JP2806182B2 - Partial net extraction device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a sub-network extracting apparatus capable of extracting an equivalent sub-network within a required analysis accuracy when analyzing a part of a queuing network.

[0002]

2. Description of the Related Art A queuing network is a method widely used for modeling and analyzing a system in which some kind of competitive process occurs, such as a computer system, a telephone switching network, and a manufacturing process in a factory. Generally, a queue having one or more input arcs and one or more output arcs and having a stochastic output branch is configured as a node.

By the way, simulation of a queuing network modeling a computer system or the like is regarded as an example of discrete event simulation, and parallel processing techniques have been studied in the past. The method, that is, the parallel discrete event simulation, is roughly classified into a time driving method and an event driving method.

The time driving method updates the simulation time every unit time, and is easy to control, but has the disadvantage of low parallelism.

On the other hand, the event-driven system updates the simulation time at the time of a change in an event. In contrast to the time-driven system, there is a possibility that a large parallelism may be extracted. It has the disadvantage of becoming complicated. The event driven method is further classified into a consistent method and a pre-processing method.

The non-contradiction method is a method in which the simulation proceeds while holding the minimum value of the parallelized simulation time of each unit as the simulation time of the entire system. It is guaranteed that no inconsistency occurs, but it impairs the parallelism. There are drawbacks.

[0007] On the other hand, in the pre-processing method, simulations of the parallelized parts are performed at respective times, and when inconsistencies are detected in the mutual simulation results, one of the simulations is canceled to eliminate the inconsistency and canceled. In general, the parallelism is high, but there is a problem that the cancellation process becomes an overhead. However, as a parallel discrete event simulation, the preceding processing method among the event driving methods is considered to be the most promising because of the degree of parallelism that can be extracted.

[0008]

As described above, various techniques have been conventionally reported as methods for analyzing a queuing network which models a computer system or the like by simulation. Depending on the accuracy, it is not always necessary to analyze the entire queuing network, but the created queuing network itself is analyzed. For this reason, especially in the analysis of a large-scale queuing network, the amount of calculation is unnecessarily increased.

If the analysis of the queuing network is to be performed within a certain precision, if only the part that is truly necessary for the analysis can be extracted in the queuing network, the extraction is performed in such a manner. The partial network will have a simpler configuration than the original network, so that the analysis prospects will be better and the computational complexity will be reduced.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has as its object the purpose of performing analysis of a queuing network within a certain accuracy. An object of the present invention is to provide a partial network extracting device capable of extracting a partial network as an analysis target.

[0011]

SUMMARY OF THE INVENTION In order to achieve the above object, a partial net extracting apparatus according to the present invention has at least one input arc and at least one output arc, and has a stochastic output branch. Input means for inputting information on a queuing network constituted by a certain queue as a node and information on an analysis target sub-network and information on analysis accuracy, and an analysis target sub-network based on the input information on the analysis target sub-network Detecting means for detecting an input arc to the detector, dependency calculating means for calculating a dependency of each input arc detected by the detecting means on another arc, calculation results of the dependency calculating means, and the input analysis Output means for extracting and outputting an equivalent partial network within the required analysis accuracy from the input information on the queuing network based on the information on the accuracy.
Therefore, the dependency calculated by the dependency calculating means is necessary.
An arc smaller than the degree of dependence required for the required analysis accuracy
And having the deleted arc as an input arc
The average arrival rate at the current node
By adding the same input arc,
Extract and output equivalent subnetwork from input queuing network
And an output means that.

[0012]

In the partial network extracting apparatus according to the present invention, the input means is constituted by a queue having one or more input arcs and one or more output arcs and having a stochastic output branch as a node. Information on the queuing network and the analysis target sub-network and information on the analysis accuracy are detected, and the detecting means detects an input arc to the analysis target sub-network based on the input information on the analysis target sub-network, and The degree calculating means calculates the degree of dependence of each of the detected input arcs on other arcs, and the output means calculates the degree of dependence on the input queuing network based on the calculation result and the information on the input analysis accuracy. From the information, an equivalent partial network within the required analysis accuracy is extracted and output.

[0013]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 1 shows an example of a queuing network, and FIG. 2 shows an example of a partial network which needs to be analyzed, which is extracted from the queuing network of FIG. 1 while maintaining an analysis accuracy of 1% or less. Show.

First, the principle of extracting a partial network as shown in FIG. 2 from the queuing network of FIG. 1 will be described in detail.

Now, arcs in the queuing network will be numbered and considered, and symbols relating to queue parameters will be defined as follows.

C _a : Square of variation coefficient of arrival time interval distribution to node (SCV) C _ai : Square of variation coefficient of arrival time interval distribution for arc i (SCV) C _b : Coefficient of variation of service time distribution (SCV) C _d : Square of variation coefficient of output time interval distribution from node (SCV) C _di : Square of variation coefficient of output time interval distribution for arc i (SCV) C _ni : From arc i While two customers are output, the square of the variation coefficient (SCV) of the distribution of the number of customers output from other arcs of the same node ρ: utilization (0 <ρ <1) α _i : Probability of arriving from arc i among a plurality of input arcs for one node β _i : probability of branching to output arc i

In the present invention, the shielding effect, which is one of the characteristics of the queue, is utilized. The shield effect is a phenomenon in which information on the distribution of queue arrival time intervals is transmitted only partially to the output side, and becomes more prominent as the utilization rate ρ increases.
This is clear when considering two extreme cases where the utilization is very close to 0 and very close to 1. That is, in the former case, the arriving customers are hardly waited, so that the distribution of the arrival time intervals greatly affects the distribution of the output time intervals. Distribution is almost determined only by the distribution of service time.

By the way, in a general queuing network having no Markov property, the distribution of arrival time intervals and service times is 2
A decomposition approximation method that approximates with the following moments is often used. This embodiment also uses this decomposition approximation method. That is, each probability distribution function is calculated as the square of the average value and the variation coefficient (SC
V). Since a steady state is considered, the average value of the output time intervals from the nodes can be easily obtained from the average value of the arrival time intervals. Therefore, in the decomposition approximation method, a method of mainly obtaining the SCV may be considered.

According to the decomposition approximation method, the following three equations hold for input / output of a certain node.

[0021] _{C a = j Σα j C aj} (1) C d = (1-ρ 2) C a + ρ 2 C b (2) C di = β i C d + C ni (3)

[0022] _{Incidentally, a 1, a 2, ...} , Σ indicates the sum of a _n
In the present specification, _{i = 1} ⁿか ら
As shown in the figure, the symbols that should be written on the lower side of Σ are written on the lower left, and the symbols that should be written on the upper side are written on the upper left.

Note that C _ni does not depend on C _{aj. For} example, the degree of dependence of the output arc A _i of a certain node on the input arc A _j of the same node is given by: ∂C _di / ∂C _aj = α _j β _i (1−ρ ² ) (4) This right side is represented as γ _ij . 0 <α _j ≦
Since 1 _, 0 <β _i ≦ 1 _and 0 <ρ <1, γ _ij <1 (5). This indicates the above-mentioned shielding effect.

Next, think about how to determine the reliance on any arc A _j of the arc A _i. Now, the distance between the arc A _i and the arc A _{j having} a dependency is defined as the number of nodes along the path through which the customer flows, and when (i, j) is fixed, the maximum value of the distance is L (i , J), except for the calculation efficiency, can be obtained in principle as follows.

When the arc A _i and the arc A _j have a dependency of a distance of 1, consider a matrix Γ such that the (i, j) component is γ _ij and the other (i, j) components are 0. That is, Γ is a matrix representing the dependence of all arcs in the queuing network on arcs separated by a distance of one.
As can be easily ascertained, the (i, j) component of Γ ^m is
The arc A _i, represents the dependence on the arc A _j at a distance m. Here, when there are a plurality of paths having a distance m between the arc A _i and the arc A _j , it indicates the degree of dependence obtained by adding all the paths. Since generally different distance path between the arc A _i and the arc A _j may be plurality of, in order to determine the total reliance on the arc A _j of the arc A _i is, gamma, gamma ^2, gamma ³ ,..., Γ All (i, j) components of ^{L (i, j)} must be obtained and added.

Next, consider a method of detecting arc A _i dependence is small arc A _j within the moments up to the second order. When SCV C _j of the arc A _j is changed by [delta], when the change of the SCV C _i of the arc A _i associated therewith is less than epsilon, reliance is to be regarded as sufficiently small. At this time, δ and ε are parameters given at the time of analysis,
Is larger, the range of the queuing network that can be handled is wider, and ε is smaller, the analysis accuracy is higher. Generally, SC
It is rare that V is very large compared to 1, and δ to 1
If it is set to about 0, most cases can be dealt with. The conditions considered above dependency is small, the gamma ^m (i,
j) When expressed by the component γ _ij ^(m) (γ _ij ⁽¹⁾ = γ _ij ), _{m = 1} ^{L (i, j)} Σγ _ij ^(m) <ε / δ (6) Since the left side can be calculated from the matrix Γ, it is possible to detect an arc having a small dependence. Incidentally, the existence region of the arc A _i of dependence on the arc A _j that does not satisfy the equation (6) is localized around the arc A _i by the shield effect.

Now, based on the above description, a procedure for extracting a partial network truly required for analysis within the accuracy ε will be described using an example of a queuing network as shown in FIG. The part to be analyzed in the queuing network will be referred to as an analysis target partial network, and the part that is truly required for analysis within a given accuracy will be referred to simply as a partial network.

In FIG. 1, circles and ladder-shaped portions denoted by symbols N _{1 to} N ₁₄ indicate nodes which are queues, and symbols A ₁ to A ₁₄ .
Arrow designated A ₂₉ represents the arc. As the parameters of the queuing network, the average arrival rate of customers coming from outside and its SCV (probability distribution function of arrival time intervals, indicated by (average value, SCV) in the figure) _, average of service time at each node A value, its SCV _, and a branch probability from each node (a numerical value such as 0.5 attached near each arc) are given. Although the specific values are shown in the figure, the information on the service time is not shown directly. Instead, the utilization at each node is underlined. The extraction of the partial network is performed in the following procedure.

1. Α _j is obtained from the external arrival rate and the branch probability β _i at each node. The result is as follows: _{N 1: α 1 = 1.00 N} 2: α 2 = 0.500 α 5 = 0.500 N 3: α 3 = 1.00 N 4: α 4 = 1.00 N 5: α 7 = 0.500 α 8 = 0.500 N 6: α 10: 1.00 N ₇ : α ₁₁ = 0.333 α ₁₂ = 0.333 α ₆ = 0.
167 α ₁₃ = 0.167 N ₈ : α ₉ = 1.00 N ₉ : α ₁₄ = 0.714 α ₁₅ = 0.286 N ₁₀ : α ₁₆ = 0.988 α ₁₉ = 1.23 × 10 ^-2 N ₁₁ : α ₁₇ = 0.952 α ₂₀ = 4.76 × 10 ^-2 N ₁₂ : α ₁₈ = 0.909 α ₂₁ = 9.09 × 10 ^-2 N ₁₃ : α ₂₂ = 1.00 N ₁₄ : α ₂₄ = 0.141 α ₂₅ = 0.182 α ₂₆ = 0.
191 α ₂₇ = 0.486

2. From the analysis accuracy required for the analysis target partial network, an allowable error in the extraction operation of the partial network is obtained. In this example, the SC of the input arc A ₂₉ of the partial network to be analyzed
The extraction is performed with the error of V being 1%, that is, ε = 0.01.

3. Determine δ. In this example, δ = 10 is set in order to guarantee that the error is within 1% even if the arrival distribution at C _aj = 10 is replaced by the Poisson distribution (C _aj = 1).

4. A reference value ε / δ for determining that the dependence between arcs is sufficiently small is obtained. In this example, 0.00
1

5. The matrix Γ is obtained by equation (4). The result (part of) is as follows:

[0034]

6. The distance from arc A ₂₉ to the farthest input arc is five. Therefore, it is sufficient to calculate Γ ² , Γ ³ , Γ ⁴ , Γ ⁵ . These include all information on the dependence of an arbitrary distance between arbitrary arcs. As an ^{_{example, γ 29,6 (3) = γ}} 29, 24 γ 24, 16 γ 16, 6 + γ 29, 25 γ 25, 17 γ 17, 6 + γ 29, 26 γ 26, 18 γ 18, 6 = 1.360 × 10 ^-4 (8).

7. _{m = 1} ⁵ Σγ _{29, j} ^(m) gives arc A ₂₉
Is determined for the arc A _j . Result (part of)
Is as follows.

A₆： 1.360 × 10^-Four A₇： 2.907 × 10^-Four A₈:
2.907 × 10^-Four A_Ten： 9.364 × 10^-Four A₁₁： 2.719 × 10^-Four A₁₂:
2.719 × 10^-Four A₁₃： 1.360 × 10^-Four A₁₄： 4.590 × 10^-3 A_Fifteen:
1.836 × 10^-3  A₁₆： 1.680 × 10^-3 A₁₇： 2.375 × 10^-3 A₁₈:
4.500 × 10^-3 A₁₉: 2.100 × 10^-Five A₂₀： 1.187 × 10^-Four A_{twenty one}:
4.500 × 10^-Four A_{twenty two}： 1.785 × 10^-2 A_{twenty four}： 1.013 × 10^-2 A_{twenty five}:
1.313 × 10^-2 A₂₆： 1.375 × 10^-2 A₂₇： 3.500 × 10^-2

8. Remove arcs with a dependence less than 0.001 and replace them with a Poisson distribution with the same average arrival rate. The result is as shown in FIG.

According to the above procedure, if the analysis is performed with an accuracy of 1%, it can be understood that the simpler partial network of FIG. 2 may be analyzed instead of FIG.

In short, the basic idea of the present invention is that a queue having one or more input arcs and one or more output arcs and having a stochastic output branch as a node is used as a queue. in the network, perform numbered nodes and arcs, arrived i th node N _i, node j th arcs a _ij input to N _i, the node N _i through the arc a _ij in yet steady state When the probability distribution function of the arrival time interval of the customer to be expressed is expressed as F _ij (t),
By using a means to quantitatively calculate the effect of a virtual change in _kl (t) on F _ij (t), and using that information to analyze the behavior of a part of the queuing network, ,
The probability distribution function F _ij (t) on the input arc A _ij to that part
The arc A _kl is deleted and F _kl (t) is redefined, while ensuring that the effect on the queuing network is within the range that satisfies the required accuracy. It is intended to perform an analysis in a steady state of a portion where the error occurs.

FIG. 3 is a block diagram of an embodiment of a partial network extracting apparatus according to the present invention based on the above-described principle.

The partial network extracting apparatus 1 shown in FIG. 3 receives information 2 on the queuing network and information 3 on the analysis accuracy, and outputs output information 15 on the partial network that is truly necessary for the analysis. The middle and thick arrows indicate the flow of control, and the thin arrows indicate the flow of data or information.

The information 2 on the queuing network includes information on the queuing network and particularly information on a subnetwork to be analyzed as to which part of the network is to be examined.
Performs an operation of inputting information 2 on the queuing network including such information and information 3 on the analysis accuracy, and stores information on the partial network to be analyzed into the storage unit 4 and information on the queuing network into the storage unit 5.
The information on the analysis accuracy is stored in the storage unit 6.

After the input operation, the detecting section 8 refers to the information on the partial network to be analyzed held in the storage section 4 and detects an arc inputted from outside to the partial network to be analyzed. This is shown in FIG.
This is a process for obtaining all the arcs corresponding to the arc A ₂₉ of FIG.

Next, the dependency calculating section 30 stores the storage sections 4, 5,
Based on each information stored in 6, the degree of dependence between each input arc of the partial network to be analyzed and each other arc within the required accuracy is calculated. As already mentioned, arc A _i arc A
_The dependency on _j must be obtained by adding up the dependencies on all the paths between them, and this is increased in a large-scale queuing network. Therefore, in the present embodiment, the dependency is determined as follows.

Now, it is assumed that the calculation of the dependence up to the distance m has been completed. That is, the gamma ^m and the distance m or less total Λ _{= ^k} = ₁ ^m ΣΓ _k dependence is known. In general, if _{j = 1} ^M Σγ _ij ^m <μ (9), it can be easily ascertained that the total sum of the dependencies on the path having a distance of m + 1 or more is smaller than μ. Here, M represents the size of Γ, that is, the total number of arcs. Accordingly, if Expression (9) is satisfied for μ sufficiently smaller than the required accuracy ε / δ, for example, μ = 0.1 × (ε / δ),
The calculation of the degree of dependence on the arc A _i is sufficient only for a path having a distance of m or less. At this time, the calculation result of the dependence is the (i, j) component (j = 1, 2,..., M) of the above Λ.
Given by The dependency calculation unit 30 in the present embodiment includes:
Through the processes 9 to 13 in FIG. 3, the above calculation is performed on all the input arcs of the analysis target partial network.

Finally, based on the calculation result of the dependency calculation unit 30 and the information of the queuing network in the storage unit 5, the output unit 14 determines whether the dependency of each input arc of the analysis target partial network is ε /
Arcs smaller than δ are deleted, and an arc having a Poisson distribution (SCV = 1) is added to the input portion of the remaining subnetwork such that the average arrival rate at the node becomes the same as before the deletion (for example, FIG. 1 and FIG. Referring to the node N ₁₀ of 2), and performs the output operation such as outputting a final extraction result.

The partial network extracting apparatus of this embodiment can be used in combination with any analysis method such as theoretical analysis and simulation of a queuing network. Hereinafter, an example applied to a parallel simulation method will be described.

FIG. 4 is a block diagram showing an example of a parallel simulation method for a queuing network to which the partial network extracting device is applied.

In FIG. 4, the decomposing means 16 divides the queuing network into a plurality of areas, and the individual processors 20 constituting the parallel processing computer are different from each other in one area. In charge of analysis.

In the individual processor 20, in the process 17, the partial network which is really necessary for the analysis of the area in charge is extracted by using the above-mentioned partial network extracting device, and in the process 18, the simulation of only the partial network is performed. I do. Therefore, no communication between the processors is required at the time of the simulation.

Then, the simulation results for each area obtained by each processor 20 are compiled by the integrating means 19, and the final result is output.

In general, the simulation takes a longer time than the time required to divide an area or extract a partial network required for analysis. Therefore, if a large-scale queuing network is divided into a large number of regions and simulated by this method, a large number-of-units effect is expected. Further, the partial networks extracted for each area by the present method can be simulated in parallel by the preceding processing method. In this case, communication and cancellation processing at the time of simulation can be localized in the partial network. Therefore, it is effective in reducing the overhead of communication and cancel processing.

[0054]

According to the partial network extracting apparatus of the present invention described above, within the analysis accuracy given to the given queuing network, it is truly necessary to analyze the target analysis target partial network. Can be automatically extracted. In this case, the size of the extracted partial network becomes smaller as the number of nodes with a higher utilization rate increases, and as the required analysis accuracy becomes larger, that is, as the coarse accuracy becomes better, the size becomes smaller. And simple analysis of the partial network.
For this reason, when used before the theoretical analysis, it is effective in improving the prospect of the analysis, and when used before the software analyzer or simulator, there is an effect of reducing the amount of calculation. In particular, simulators are generally computationally expensive,
The effect of the present invention is great.

In the analysis of a computer system or the like using a queuing network, what is of most interest is the behavior when the average arrival rate of the customers is large with respect to the service capacity, that is, when the utilization rate ρ is close to 1. . As described above, the size of the sub-network extracted by the sub-network extraction device of the present invention is larger as the number of nodes with a higher utilization rate is larger, the shielding effect is larger, and the size of the sub-network is localized in a smaller area. The effect is even greater. In such a case, of course, the degree of parallelism increases, and it can be said that the effect of the present invention is great also from the viewpoint of parallel processing. As described above, the present invention has a feature that a remarkable effect is obtained under the condition that requires the most analysis.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating an example of a queuing network.

FIG. 2 is a diagram illustrating an example of a partial network that needs to be truly analyzed, extracted from the queuing network of FIG. 1 while maintaining an analysis accuracy of 1% or less.

FIG. 3 is a configuration diagram of an embodiment of a partial network extraction device according to the present invention.

FIG. 4 is a diagram showing a configuration example of a parallel simulation method for a queuing network to which a partial network extraction device according to the present invention is applied.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Subnetwork extraction device 2 ... Information about queuing network 3 ... Information about analysis accuracy 4 ... Storage part which holds information on analysis target subnetwork 5 ... Storage part which holds information on queuing network 6 ... Information about analysis accuracy 7 ... Input unit 8 ... Detection unit 9-13 ... Process of dependency calculation unit 14 ... Output unit 15 ... Output information 30 ... Dependency calculation unit

Claims (1)

(57) [Claims] 1. A queuing network having one or more input arcs and one or more output arcs and having a queue whose output branch is stochastic as nodes, and information on a subnetwork to be analyzed. Input means for inputting information relating to analysis accuracy; detecting means for detecting an input arc to the analysis target sub-network based on the input information regarding the analysis target sub-network; A degree-of-dependence calculating means for calculating a degree of dependence on another arc; and a request from the inputted information on the queuing network based on the calculation result of the dependence degree calculating means and the inputted information on the analysis accuracy. Output means for extracting and outputting an equivalent partial network within the analysis accuracy , wherein
Analysis that requires the degree of dependence calculated by the output means
Arcs smaller than the degree of dependence corresponding to accuracy are deleted.
The node that had the input arc as the input arc
The average arrival rate at the node is the same as before the deletion
By adding an input arc, the input queue
Output means for extracting and outputting an equivalent partial network from the row network .