Informatics and Applications

2025, Volume 19, Issue 1, pp 52-60

ONE QUEUING SYSTEM WITH CORRELATED INPUT FLOW

A. K. Bergovin
A. M. Ryazanov
V. G. Ushakov

Abstract

A single-line queuing system with an infinite number of waiting places, an arbitrary distribution of service time, and a Poisson incoming flow with random intensity is considered. The intensities are subordinated to the autoregressive dependence of the first order. The j oint distribution of the number of total customers in the system is obtained as well as the sojourn time of a customer in the system in a nonstationary regime. Expressions for stationary distributions and their probabilistic characteristics are also presented. The average sojourn time in the system in the stationary regime is numerically studied and illustrated under different assumptions on the distribution of service time and on the characteristics of the incoming flow. Comparison is made with the classical M |G| 1 queue.

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