Pseudo-random sequences and procedures for their machine generation

In statistical modeling of systems, one of the main issues is the consideration of stochastic effects. The number of random numbers used to obtain a statistically stable estimate of the performance characteristics of the system 5 when implementing the modeling algorithm on a computer varies within a fairly wide range, depending on the class of the simulation object, the type of the characteristics to be evaluated, the accuracy and reliability of the simulation results. For the statistical computer simulation method, it is characteristic that a large number of operations, and correspondingly a larger proportion of computer time, are expended on actions with random numbers. In addition, the results of statistical modeling essentially depend on the quality of the initial (basic) sequences of random numbers. Therefore, the presence of simple and economical ways of forming sequences of random numbers of the required quality in many ways determines the possibility of practical use of computer modeling of systems [31, 37, 46].

Let's consider opportunities and features of obtaining sequences of random numbers in the statistical simulation of systems on a computer. In practice, three basic ways of generating random numbers are used: hardware (physical), table (file), and algorithmic (software).

Hardware method.

With this generation method, random numbers are generated by a special electronic prefix - a random number generator (sensor) serving as one of the external devices of the computer. Thus, the implementation of this generation method does not require additional computational operations of the computer for generating random numbers, but only the operation of accessing an external device (sensor) is necessary. As the physical effect underlying such generators of numbers, noise in electronic and semiconductor devices, the phenomena of decay of radioactive elements, etc. are most often used. Let us consider the principle of obtaining random numbers from a prefix, based, for example, on the noise effect in semiconductor devices.

The block diagram of the hardware random number generator is shown in Fig. 4.8, a. Here IN is the source of noise; CS - the key scheme; FI - the driver of pulses; PS is a recalculation scheme. When the noise is amplified at the output ИШ , the voltage Мц, (0, which is a random process shown in the time diagram of Fig. 4.8, б. is obtained. Moreover, the noise realization segment and to (/), formed on the time interval (0, 7) with CS, contains a random number of outliers Comparison of voltage and (0 with the threshold 0 and allows to generate a series of pulses Fφ (r) at the output FI . output PS can be obtained a sequence of random numbers *, (/) .For example, if you scale and (t, t, T) per unit, then the values ​​of the time intervals A *, =/ & lt; + | -/& lt; between adjacent pulses m φ (/) are random numbers */€ (0, 1).

Fig. 4.8. Hardware method for obtaining random numbers

Other circuit solutions of hardware generators of random numbers are possible [29, 37]. However, the hardware method of obtaining random numbers does not allow to guarantee the quality of the sequence directly during the simulation of system 5 on a computer, and also to obtain the same sequence of numbers in the simulation.

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