SU1612311A1 - Device for modeling queueing systems - Google Patents

Abstract

The invention relates to computing and can be used for statistical modeling of queuing systems. The purpose of the invention is to improve the accuracy of modeling a nonlinear dynamic priority in servicing a quotation. The device contains a block of delay elements, a control trigger, two pulse generators, two OR elements, two AND elements, a pulse shaper, and a group of service channels for the batch, and in each channel a random flow generator for the batch, two triggers, three And elements, two counters, a decoder, P registers, P blocks of AND elements, a block of OR elements, and a random time delay block. The device is intended to simulate QS with dynamic priorities, i.e. such QS, in which the priority of service quotation depends on the duration of the waiting quota in the queue. The selection of a service quotation is made taking into account the current value of the priority function depending on the request of each type on the waiting time and having a generally non-linear form. The service of the request is performed in the order of relative priority in such a way that the service comes in with the application possessing at the given time the maximum value of the priority function from among the applications in the queue. 1 il.

Description

(21) 4629509 / 24-24

(22) 02.01.89

(46) 12/7/90. Bul.M 45

(72) Yu.A. Kapinos. A.N. Bashkirov

I.А.Vetrov and О.N.Ivanenyuk

(53) 681.3 (088.8)

(56) USSR Author's Certificate No. 983715, cl. G 06 F 15/20, 1981.

USSR author's certificate Mg 1406600, cl. G 06 F 15/20 1986 (54) DEVICE FOR MODELING MASS SERVICE SYSTEMS

(57) The invention relates to computing and can be used for statistical modeling of queuing systems. The purpose of the invention is to improve the accuracy of modeling

nonlinear dynamic priority in servicing a stock. The device contains a block of delay elements, a control trigger, two pulse generators, two OR elements, two AND elements, a pulse shaper, and a group of service channels for the batch, and in each channel a random flow generator for the batch, two triggers, three And elements, two counters, a decoder P of registers, P blocks of AND elements, a block of OR elements, and a random time delay block. The device is designed to simulate a QS with dynamic priorities, i.e., such QSs in which the priority: service depends on the value of waiting for queuing in a queue. dependent for each type of application on waiting time and generally having a nonlinear form. The service of the request is carried out in the order of relative priority in such a way that the service comes in with the application possessing at a given time the maximum value of the priority function from among the applications in the queue. 1 silt

The invention relates to computing and can be used to model queuing systems (QS).

The purpose of the invention is to improve the accuracy of modeling a nonlinear dynamic priority in servicing a quotation.

The drawing shows a block diagram of the device.

The device contains service channels 1 of the request, each of which consists of a random flow generator 2 of the first element AND 3, the first trigger 4, the second element AND 5, the first counter 6 of the decoder 7, the registers 8, the blocks of elements AND 9, the block of elements OR 10, the second counter 11, the second trigger 12, the third element I 13, and the block 14 of the random time delay.

The device also includes the second element OR 15, the prohibition element 16, the second pulse generator 17, the delay element block 18, the pulse generator 19, the AND element 20, the first pulse generator 21, the first element And 22 trigger 23, the first element OR 24. On The circuit also indicates the inputs 25 of the counter 11 of the write bit 26, the counting 27 and the reset 28 of the first 29, second 30, third 31 and fourth 32 outputs of the block 18 delay elements.

The device is intended to simulate QS with dynamic priorities, i.e. such QS, in which the priority of servicing the incoming stock depends on the waiting time of the queued queue. The selection of a quota for service is carried out based on the current value of the priority function, depending on the request of each type on the waiting time. The service of the request is performed in the order of relative priority in such a way that the service comes in with the application possessing at the given time the maximum value of the priority function from among the applications in the queue. The priority function of the order is non-linear.

The values of the known priority function in discrete time values are pre-loaded onto the group of registers 8 and are read sequentially at a quantization frequency specified by the pulse generator 17.

For definiteness, we will assume that applications in service channels that have a smaller number have a higher initial (initial) priority compared to applications in service channels that have a higher number. Generators 2 random flow requests simulate the input flows of the application for servicing different priority classes.

A random time delay unit 14 simulates a serving device with an arbitrary service time.

The elements that determine the priority of a request for any channel at any time from the moment it arrives to the moment it is accepted for service are counter 6, decoder 7, registers 8, blocks 9 of the AND elements and block 10 of the OR elements of each channel. At the output of the block 10 elements OR there will be a code that determines the value of the priority function of the application at the given time.

Pulse generator 21 and channel counters 11 compare the priority codes of the application at the time of release of the service device and provide the choice of service application having the highest priority at the moment. The pulse generator 17 generates pulses with a frequency of quantization of the priority functions of the wok.

The device works as follows

In the initial state, the triggers 4, 12, and 23 are in the zero state, and in the 6 and 11 channel counters, zeros are written. Single potentials with inverse outputs

flip-flops 4 are present at the inputs of flip-flops AND 3. In addition, unit potentials from the inverse outputs of flip-flops 12 are attached to the corresponding inputs of the And 5 element 22 and to the corresponding inputs of the And 13 elements. The 8 channel registers contain the values of priority functions of different types at discrete moments of time.

10 The pulses from the generators 2 of the random flow of the flow, imitating the input flow of the flow to service different priority classes, pass through the open elements And 3 corresponding channels on

15 single inputs of the triggers of these 4 channels, set them to the single state. The unit potential from the outputs of these triggers 4 through the OR element 15 and the prohibition element 16 starts the generator 17 of pulses,

20 from the output of which the pulses with the frequency of quantization of the priority functions for the channels are fed to the inputs of the And 5 elements of all the channels for the service of the channel. These pulses arrive at the counting

The 25 inputs of the counters 6 of those channels in which the requests for servicing are fixed, since the high potentials from the single outputs of the flip-flops 4 ensure the opening of the elements AND 5 of these channels. As a result, at the outputs of the decoder 7 of these channels, successively with the quantization frequency, high potentials appear, opening in turn blocks of 9 AND elements, and discrete value codes

35 priority functions from the corresponding registers 8 are fed to groups of inputs of blocks of 10 OR elements. Thus, on the groups of inputs of the initial installation 26 of the counters 11 f-1, the values of the priority functions of the application depend on the time of receipt of the application.

The choice of the next request for service is carried out as follows. five

With the appearance of a signal, the formation order of which is considered below, at the output of the delay element 14 of one of the channels simulating the end of service signal (RMS). The preparation of individual components of the modeling device for the selection of the next request for service begins. For this purpose, this signal, the passage through the OR element 24, sets to the null the left state of the trigger 23, the triggers 12 and the counters 11 of all channels. As a result, the element And 22 opens, the high potential from its output goes to the input of the element And 20 and to the input of the block 18 elements

delays.

The signal from the second output 30 of block 18 of the delay elements, delayed by the time required to set the outcomes of the triggers 12. 23 and counters 11, simulates the ready-for-service signal (CDF) of the serving device and goes to the control input of the prohibition element 16, stopping that the most operation of the generator 17 pulses. After that, the signal from the third output 31 of the block 18 of the delay elements, delayed by the time required to stop the operation of the pulse generator 17, is fed to the input of the driver 19, which gives a pulse to the pack

ten

 - 1 yr - - - iJ- j f t4j

counters 11 all channels. The former 19 converts a constant high potential into a short pulse with a duration that ensures the recording of codes into 11-channel counters. As a result of this, the values of the codes from the outputs of the corresponding registers of the corresponding registers 8 through the corresponding open blocks of 9 elements AND and the blocks of 10 elements OR will be the outputs of the triggers 12 of the corresponding channels will still be zero potentials. In addition, the zero potential of the inverse output of the trigger 12 of the priority channel will be applied to the corresponding inputs of the elements And 13 channels

having a number larger than the priority channel.

After completion of the transient processes caused by the step of allocating the priority channel, the signal from the output 29 of the block 18 of the delay elements is set to one state the trigger 23, the Single signal from the direct output of the trigger

20

When counters are 11, those in them will be zapikgi H i vnnnogo passv, the values of ФвнкииГпn fnl ± Л r l., of the priority channel and channels, are indicated, only the one that belongs to the priority channel opens. As a result, at the output of the element And 13 of the priority channel and, consequently, on the corresponding block 14 of this channel, a signal appears, imitating the start of application service.

After a time equal to the service time of the application of this class,

The values of the priority functions of the orders of various classes at the time of arrival of the signal of CGO are specified. In the absence of the ready signal, the inhibit element 16 opens and the pulse generator 17 resumes its operation.

After the time required to write the codes to the counters 11 has expired, a signal from the fourth output 32 of the block 18 of delay elements through the open element 20 starts the pulse generator 21.

Pulses from the output of the generator 21 with a high repetition rate arrive at the counting inputs of 27 counters 11 of all service channels of the quota. Counters 11 perform the function of determining the application (channel) with the maximum value of the priority function at the time of the arrival of the CX signal. Since the capacity of the counters 11 is the same.

thirty

1- - f-- - -., .-, -, rvuiic / fa m

are the end of service signals, which sets to zero the trigger 4 of this channel, which, in turn, zeroes the counter 6 and opens the element AND 3 of this kenal by a signal from the zero output. In addition, through the OR element 24, the triggers 12, 23 and the counters 11 of all channels are reset. Further operation of the device is similar to that discussed above.

There are cases when two or more service bids have the same priorities, i.e. The counter codes of these 11 channels at the time of arrival of the signal for service readiness will be equal. Then the signal appears at the output of the element And 13 of that channel in which the applications of a higher priority class are imitated, since the zero signal from the inverse

35

and: G: eGeG „::: GGGa G; GG, eGe; i rS VC.po.ce go in „„ on „all state .r„ „er 2 s ™ ka-50 th ™,„ and; ggogd „gsg ;; oG“ o „: Go ° a

Nala

The low potential from the inverse output of this trigger 12 is fed to the corresponding input of the element And 22, as a result of which the elements 22 and 20 are closed, and the pulse generator 21 stops its operation. At the second input of the element And 13 of the priority channel there is a single potential, while at the second inputs of the elements And 13 of the other channels from the direct

55

the triggers 12, 23 and counters 11 are set to the initial state, and the ready-to-service signal will not be generated, since the AND 22 element is closed with zero potential from the output of the OR 15 element. Such a condition is characteristic of the device when it is initially turned on work

When one of the generators 2 produces a random flow, the order is carried out

the outputs of the triggers of the 12 corresponding channels will still be zero potentials. In addition, the zero potential from the inverse output of the trigger 12 of the priority channel will be applied to the corresponding inputs of the elements And 13 channels,

having number more than at the priority channel.

After completion of the transient processes caused by the step of allocating the priority channel, the signal from the output 29 of the block 18 of the delay elements is set to one state the trigger 23, the Single signal from the direct output of the trigger

 The first pass channel, in the l channel, of the channels, opens only one of them that belongs to the priority channel. As a result, at the output of the element And 13 of the priority channel and, consequently, on the corresponding block 14 of this channel, a signal appears, imitating the start of application service.

After a time equal to the service time of the application of this class,

The main passw, in l., Priority channel p o0

1- - f-- - -., .-, -, rvuiic / fa m

are the end of service signals, which sets to zero the trigger 4 of this channel, which, in turn, zeroes the counter 6 and opens the element AND 3 of this kenal by a signal from the zero output. In addition, through the OR element 24, the triggers 12, 23 and the counters 11 of all channels are reset. Further operation of the device is similar to that discussed above.

There are cases when two or more service bids have the same priorities, i.e. The counter codes of these 11 channels at the time of arrival of the signal for service readiness will be equal. Then the signal appears at the output of the element And 13 of that channel in which the applications of a higher priority class are imitated, since the zero signal from the inverse

five

 , eGe; i rS VC.po.c.e 50 ™ ™, “and; GGoGd“ gGS ;; oG “o”: H o ° a

55

the triggers 12, 23 and counters 11 are set to the initial state, and the ready-to-service signal will not be generated, since the AND 22 element is closed with zero potential from the output of the OR 15 element. Such a condition is characteristic of the device when it is initially turned on work

When one of the generators 2 outputs a random flow, the application installs the corresponding trigger 4 into one state, which starts the pulse generator 17, opens element 5 of this channel and opens element 22 of the device, the output signal of which signal ready for service. In the course of further operation of the device, the incoming application is issued for maintenance, as in counters 6 and. therefore, in the counters of the 11 remaining channels, zeros are written.

Characterization of QS is carried out by known methods.

Claims (1)

Invention Formula A device for simulating queuing systems comprising two OR elements. two elements I. a block of delay elements, a trigger and a group of service channels of the order, each of which consists of a random flow generator, two triggers, three AND elements, a block of I. elements of the counter, and a random time delay block, with each service channel The output of the random flow generator is connected to the first input of the first element I. The output of which is connected to the single input of the first trigger, the direct output of which is connected to the first input of the second element I. The output of the third element key to the random time delay block input, the output of which is connected to the zero input of the first trigger, the inverse output of which is connected to the second left and right I element I. the outputs of the random time delay blocks of all service channels of the group, respectively, the output of which is connected to the zero inputs of the second triggers of all service channels of the group's order and to the zero input of the device trigger, the direct output of which is connected to the first inputs of the third elements all service channels of the group's order, the direct outputs of the first triggers of all service channels of the group's orders are connected respectively to the inputs of the second element OR device whose output is connected to the first input of the first element AND device, the first output of the block of delay elements the device triggers, the inverse output of the second trigger of the K-th service channel, the group's quotes (K 1, M) are connected to the (K + 1) th input of the first element AND device and to the (K + 2) th inputs of the third element The service channels of the group's order, having a number greater than K, the direct output of the second trigger of the Kth service channel, the group's subscription is connected to (K +1} th input 5 of the third element And its service channel of the group's request, which, in order to increase the accuracy of modeling the dynamic priority in servicing a claim, it additionally contains 10 a prohibition element, two pulse generators and a pulse shaper, and each service channel of the group request additionally contains a decoder, a second counter, a block element OR, P registers (where.Р is the number of discrete values of the priority function) and (P-1) blocks of elements I. And in each service channel of the group’s order, the output of the second element I is connected to the counting 20 input of the first counter, These outputs are respectively connected to the inputs of the decoder, the outputs of which are connected to the control inputs of the corresponding blocks of units And, the bit 5 inputs of registers are connected to the information inputs of the corresponding blocks of elements And, the outputs of which are connected respectively to moves block elements OR. the outputs of which are connected respectively to the bits of the second counter, the overflow output of which is connected to the single input of the second trigger, the inverse output of the first trigger is connected to the zero input of the first 5 counter, the output of the first And device element is connected to the first input of the second element And device and the input of the block of delay elements, the second output of which is connected to the control input of the prohibition element 0, the third output - to the input of the pulse former, and the fourth output - to the second input of the second element I The output of which is connected to the input of the first pulse generator, the output 5 of which is connected to the counting inputs of the second counters of all service channels of the station, the output of the second OR element is connected to the information input of the prohibition element, the output of which is connected to the input of the second pulse generator, the output is connected to the counting inputs of the first counters of all ka-. The service unit of the group orders, the output of the pulse generator is connected to the recording inputs of the second counters of all the service channels of the group request, the set inputs to the zero state of which are combined and connected to the output of the first OR element of the device.