Stationary tail asymptotics of a tandem queue with feedback
The paper deals with the following tandem queueing system with feedback: a Poisson process of customers arrives at the first station (one server and infinite waiting room), where the customers receive, after a waiting time if the server is busy, an exponentially distributed service time. Upon completion of the service at the first station the customer moves to the second station (one server and infinite waiting room) to receive service in the same manner as at station 1. Upon completion of the service at the second station the customer either leaves the system with probability \(p\) or goes back, together with all customers currently waiting in the second queue, to the first queue with probability \(1-p\). For this model the geometric tail decay of the stationary distribution of the number of customers in queue 1 (queue 2) for a fixed number of customers in queue 2 (queue 1) is proved. The paper is based on matrix geometric asymptotic methods and extends results of \textit{L. Haque} [Tail behaviour for stationary distributions for two-dimensional stochastic models. Ph.D. thesis, Carleton University. (2003)] and \textit{L. Haque} et al. [Stoch. Models 21, No. 1, 77--99 (2005; Zbl 1065.60133)].
scientific article; zbMATH DE number 5286508
scientific article