RU2413284C2 - Method of lowering self-similarity effect in network structures and apparatus for realising said method - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: during the phase of establishing a connection between a switching centre and a calling party, the length of the message is determined and compared with a certain threshold value which is defined when designing the network. If the length of the message is greater than the threshold value, a physical connection is established and the message is sent in channel switching mode. If the length of the message is less than the threshold value, the message is stored, broken into packets and the obtained sequence of packets undergoes functional transformation. The object of transformation is one-dimensional distribution density of time intervals between packets of the input stream. By applying functional transformation, processes with given properties can be obtained from the initial distribution function of time intervals between packets, which describes the behaviour of a self-similarity process.

EFFECT: high frequency of a communication network when servicing a self-similarity schedule by increasing efficiency of using its resources.

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Description

FIELD OF THE INVENTION

The invention relates to the field of information and computer networks and can be used in the design of digital integrated service networks.

State of the art

Known methods for converting random processes to increase the uniformity of the initial value (Krisilov V. A., Kondratyuk A. V. Converting the input data of the neural network in order to improve their distinguishability. Odessa National Polytechnic University, 2005 http: neuroschool.narod.ru).

The problem is solved using one of the known methods for approximating the probability density for selected points, the position of which on the time axis is formed by finding time intervals whose durations are determined by a value proportional to the corresponding values of the distribution density. The interval parameters are found empirically. The disadvantage of this method of conversion is the inability to implement in real time using the automatic mode to determine the required duration of the intervals with an arbitrary distribution of the initial value, as a result of which it is not possible to use it in real telecommunication systems.

The closest in technical essence to the proposed method is the "Method of hybrid switching of digital communication channels" (Fomin LA, Linets GI, Budko PA, Zdanevich SN, Pavlenko NA, Gakhova N .N. Hybrid switching method of digital communication channels. Patent No. 2195080, H04L 12/64, publication date 12/20/2002).

The essence of this method is that in the phase of establishing a connection as a result of a dialogue between the switching center and the caller, the length of the message is determined, which is compared with a certain threshold value that is specific for each particular network.

If the message length exceeds the threshold value, a physical connection is established and the message is transmitted in the circuit switching mode. If the message length is less than the threshold value, then it is remembered, broken into packets, a virtual connection is established and transmitted in packet switching mode.

The block diagram of the switching center has a modular structure and contains a control module, an identification module, an intermediate memory module, a subscriber access module, a module for interfacing communication lines with the switching center, connected by a common bus. In this case, the input line through the access module is connected to the input of the identification module, connected by the first output to the input of the intermediate memory module, the output of which through the interface module is connected to the outgoing packet switching line, the second output of the identification module through the interface module of the communication center with the switching center is connected to the outgoing line channel switching.

All modules exchange information with the control module and with each other via a common bus.

Thus, notification of each switching center about the length of the message to be transmitted in the connection establishment phase allows:

prevent network collisions associated with overflow of the buffer memory of switching nodes; to increase the efficiency of using communication channels by transmitting long messages in real time; reduce the total number of failures due to the lack of free buffers.

The disadvantage of this technical solution is the relatively low network performance in the case of packet switching when serving self-similar traffic. The self-similarity that occurs in the process of converting a bitstream to a packet stream in the intermediate memory module significantly reduces network performance. This is due to the limited availability of network resources, the significant unevenness of incoming packets, and, as a consequence, the presence of high burstiness, formed to transmit traffic. Thus, self-similarity is an integral property of packet networks.

Disclosure of invention

The objective of the invention is to increase the performance of the communication network when serving self-similar traffic by increasing the efficiency of use of its resources.

Technical result

The technical result, which can be achieved using the proposed method, is to increase the performance of the communication network when serving self-similar traffic by increasing the efficiency of use of its resources. The specified technical result is achieved by the fact that in the phase of establishing a connection between the switching center and the caller, the length of the message is determined, which is compared with a certain threshold value set during network design. Moreover, if the length of the message exceeds the threshold value, a physical connection is established and the message is transmitted in the circuit switching mode. If the length of the message is less than the threshold value, then the message is stored, divided into packets and the resulting sequence of packets is subjected to functional transformation. The object of the transformation is the one-dimensional distribution density of time intervals between packets. The invariance property of the probability differential is used.

where: τ ₁ - the duration of the time intervals between packets in the input sequence; τ ₂ - the duration of the time intervals between packets in the output sequence; ƒ (τ ₁ ) is the probability density of the intervals of the input sequence; g (τ ₂ ) is the probability density of the intervals of the output sequence.

The transformation law τ ₂ = φ (τ ₁ ) is a unique differentiable function determined from the solution of differential equation (1). It provides a pulse sequence g (τ ₂ ), after which packets of the output stream are transmitted over a virtual channel in packet switching mode.

In packet networks, the distribution of the interval time between packets with a constant length of each packet fully describes the statistical properties of the packet stream.

The technical result of the device, which implements a method of reducing the effect of self-similarity in network structures, is that in a device containing a control module, an identification module, an intermediate memory module, a subscriber access module, an interface module for connecting communication lines to a switching center connected by a common bus, the incoming the line is connected through the subscriber access module to the identification module connected to the first output through the module for pairing communication lines with the switching center with the outgoing switching line ka als, and a second output connected to the input buffer memory module, the first output is connected via the interface unit with communication lines from the first switching center line outbound packet switching functional module introduced transformations input coupled to the second output of the intermediate storage unit. At the same time, the output of the functional transformation module through the module for interfacing communication lines with the switching center is connected to the second outgoing packet switching line.

The functional transformation module comprises a control unit, first and second random access memory devices connected via the write and read buses to the control unit, input and output switches connected directly to the second output of the intermediate memory module, and connected to the second through the interface module for connecting communication lines to the switching center outgoing line of packet switching, respectively, a timer whose output is connected to the control input of the input switch and one control input of the control unit dstvenno and the control input of the output switch, and another input of the control unit through the inverter, actuating the input switch outputs are connected to inputs of the first and second random access memory, and output the switch actuating inputs connected to the outputs of the first and second random access memory, respectively. In this case, the information input of the control unit is connected to the output of the computing device.

Brief Description of the Drawings

Figure 1 shows a block diagram of a device for reducing the influence of self-similarity in network structures (switching center).

Figure 2 shows the structural diagram of the module functional transformations.

Figure 3 presents an example of the execution of the structural diagram of the identification module.

4 is an explanation of the functional conversion of a self-similar input packet stream to an output stream in hardware implementation of a computing device.

Figure 5 presents an example of the conversion of uniform and exponential distribution laws into Pareto and Weibull laws.

Figure 6 presents the program for converting the Pareto law into an exponential law in the environment of "Mathcad".

The implementation of the invention

A way to reduce the effect of self-similarity in network structures, including the phase of establishing a connection with receiving information about the length of the message, at which the length of the message is compared with a threshold value set during the design of the communication network. Moreover, if the message length exceeds a threshold value, then a physical connection is established and the message is transmitted in the circuit switching mode. If the message length is less than the threshold value, then the message is stored and divided into packets, characterized in that the obtained sequence of packets is subjected to functional transformation. The object of the transformation is the one-dimensional density of the distribution of time intervals between packets, in which the probability differential invariance property (1) is used, and the transformation law τ ₂ = φ (τ ₁ ) is a unique differentiable function determined from the solution of equation (1) and allowing the inverse transformation ψ = φ ^-1 , after which packets of the output stream are transmitted over the virtual channel in packet switching mode.

With this in mind, the relationship between the instantaneous values of a random process and the time intervals between the packages thus formed is converted into the following form:

where G (τ ₂ ) is the distribution function of the random variable τ ₂ .

Solution (2) in general is based on the use of the Newton-Leibniz formula

Thus, we have:

where do we find

We define a random variable τ ₂ :

Given that ψ ^-1 = φ, we obtain

(4) The value of α is found from the normalization condition

A pulsed flow with intervals between incoming packets distributed according to the law (3) can be obtained by nonlinear transformations of a random variable. That is, to generate a random variable with distribution function (2), it is necessary to construct a deterministic function τ ₂ = F ^-1 (y) and obtain the desired random numbers as the values of this function from the argument determined by a number that is a random variable with a uniform distribution law over the interval ( 0, 1).

Thus, in view of the foregoing, we represent expression (4) in the form

where rnd is a random variable uniformly distributed over the interval (0, 1).

Applying functional transformations, one can obtain processes with specified properties from the initial distribution function of time intervals between packets describing the behavior of a self-similar process, for example, a process described by an exponential distribution law for which there are methods for calculating the performance of communication networks. Thus, a way to reduce self-similarity in network structures in such a formulation can be implemented using software methods.

The block diagram of the device to reduce the influence of self-similarity in network structures is presented in figure 1. The device comprises a control module 1, an identification module 2, an intermediate memory module 3, a subscriber access module 4, a communication line interface module with a switching center 5 connected by a common bus 6, and an input line 7 connected through a subscriber access module 4 to the input of the identification module 2, connected by the first output through the interface module of the communication lines to the switching center 5 with the outgoing switching line of channels 8, and the second output is connected to the input of the intermediate memory module 3, the first output of which is connected through the interface module communication lines with the switching center 5 with the first outgoing packet switching line 9, the functional transformation module 10 connected to the input of the second output of the intermediate memory unit 3, and the output of the functional transformation module 10 through the interface module of the communication lines with the switching center 5 connected to the second outgoing line packet switching 11. The functional transformation module 10 (Fig.2) contains a control unit 12, the first 13 and second 14 random access memory associated with the write and read buses with the unit lines 12, input 15 and output 16 switches connected to the second output of the intermediate memory module 3 directly and through the module for interfacing communication lines with the switching center 5 with the second outgoing packet switching line 11, respectively, a timer 17, the output of which is connected to the control input of the input switch 15 and one control input of the control unit 12 directly and with the control input of the output switch 16 and the other input of the control unit 12 through the inverter 18, the executive outputs of the input switch 15 are connected are connected to the inputs of the first 13 and second 14 random access memory, and the executive inputs of the output switch 16 are connected to the outputs of the first 13 and second 14 random access memory, respectively, while the information input of the control unit 12 is connected to the output of the computing device 19 connected to the common bus 6 .

An example implementation of the identification module 2 is presented in figure 3. It contains the first digital-to-analog converter 20, the input of which is the input of identification module 2, and the output is connected to the first input of the comparison circuit 21, the output of which is connected to the S-input of the control trigger 22, the inverse and direct outputs of which are connected to the first inputs of the first 23 and second 24 elements And, respectively, connected by second inputs to the input of the identification unit 2, the outputs of the first 23 and second 24 elements And are connected to the first and second outputs of the identification unit 2, respectively, the second input of the comparison circuit 21 is connected to the output of the summing amplifier 25, one input of which is connected directly to the output of the second digital-to-analog converter 26 and the other input through a differentiating element 27, while the input of the digital-to-analog converter 26 is connected to the highway 6, and the R-input of trigger 22 is connected to the terminal Reset "28.

A device for reducing the influence of self-similarity in network structures works as follows. The control module 1, having received information about the length of the message, transmits this information to the identification module 2, which makes the decision to transmit the message depending on its length in the mode of switching channels or packets. Some messages in which the self-similarity properties of its structure are clearly manifested (determined by the value of the Hurst index) are sent to the functional transformation module 10, where they are converted in the computing device 19 in accordance with formula (1) into a sequence of packets with specified properties. In the module of functional transformations, the input sequence of packets is divided into two cycles using the input switch 15. This makes it possible to separately control the even and odd cycles in the first and second random access memory 13 and 14, adjusting the writing and reading processes so as not to lose information , after which the process is combined into a common stream using the output switch 16. The writing and reading processes are determined by the control unit 12 in turn. When, for example, the input information is recorded during the cycle in the first random access memory 13, then it is read from the second random access memory 14 and fed through the output switch 16 to the output of the functional transform module and fed through the module 5 to the output 11 of the device. The timer 17 sets the cycle length, which determines the amount of memory of random access memory 13, 14 and depends on the parameters of the converted process. The inverter 18 provides the antiphase operation of blocks 15, 16, as well as the processes of writing and reading.

Examples of specific implementation of the method of reducing the influence of self-similarity in network structures

Example 1. The software implementation of the computing device 19.

In module 10, condition (1) determines the equality of the integral distribution functions of the initial and final processes

whence we find the given transformation law τ ₂ = φ (τ ₁ ), in cases where the solution with respect to one of the variables is determined explicitly. This requirement also applies to the second variable, since there must exist a unique inverse function τ ₁ = ψ (τ ₂ ), where ψ = φ ^-1 .

Consider a transformation of practical interest. Let a continuous random variable τ ₁ with the distribution function F (τ ₁ ) undergo a transformation τ ₁ = φ (τ ₂ ) so that the result of the transformation is a distribution law with a uniform probability density of a random variable τ ₂

By condition (6) we obtain

Then the desired transformation function has the form

Indeed, for the maximum possible values of the random variable - ∝ <τ ₁ <∝, the equality

F (-∞) = 0, F (+ ∞) = 1.

Then, by condition (2), all values of τ will be enclosed in the interval [a, b]:

Differentiating (9) with respect to τ ₁ , we obtain

Substituting (11) into (10), we obtain

Therefore, any continuous probability density can be transformed into a uniform one. Obtained by functional transformation of an arbitrary distribution law, a law with a uniform density is, apparently, the best distribution, since it allows you to fill the transmission medium most evenly with packets. However, due to the lack of methods for calculating communication networks that are under the influence of traffic distributed according to a law with uniform density, the issue of converting an arbitrary distribution law into the Poisson (exponential nature of the distribution of the duration of intervals between packets) law for which such methods exist deserves attention.

Let a continuous random variable τ ₁ with a distribution density ƒ (τ ₁ ) undergo a transformation τ ₂ = φ (τ ₁ ). It is necessary to choose a function φ such that as a result of the transformation the distribution law

where τ is the interval between packets.

According to (2), the distribution functions must be equal

откудаSolving (13) with respect to τ ₂ , we obtain

where from

Differentiating (14) with respect to τ ₁ , we obtain

Substituting (15) into (1) and taking into account (14), we obtain the final formula (12) found as a result of transformation (2).

As an example, we consider the transformation according to formula (6) of two initial distribution laws: uniform and exponential (column 1 of Fig. 5). The transformation functions in the first case are the inverse power function, and in the second, the power function (column 2 of Fig. 5). The choice of such conversion functions for these distribution laws is dictated by the possibility of obtaining the distribution density of the duration of the intervals between packets in the form of distributions with obviously heavy “tails”: Pareto and Weibull (column 3 of Fig. 5). The probability distribution functions of the intervals and the intervals between the packets of these laws are presented in columns 4 and 5 of FIG. 5, respectively.

Figure 6 shows the program for converting the Pareto law in the Mathcad environment, with the distribution of the duration of the intervals between packets with obviously heavy "tails" (Hurst exponent H = 0.8 - self-similarity), into an exponential distribution (Hurst exponent H = 0.5 - lack of self-similarity) in the case of the software implementation of block 10. Block A - Random Number Generator; block B - Pareto distribution; block B - Exponential distribution; block G - Assessment of normalized span: Pareto distribution; block D - Estimation of normalized span: exponential distribution.

Information τ ₂ (100) from the computing device 19, which is used as a personal computer in this case, can be output via the COM port, or via the RS-232 interface, or via the USB port.

Example 2. Hardware implementation of a computing device.

The random variable τ _{1 is} distributed according to the Weibull law

It is required: a) to obtain a process in which time intervals between packets are distributed exponentially G (τ ₂ ) = 1-exp (-λτ ₂ ); b) determine the transformation function τ ₂ = φ (τ ₁ ).

Given condition (6), we obtain

The desired transformation is illustrated in Fig. 4 for the parameters α = β = λ = 2, for which τ ₂ = τ ₁ ² .

This means that to implement such a conversion as a computing device 19, you can use a quadratic detector with a gain of K = 1.

Example 3. The implementation of the identification module.

In the example implementation of the identification block circuit shown in FIG. 3, the threshold value of the message duration L _n can be calculated by the formula:

- производная по времени от занятого объема памяти; m_з(t) - текущее значение занятого объема памяти; β - коэффициент пропорциональности.where: L _cr - the critical length of the message; m is the total amount of memory;

- time derivative of the occupied memory; m _z (t) is the current value of the occupied memory size; β is the coefficient of proportionality.

In the initial state, the device supports packet switching mode. Further, if the true message length, converted into voltage by the digital-to-analog converter 20, exceeds the threshold U _n = αL _n (α is the transfer coefficient of the digital-to-analog converter), then a high potential will appear at the output of the comparison circuit 21, at which the trigger 22 will switch to the second stable state and at its direct exit there will be a high potential. The first element And 23 closes, and the second element And 24 opens. Identification module 2 is ready for message transmission through module 5 to outgoing line 8, providing a mode of switching channels. After establishing the end-to-end channel to the destination, the switching center initiates the transmission of the message. Otherwise, if the connection is not established, the subscriber is denied.

The summing amplifier 25 and the differentiating device 27 implement the second term in the formula (16), taking into account the dynamics of the buffer volume.

After transmitting the message, the control trigger 22 is returned to its original state, for example, by applying a “Reset” signal to its R-input from the control module 1 through terminal 28.

Thus, with long messages and increasing traffic, the channel switching method will prevail, and, conversely, if short messages are received with very pulsating traffic, it is advisable to transmit messages using the packet switching method. The use of a particular mode is determined by the choice of L _cr . If the number of occupied buffers (m _s ) and the value of β can be controlled within a given switching node or throughout the network depending on the accepted routing method, then the critical message length (L _cr ) is a design parameter and is set at the design stage of a specific network.

Conclusion

As the experience of introducing new equipment shows, traditional methods for calculating the volume of equipment (capacity of communication channels and especially the capacity of drives) based on Markov models lead to a significant underestimation of the load and provide unjustifiably optimistic solutions in cases where the input traffic has a long-term dependence (self-similarity property) ) In recent years, a large number of publications have appeared devoted to the creation of mathematical models of self-similar traffic for analyzing network performance when building queues in packet communication networks. However, significant success in this direction has not been achieved. The present invention aims to compensate for this gap to some extent. The use of the "Hybrid switching method of digital communication channels" as a prototype is justified by the fact that in this method a significant part of the longest messages is sent in channel switching mode, in which there is no self-similarity as a property of packet networks. In most of the shortest messages sent in packet switching mode, self-similarity does not manifest itself clearly due to the short observation (integration) time. For such messages, the control module 1 can use the hybrid switching method in the traditional form, directing packets from the intermediate memory module 3 to the outgoing line 9. Only a limited number of medium-length messages from the intermediate memory module 3 enter the functional transformation module 10, where it is converted into a sequence with given by the law of the distribution of time intervals between packets with weakened self-similarity properties. This improves network resource utilization and increases communication network performance.

Claims (3)

1. A way to reduce the effect of self-similarity in network structures, including the phase of establishing a connection with receiving information about the length of the message, at which the length of the message is compared with a threshold value determined during the design of the communication network, and if the length of the message exceeds the threshold value, a physical connection is established and the message is transmitted in the circuit switching mode, and if the message length is less than the threshold value, the message is stored and divided into packets, characterized in that the received sequence elnost packets subjected to functional transformation, the transformation is the object of one-dimensional density distribution of time intervals between packets, which uses differential probability invariance property
ƒ (τ ₁ ) dτ ₁ = g (τ ₂ ) dτ ₂ ,
where τ ₁ - the duration of the time intervals between packets in the input sequence; τ ₂ - the duration of the time intervals between packets in the output sequence; f (τ ₁ ) is the probability density of the intervals of the input sequence; g (τ ₂ ) is the probability density of the intervals of the output sequence; the transformation law τ ₂ = φ (τ ₁ ) is a unique differentiable function determined from the solution of the differential equation; this function provides a pulse sequence g (τ ₂ ), after which packets of the output stream are transmitted over a virtual channel in packet switching mode. 2. A device for reducing the influence of self-similarity in network structures, comprising a control module, an identification module, an intermediate memory module, a subscriber access module, a communication line interface module with a switching center connected by a common bus, the incoming line being connected through a subscriber access module to the input of the identification module, connected by the first output through the interface module of the communication lines to the switching center with the outgoing line of switching channels, and the second output is connected to the input of the intermediate memory module, the first the first output of which is connected through a module for coupling communication lines to a switching center with a first outgoing packet switching line, characterized in that it additionally includes a module for functional transformations connected to an input with a second output of an intermediate memory unit, the output of a module for functional transformations through a module for pairing communication lines with the switching center is connected to the second outgoing packet switching line. 3. The device according to claim 2, characterized in that the functional transformation module comprises a control unit, first and second random access memory devices connected via the write and read buses to the control unit, input and output switches connected directly to the second output of the intermediate memory module, directly , and through the module for interfacing communication lines with the switching center with the second outgoing packet switching line, respectively, a timer whose output is connected to the control input of the input switch and one control the input of the control unit, directly, and with the control input of the output switch and another input of the control unit, through the inverter, the executive outputs of the input switch are connected to the inputs of the first and second random access memory, and the executive inputs of the output switch are connected to the outputs of the first and second random access memory, accordingly, the information input of the control device is connected to the output of the computing device associated with the common bus.

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