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