Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Two M/M/1 Queues with Transfers of Customers
Queueing Systems: Theory and Applications
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We consider a queueing model with c (≥ 2) heterogeneous servers, where each server has its own queue with infinite capacity. Customers arrive according to a Markovian arrival process and join the shortest queue. Service times at each server are assumed to have a phase type distribution, and to be independently and identically distributed. We further assume that jockeying between queues is permitted if the difference of their queue lengths exceeds a pre-determined threshold. The main objective of this paper is to get the tail decay rate of the stationary distribution for the longest queue of this queueing model. Specifically, we show that the decay rate equals the c-th power of the ones for the corresponding queueing model with a single waiting line. We prove this result using a quasi-birth-and-death process with finitely many background states.