SU1541604A1 - Device for shaping flow of pulses described by second order by erlang distribution - Google Patents

Abstract

The device relates to computing and can be used to statistically simulate the flow of applications in queuing systems. The purpose of the invention is to increase the speed; this is achieved by introducing into the device a second generator of uniformly distributed random numbers, a second digital-to-analog converter, a multiplication unit, and a delay element. Increased speed is expressed in ensuring the generation of each successive pulse from a sequence of pulses, the intervals between which are subordinate to the Erlang distribution of the second order, for one cycle of operation of the exponential voltage generator.

Description

The invention relates to computing and can be used to statistically simulate the flow of applications in mass inspection systems.

The purpose of the invention is to increase the speed in the formation of a sequence of pulses, the intervals between which are subject to the second order Erlang distribution.

The drawing shows a block diagram of a device for generating a stream of pulses described by a second-order Erlang distribution.

The device contains the first 1 and second 2 generators of uniformly distributed random numbers, the first 3 and second 4 digital-to-analog converters, multiplication unit 5, comparison unit 6, exponential generator 7

voltage, driver 8 pulses C and the element 9 delay.

The device works as follows.

At the moment of formation of the next pulse at the output of the pulse generator 8, the first 1 and second 2 generators of uniformly distributed random numbers start, the exponential voltage generator 7 is reset to its initial state, and the delay element 9 is started. The generators of uniformly distributed random numbers produce two independent random numbers subject to a uniform distribution. These numbers are converted in the first 3 and second 4 digital-to-analog converters to analog signals Y, and Y4, respectively, arriving at the first

bi

four

to

s

R

J

and the second inputs of block 5 multiplication. The output of the multiplier produces a signal equal to the product of the Y, Y4 input signals. At the same time, a pulse appears at the output of the delay element 9 (the delay time is equal to the total response time of the generators of uniformly distributed random numbers, analog-to-digital converters and the multiplication unit), which triggers the exponential generator 7 that changes according to the law e. This voltage is applied to one of the inputs of the comparison unit 6; The signal from the output of block 5 is received at the other e | o input. At the moment of equality of the signals at both inputs, the comparison unit generates an output signal supplied to the input of the driver 8 pulses. As a result, another pulse appears at the output of the former, which is the output of the device. This cycle of operation of the device ends and a new one begins, similar to that described.

As the next 1st cycle ends at the moment of time t T- (t is counted from the beginning of the cycle), determined by the ratio

Y, (i) Y2 (i),

ts, therefore, the duration of the interval T; between the previous and next pulses is equal

T - (i) -Y4 (i) - | lnY, (iJ +

.. + - llnYt (i) J.

Since random variables Y and Y4 have a uniform distribution

then the random variables are lnY and

- lnY2 are exponential

distribution with parameter 7. Then the intervals,, which are the sum of two independent exponentially distributed terms with the same parameter A, obey the second-order Erlang distribution.

In the proposed device, the generation of each successive impulse is i

It exists in one cycle of the exponential voltage generator, in contrast to the known devices designed to simulate the second-order Erlang flows, where such generation takes place in two cycles of the exponential voltage generator.

Claims (1)

Invention Formula A device for generating a stream of pulses described by a second-order Erlang distribution, containing a first generator of uniformly distributed random numbers, a first digital-to-analog converter, an exponential voltage generator, a comparison unit, and a pulse shaper, with the output of the first generator of uniformly distributed random numbers connected to the information input of the first digital-analog the converter, the output of the exponential voltage generator is connected to the first input of the comparison unit, the output of which is connected to the input of the pulse generator, the output of which is connected to the start input of the first generator of uniformly distributed random numbers, characterized in that, in order to improve speed, a multiplication unit, a delay element, a second digital-to-analog converter, a second generator of uniformly distributed are introduced into it random numbers, the output of which is connected to the information input of the second digital-to-analog converter, the first and second inputs of the multiplication unit are connected respectively to the outputs the first and second digital-to-analog converters, and the output to the second input of the comparison unit, the output of the pulse shaper is the output of the device and is connected to the start input of the second generator of uniformly distributed random numbers, the zeroing input of the exponential voltage generator and the input of the delay element whose output connected to the trigger input of the exponential voltage generator.