Rare event asymptotics for a random walk in the quarter plane

Rare event asymptotics for a random walk in the quarter plane

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Article ID: iaor20108997
Volume: 67
Issue: 1
Start Page Number: 1
End Page Number: 32
Publication Date: Jan 2011
Journal: Queueing Systems
Authors: ,
Keywords: random walk, tandem queues, rare events
Abstract:

This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.

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