining the probability that the internal residence time is in the intermediate state and storing the state of the system at the time of entering the intermediate state.

First, the simulation is started from the state where the in-system stay time of all cells is "0" as the initial state.
Then, the probability (P1) that at least one cell stay time in the system is in the intermediate state and the state thereof are stored. Then, under the condition that the intermediate state is the condition, the occurrence probability (P2) of the event that the cell stay time reaches the target set value of CDV is obtained by simulation. Then, the probability of the event of exceeding the target CDV set value can be obtained by P1 × P2. The evaluation of the confidence interval is the same as described above. Also, a plurality of intermediate states may be set. Further, when the simulation is performed by the synchronous clock method, the increment amount of the clock is one, so that the intermediate state may be defined by one clock time.

(Effects of First to Ninth Embodiments) As described above, according to the first to ninth embodiments, for example, cell discard occurs in the communication system in which the states are probabilistically changed. When evaluating the occurrence frequency of a state with a low occurrence probability (rare event), from the initial state to the final state where the target rare event occurs, based on the appropriate traffic model of the system under evaluation. One or more intermediate states are set, a simulation for statistically obtaining the probability of transition between these states, that is, the conditional probability (transition probability between states), and the occurrence frequency of the target rare event are calculated. By multiplying by the transition probabilities between states, the frequency of rare events can be evaluated at high speed.

Further, unlike the conventional IS method, since it is not necessary to distort the state transition series, it is easy to secure the convergence of the simulation.

Further, since the simulation can be carried out step by step while setting the intermediate state, the intermediate results can be reused as described with reference to FIG.
It can be applied to the performance evaluation of a wide range of queuing networks.

(Tenth Embodiment) Assuming that the statistics such as the average traffic and the average delay time as well as the packet discard characteristics can be obtained by the Monte Carlo simulation of enormous stochastic event occurrence, the following conditions are set. There is.

Condition 1. The system has a stable steady state.

Condition 2. The system is ergodic. That is, the time average converges to the sample average.

Condition 1 is considered to have a statistical characteristic that the system does not depend on the initial value and is constant regardless of time, and can be described only by the statistical parameters. For example, the packet discard characteristic is determined as a function of the average parameter such as the average amount of input traffic of a network having a plurality of input / output ports, but from which input port the packet came in at time 0. This means that it does not depend on the time-dependent micro state. Further, the condition 2 means that if a simulation for a sufficiently long time is possible, the statistic of the system to be obtained (this is a sample average) can be obtained as a time average.

Under these conditions, when trying to determine the cell discard characteristics by simulation,

(Equation 34)

[0246] This is almost certainly converged to the cell loss rate CLR obtained by T → ∞. However, since the actual simulation has a finite time, the limit of the equation (22) cannot be accurately determined.

A concrete description will be given with reference to FIG.
In (a), a locus of a state of a general stochastic process or a transient state (transient state) is shown from the initial state of the system. As the state of the system, let us consider the number of packets in the system. If the simulation is started with the number of packets in the system being “0”, the system proceeds to the equilibrium state from time t = 0. Then, or when the time Ts is reached, the system is in an equilibrium state. Up to this point, it is a time-dependent system, more specifically, a system that depends on the initial state (in this figure, the simulation was started from Q = 0).
In order to know the characteristic of the equilibrium state that is originally desired, it is necessary to start collecting statistics from time Ts. That is, from time t = 0 to t = Ts, the system is in the transient state,
You can turn off statistics as a "warm-up" in your simulation.

The fact that the warming-up period (that is, the transient period) does not take statistics means that the occurrence probability P {E _m } of the target rare event occurs in the equations (1) to (6) described in FIG. This is equivalent to a case where a new T is obtained by excluding the transient period Ts from the total time section T when obtaining.

In the simulation method of the present invention, the system state can be recorded and held, and the simulation can be restarted from the held state. Therefore, as the function of the simulator, the final state Qeq during the simulation period is also recorded as shown in FIG. Then, the next simulation restarts from this Qeq.

As a result, it becomes possible to simulate the statistics in the equilibrium state stepwise as shown in FIG.

The flowchart shown in FIG. 26 shows the general procedure of the simulation method of this embodiment, and will be described with reference to this flowchart.

First, as the first stage of the simulation, the warm-up for the period Ts is executed (step S2).
0). The final state Qeq is recorded (step S21).
No statistics are collected during this warm-up period.

Subsequently, as a second step, the simulation is started with the state Qeq obtained by the warming-up simulation as the initial state (step S22).
In this simulation, a Monte Carlo simulation that takes statistics of the simulation time T is executed.
In the second-stage main simulation in step S22, the statistic can be obtained at high speed by using the above-described simulation using the conditional probability (see FIG. 1).

The first-stage warm-up simulation is for obtaining the characteristics of the system in the equilibrium state (for example, the queue length when trying to obtain the packet discard rate of the packet queuing network). Since it is not included in the statistic when calculating the occurrence probability of rare events, it is not necessary to execute the simulation using the above-mentioned conditional probabilities, and the conventional Monte Carlo simulation may be used. However, a warm-up that is long enough for the system to enter equilibrium is required.

In FIG. 26, the warming-up and the main simulation are actually flowed as two separate simulations, but it goes without saying that the actual simulation may be automatically started following the warming-up. Ah

Further, since the purpose of warming up is to obtain the equilibrium state Qeq, there may be a method that does not rely on Monte Carlo simulation. For example, the equilibrium state of a system may be obtained analytically as the average state of the system. In that case, this simulation can be started by setting the average state to the equilibrium state Qeq.

FIG. 27 is a flowchart showing an example of the evaluation processing operation when the method of ignoring the statistic of the transient period of the system and determining the occurrence probability of a rare event is applied to the simulator having the configuration shown in FIG. It will be described with reference to FIG. 27, the same parts as those in FIG. 10 are designated by the same reference numerals, and only different parts will be described. That is, in step S11, the information necessary for setting the initial state and the intermediate state of the system are input through the input unit 49, and further the time for setting the period Ts of the warming-up simulation is input. To do.
Then, after step S13, step 20 for performing a warm-up simulation may be inserted.

The warming-up period Ts input in step S11 may be arbitrary.

In step S20, the evaluation section 51 first reads the information of the initial state stored in the state storage section 52, and when the information is compressed, it is subjected to non-compression processing and then the information is also stored. Then, the parameters in the simulator are set to the initial state {MS0}. Then, when the period Ts set in step S11 has elapsed, information on the state (equilibrium state) {Qeq} at that time is stored in the state storage unit 52. In the following steps, the equilibrium state {Qeq} is set to {MS0}.

In step S14, in the evaluation unit 51, first, the equilibrium state {MS
0} information is read, and when the information is compressed, it is decompressed and then the parameters in the simulator are set to the equilibrium state {MS0} based on the information. Subsequent processing operations are the same as in FIG.

As described above, according to the tenth embodiment, the warming-up simulation is performed as a pre-stage of this simulation, so that the transient state until the network state of the simulation object reaches a stable equilibrium state. Since the period can be excluded from the statistics, the occurrence probability of the rare event can be obtained with higher accuracy.

(Eleventh Embodiment) In the case of a network composed of a plurality of queues, it will be shown by way of an example how it is efficient to set an intermediate state.

Consider a switch network composed of a plurality of queues or buffers as shown in FIG. FIG.
8 has four switches 100, 200, 300, 40
There are 0, in which buffers 111, 221, 33
It is assumed that there are 1, 332, and 441. Here, switch 3
Suppose that the flow control signal is fed back to the switches 100 and 200 from 00 and 400, respectively. For example, a flow control signal is applied from the buffer 331 of the switch 300 and the buffer 441 of the switch 400 to the buffer 111 of the switch 100.

The flow control signal becomes active when the number of packets in the transmission buffer exceeds a certain threshold value, and has a mechanism for instructing the switch in the preceding stage to stop sending any more packets. Try. The same applies to the flow control signal from the second buffer 332 of the switch 300.

This flow control signal causes the switch 30
Packet discard no longer occurs at 0 and 400.
That is, if packet discard occurs, the switch 10
There are 0 and 200 buffers. According to this property, the buffers to be monitored for the evaluation of the rare event of packet discard are 111 and 221.

Therefore, as the setting of the intermediate state, paying attention only to the buffers 111 and 221, the states in which the number of packets Q11 and Q21 are above a certain level, K11 and K21, respectively, are defined as the intermediate state. Then, the space that describes the intermediate state is a two-dimensional space having axes Q11 and Q21 as shown in FIG. Since there are five buffers in the system, it is described in a five-dimensional space, but for the reasons described above, it is sufficient to use a two-dimensional space to monitor the event of actual packet discard.

That is, the intermediate state may be defined for the function that directly causes the occurrence of the event under consideration. However, in order to maintain the intermediate state, it is generally necessary to know the state of the entire system.

As described above, according to the eleventh embodiment, of all the functional units forming the network, only the functional units in which a rare event occurs are picked up, and the intermediate state is defined for them. Can be done efficiently.

(Twelfth Embodiment) Next, as a twelfth embodiment, a CDV evaluation method slightly different from that of the ninth embodiment will be described.

The CDV evaluation method has been described in the ninth embodiment, but here, as the CDV evaluation,
A fixed delay on a path of a cell (fixed length packet) or a bucket (variable length and fixed length packet) and a stochastically varying delay are separated, and CDV is stochastically varying delay (delay time of delay time). Internal random variable).

Details will be described below by using an example. First,
Cell delay time fluctuation CDV in the queue will be described again. Although a single queue model is shown in FIG. 30, the entire queue model is processed by the processing unit 50.
1 and the queue unit 502 waiting for the processing can be considered separately. Here, the processing time is assumed to be constant. Therefore, the processing time f is constant, and the waiting time D becomes a random variable. The sum of the processing time taken by the processing unit 501 and the waiting time for waiting processing in the queue is the cell transfer delay time (CTD: Cell Transfer Delay) in this queue.
y). That is, CTD = f + D.

In the queuing network constructed by connecting a plurality of queues as shown in FIG. 31, the cells pass through the queues Q1, Q2 and Q3 from the terminal A to the terminal B. The entire cell transfer delay time CTD in this case is expressed as CTD = CTD1 + CTD2 + CTD3 = f1 + f2 + f3 + D1 + D2 + D3, where D1 + D2 + D3 is a random variable and has a fluctuation characteristic. Therefore, the cell delay time fluctuation (CDV) corresponds to D1 + D2 + D3. Also, f
1 + f2 + f3 corresponds to the fixed delay time F.

FIG. 32 shows an example of the probability distribution density of CTD.

Here, CDV ≧ CDVF (α-quant
Consider confirming the specification "tile) by simulation. That is, in the system under consideration, it is attempted to confirm that the probability that the CDV of the cell will be CDVF or more is α or less. The cell delay fluctuation CDVn of the cell in the queue Qn is given by the following equation.

[0275]

(Equation 35)

Here, i = 1, ..., N are numbers in order from the input side of the queues on the route in the system of the target cell. This depends on each cell or each connection. CTDn can be confirmed by looking at the value of the time stamp added to each cell at the time of input to the system. Further, each fi can be known as the processing time of the matrix forming the system before the simulation. Therefore, CDVn can be calculated from the above equation. Calculated CDV
The threshold value CDVT determined by looking at the value of
A state in which at least one cell exceeding (0 ≦ CDVT <CDVF) exists is defined as an intermediate state.

MS = {arbitrary cell | CDV> CDVT} Here, for all queues in the system, CDV is calculated for cells existing in them, and as a result, CDVT (0 ≦ CDVT <CDVF) The MS is defined as an event that exceeds at least one cell or exists.

Occurrence establishment Pr of MS as a ratio of time slots whose state is MS among all time slots
You can request {MS}.

Next, with the intermediate state MS as the initial state, the ratio Pr {CDV of cells satisfying the target CDV ≧ CDVF.
Find ≧ CDVF | MS}. The required probability is Pr {CDV ≧ CDVF} = Pr {CDV ≧ CDF | M
S} · Pr {MS} can be obtained as a product of conditional probabilities.
It suffices to confirm that this becomes α or less.

Next, the above procedure will be specifically described.
For example, with the simulator having the configuration shown in FIG.
The processing operation when the V evaluation method is applied is the same as in FIG. However, in this case, in the case of cell discard evaluation for each processing content, a part different from the description of FIG. 27 will be specifically described below.

First, in the modeling of the system to be evaluated in step S10, the fixed delay amount f as the cell or packet processing time of each queue in the queue is calculated. In addition, each parameter in the simulator, such as source traffic modeling, is set to the simulation model corresponding to the evaluation system.

Next, in setting the intermediate state in step S11, the intermediate state MSt (0 <t <k) is set as follows.
It is defined as an event in which the CDV of at least one cell or packet in the system at that time is a positive value CDVt or more. Here, 0 <CDVt <CDVt + 1 and CDVk = CDVF.

Steps S12 and S13 are the same as in FIG.

In step S20, the simulation is started from the initial state, and warming up is appropriately performed as described in the tenth embodiment. Then, in step S14, the cells in the system or Find the CDV of the packet. And first,
The occurrence state Pr {MS1} of the occurrence of the event of MS1 is sought, and the state of the system when the state is entered is recorded. Then, the occurrence probability P of the next state MS2 under the condition of MS1
Record r {MS2 | MS1} and the state of entry into that state. Similarly, it is determined by Pr {MSk | MSk-1}, but the last Pr {MSk | MSk-1} is a CD that exceeds CDVF.
Calculate the ratio of V (step S14 to step S1)
6).

Then, in step S17, the probability that the target CDV ≧ CDVF can be obtained as the product of the conditional probabilities.

As described above, according to the twelfth embodiment, not only the rare event occurrence probability evaluation for packet discard but also the time at which an arbitrary cell should originally arrive, for example, in an ATM cell transfer device, etc. 2 as a phase shift from
The simulation method and simulator of the present invention can also be applied to the case of evaluating an event in which the probability of exceeding 60 μsec is 10 ⁻¹⁰ or less.

Note that the method described in the above embodiment is
As shown in FIG. 33, as a program that can be executed by a computer, a magnetic disk (floppy disk, hard disk, etc.), optical disk (CD-RO)
It can also be stored in a recording medium such as an M or a DVD) or a semiconductor memory and distributed.

[0288]

As described above, according to the present invention,
It is possible to provide a simulation method capable of quickly evaluating the occurrence frequency of a state having a low occurrence probability in a system in which a state transitions stochastically, and a simulator using the simulation method.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a schematic procedure of a simulation method of the present invention.

FIG. 2 is a diagram illustrating the principle of the present invention.

FIG. 3 is a diagram for explaining the simulation method of the present invention based on a mathematical model.

FIG. 4 is a diagram for explaining a maximum likelihood trajectory that occurs in an intermediate state.

FIG. 5 is a diagram for explaining a method of setting an intermediate state.

FIG. 6 is a diagram for explaining a burst traffic source model.

FIG. 7 is a diagram for explaining a state population.

FIG. 8 is a block diagram showing a configuration of a simulator according to the first embodiment of the present invention.

9 is a diagram showing a specific example of the configuration of the state storage unit in FIG.

10 is a flow chart for explaining an evaluation processing operation by the simulator of FIG.

FIG. 11 is a diagram for explaining a simulation method when a plurality of intermediate states according to the third embodiment of the present invention are set.

FIG. 12 is a diagram showing a simulation model of a common buffer switch according to a fifth embodiment of the present invention.

13 is a diagram showing a specific example of simulation results in the case of random traffic based on the simulation model shown in FIG.

14 is a diagram showing a specific example of simulation results in the case of burst traffic based on the simulation model shown in FIG.

15 is a diagram showing a specific calculation result of the cell discard probability including the process of calculating the occurrence probability of the intermediate state in the case of burst traffic based on the simulation model shown in FIG.

FIG. 16 is a diagram showing a network model for simulating a discard characteristic of a two-stage cross delta network according to a fifth embodiment of the present invention.

FIG. 17 is a diagram showing a simulation model of an output buffer according to the fifth embodiment of the present invention.

18 is a diagram showing a specific example of a simulation result based on the simulation model shown in FIG.

FIG. 19 is a diagram for explaining a sequential simulation execution method according to the sixth embodiment of the present invention.

FIG. 20 is a diagram for explaining an event-driven simulation execution method according to a seventh embodiment of the present invention.

FIG. 21 is a block diagram showing the configuration of a call admission control device according to an eighth embodiment of the present invention.

FIG. 22 is a diagram for explaining a conventional simulation method (Monte Carlo simulation method) in the case of a G / G / 1 / K queuing model.

FIG. 23 is a diagram for explaining a conventional high-speed simulation method (IS method) in the case of a G / G / 1 / K queuing model.

24 is a diagram showing a specific example of a time-series fluctuation locus of the queue length obtained by the conventional simulation method shown in FIG.

FIG. 25 is a diagram for explaining the principle of the simulation method according to the tenth embodiment, for explaining a transient state (transient state) on the locus of the state of a general stochastic process. Figure (a) shows an example of the state from the initial state of the system to the equilibrium state after passing through the transient state. Figure (b) shows the state from the initial state to the final state of the warm-up simulation period (transient state). ) Shows an example of the situation.

FIG. 26 is a flowchart for explaining a schematic procedure of a simulation method in the case of performing a warming-up simulation, a main simulation, and a stepwise simulation.

FIG. 27 is a flowchart for explaining processing operation of a simulator to which the simulation method according to the tenth embodiment is applied.

FIG. 28 is a diagram for explaining the principle of the simulation method according to the eleventh embodiment, and shows how it is efficient to set the intermediate state in the case of a network composed of a plurality of queues. It is shown.

FIG. 29 is a diagram for explaining a method of defining an intermediate state by picking up only a component in which a rare event occurs in the network configuration shown in FIG. 28.

FIG. 30 is a diagram for explaining the simulation method for evaluating the cell delay time fluctuation CDV according to the twelfth embodiment of the present invention, showing the simplest model (single queuing model) of the system to be evaluated. This is an example.

FIG. 31 is a diagram for explaining cell transfer delay time (CTD) and cell delay time fluctuation (CDV) in a queuing network configured by connecting a plurality of queues.

FIG. 32 is a diagram showing an example of the probability distribution density of CTD.

FIG. 33 is a schematic diagram of a system configuration example to which the present invention is applied.

[Explanation of symbols]

49 ... Input unit, 50 ... Environment setting unit, 51 ... Evaluation unit, 52
... State storage unit, 53 ... Statistical processing unit, 54 ... Evaluation result output unit.

Claims (8)

[Claims] 1. A simulation method for evaluating the occurrence frequency of a desired state in a system in which a state transitions stochastically, wherein a simulation model of the system is set based on given characteristic information of the system. Step 1, a second step of setting the state of the simulation model set in the first step to the initial state of the system based on given conditions, and an initial state set in the second step To at least one intermediate state through which the state transition sequence from the desired state to the desired state is set, the frequency of transition from the initial state to the intermediate state, transition from the intermediate state to the next intermediate state Frequency, the frequency of transition from the intermediate state to the desired state is obtained stepwise, and from the frequency of transition between these states A third step of calculating a transition probability between states, and a fourth step of multiplying the transition probability between states calculated in the third step to calculate a probability of occurrence of the desired state. What you did is a simulation method. 2. In a packet transfer system for transferring a packet via at least one buffer memory for temporarily storing an input packet, the occurrence frequency of the state where the packet in the buffer memory is discarded is evaluated. A simulation method comprising: a first step of setting a simulation model of the system based on the given characteristic information of the system; and a step of giving the state of the simulation model set in the first step. There is a second step of setting an initial state of the system based on the amount of packets accumulated in the buffer memory, and a process of transitioning from the initial state set in the second step to a state of discarding the packet. Packets stored in the buffer memory given an intermediate state At least one is set based on the amount, and the frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, and the frequency of transition from the intermediate state to the state where the packet is discarded are set. Seeking in stages,
The third step of calculating the inter-state transition probability from the frequency of transition between these states and the inter-state transition probability calculated in this third step are multiplied to determine the state of the packet being discarded. A fourth step of calculating a probability of occurrence, and a simulation method comprising: 3. A packet transfer system for transferring a packet via a plurality of buffer memories for temporarily storing an input packet, wherein a delay time when the packet arrives at any one of the plurality of buffer memories is previously set. A simulation method for evaluating the occurrence frequency of occurrence of a state of being equal to or more than a predetermined value, which comprises a first step of setting a simulation model of the system based on given characteristic information of the system, A second step of setting the state of the simulation model set in step 1 to the initial state of the system based on the delay time when the packet arrives at the buffer memory, and in the second step The packet arrives at one of the buffer memories from the set initial state At least one is set based on the delay time when the packet given the intermediate state existing in the process of transiting to the state where the delay time at the time of reaching the predetermined value or more, The frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, and the delay time when the packet arrives from the intermediate state to any of the plurality of buffer memories are predetermined. The step of calculating the frequency of transition to a state that is greater than or equal to the specified value, and statistically calculating the transition probability between states from the frequency of transition between these states, and the calculation in this third step Occurrence probability of a state in which the delay time when the packet arrives at any of the plurality of buffer memories is equal to or greater than a predetermined value A fourth step of calculating, and a simulation method comprising: 4. The error estimation of the occurrence probability is performed by estimating the interval of the occurrence probability of the desired state based on the interval estimation of the transition probability between states. The simulation method according to any one. 5. A simulator for evaluating the occurrence frequency of a desired state in a system in which the states transition probabilistically, wherein a model for setting a simulation model of the system based on the given characteristic information of the system. Setting means, setting means for setting the state of the simulation model set by the model setting means to the initial state of the system based on given conditions, and from the initial state set by the setting means to the desired state At least one intermediate state is set based on a given condition, the frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, the intermediate state To obtain the frequency of transition to the desired state in stages, and the transition probability between states is calculated from the frequency of transition between these states. A first calculating means for calculating; and a second calculating means for multiplying the transition probability between states calculated by the first calculating means to calculate the occurrence probability of the desired state. Characteristic simulator. 6. A packet transfer system for transferring a packet via at least one buffer memory for temporarily storing an input packet, wherein the occurrence frequency of a state where the packet in the buffer memory is discarded is evaluated. A simulator, comprising: model setting means for setting a simulation model of the communication system based on the given characteristic information of the communication system; and a state of the simulation model set by the model setting means. Setting means for setting the initial state of the communication system based on the amount of packets accumulated in the buffer memory, and an intermediate state existing in the process of transiting from the initial state set by the setting means to the state of discarding the packet Based on the amount of packets accumulated in the given buffer memory At least one of them is set, and the frequency of transition from the initial state to the intermediate state, the frequency of transition from the intermediate state to the next intermediate state, and the frequency of transition from the intermediate state to the state where the packet is discarded are stepwise. And a first calculation means for calculating the inter-state transition probability from the frequency of transition between these states, and the inter-state transition probability calculated by the first calculation means are multiplied to obtain the packet A second calculation means for calculating a probability of occurrence of a state of being discarded, and a simulator comprising: 7. A packet transfer system for transferring a packet via a plurality of buffer memories for temporarily storing an input packet, wherein a delay time when the packet arrives at any one of the plurality of buffer memories is previously set. A simulator for evaluating the occurrence frequency of occurrence of a state of being equal to or more than a predetermined value, and model setting means for setting a simulation model of the system based on the given characteristic information of the packet transfer system, Setting means for setting the state of the simulation model set by the model setting means to the initial state of the system based on the delay time when the packet arrives at the buffer memory; and the initial setting set by the setting means. When the packet arrives at any of the buffer memories from the state At least one intermediate state existing in the process of transiting to a state in which the delay time of the packet becomes a predetermined value or more is set based on the delay time when the packet arrives at the buffer memory, Frequency of transition to state,
The frequency of transition from the intermediate state to the next intermediate state, the frequency of transition from the intermediate state to a state in which the delay time when the packet arrives at any one of the plurality of buffer memories is a predetermined value or more. First calculation means for statistically calculating the inter-state transition probabilities from the frequency of transitions between the respective states obtained stepwise, and the inter-state transition probabilities calculated by the first calculation means are multiplied. And second calculating means for calculating a probability of occurrence of a state in which the delay time when the packet arrives at any one of the plurality of buffer memories is equal to or more than a predetermined value. Simulator to do. 8. The error of the occurrence probability by performing the interval estimation of the occurrence probability calculated by the second calculating means based on the interval estimation of the inter-state transition probability calculated by the first calculating means. The simulator according to any one of claims 5 to 7, further comprising error evaluation means for performing evaluation.