ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 10. Vol. 28. 2022

DOI: 10.17587/it.28.507-513

V. N. Tarasov, Dr. of Tech. Sc., Professor, Head of Department of POUTS,
Volga State University of Telecommunications and Informatics, Samara, 443010, Russian Federation

New Possibilities of Queuing Systems with Time Delay

From the classical theory of queuing, it is known that the average delay of requests in the queue is directly proportional to the variances of random intervals between arrivals of requests and service time, which means that it depends quadratic on the coefficients of variation of these random variables. Classical QS are applicable only in the case of fixed values of these coefficients of variations, which is a serious limitation for them. In contrast to the classical theory, the article presents the results of research on QS described by distribution laws shifted to the right from the zero point. Such a transformation of distribution laws with the introduction of a time shift parameter increases the mathematical expectations of random arrival and service intervals. This, in turn, reduces the coefficients of variation of time intervals, and, consequently, the average delay of requests in the queue will decrease many times depending on the value of the shift parameter. In the previous works of the author, spectral solutions and calculation formulas obtained on their basis for the average delay of requests in the queue for a set of QS with time delay are presented. These systems are obtained using four distribution laws used in queuing theory: exponential, hyperexponential, Erlang and hyper-Erlang. It has been theoretically and practically proven that in systems with a time delay, the average delay is less than in classical systems with the same load. Taking into account the Little formulas that fix the dependence of such QS characteristics as the average queue length, the average number of requests in the system, and the average residence time of requests on the average delay, we obtain an important feature for systems with delay. The distribution law shift parameter can regulate the average delay, and through it the other characteristics of the QS.
Keywords: time delay system, shifted distribution laws, Laplace transform, Lindley integral equation, spectral expansion method

P. 507–513

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