Geodesic
Analysis of the steady-state behavior of a queueing system with autoregressive arrivals
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2016), pp. 39-48

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The paper studies a single server queueing system with infinite capacity and with batch Poisson arrival process. A feature of the system under study is autoregressive dependence of the arriving batch sizes: the size of the $n$-th batch is equal to the size of the $(n-1)$-st batch with a fixed probability, and is an independent random variable with complementary probability. Service times are supposed to be independent random variables with a specified distribution. The steady-state behaviour is studied; expression for the probability generating function of the queue length is derived, as well as the mean queue length for a special case.
Keywords: queueing theory, steady-state behaviour, batch arrivals. 
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     author = {N. D. Leontyev},
     title = {Analysis of the steady-state behavior of a queueing system with autoregressive arrivals},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {39--48},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2016_2_a2/}
}
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N. D. Leontyev. Analysis of the steady-state behavior of a queueing system with autoregressive arrivals. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2016), pp. 39-48. http://geodesic.mathdoc.fr/item/VTPMK_2016_2_a2/