Stationary tail asymptotics of a tandem queue with feedback

Jiashan Tang () and Yiqiang Zhao ()

Annals of Operations Research, 2008, vol. 160, issue 1, 173-189

Abstract: Motivated by applications in manufacturing systems and computer networks, in this paper, we consider a tandem queue with feedback. In this model, the i.i.d. interarrival times and the i.i.d. service times are both exponential and independent. Upon completion of a 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 any fixed number of customers in one queue (either queue 1 or queue 2), using newly developed methods we study properties of the exactly geometric tail asymptotics as the number of customers in the other queue increases to infinity. We hope that this work can serve as a demonstration of how to deal with a block generating function of GI/M/1 type, and an illustration of how the boundary behaviour can affect the tail decay rate. Copyright Springer Science+Business Media, LLC 2008

Keywords: Tandem queue; Feedback; Tail asymptotics; α-positivity; Geometric decay (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10479-007-0303-0

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