This article is cited in 2 papers

A study of queueing systems with discrete time, autoregressive arrivals, and feedback

N. D. Leontyev^a, V. G. Ushakov<sup>ab

a</sup> Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, Moscow 119991, GSP-1, Russian Federation
^b Institute of Informatics Problems, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The paper studies two discrete-time single server queueing systems with infinite capacity and feedback. The arrivals in both systems are driven by discrete autoregressive models, i.e., the size of each arriving batch may be equal to the size of one of the previously arrived batches with some fixed probability, or is a random variable independent of the history with complementary probability. The main object of the study is the stationary queue length. For the system with discrete autoregressive arrivals of order 1, expressions for queue length distribution are derived, and for the system with discrete autoregressive arrivals of order 2, the expected queue length is found.

Keywords: queueing theory; discrete-time queueing systems; discrete autoregressive model; batch arrivals; feedback.

Received: 17.02.2015

DOI: 10.14357/08696527150203

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