Rare event asymptotics for a random walk in the quarter plane |
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Authors: | Fabrice Guillemin Johan S H van Leeuwaarden |
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Institution: | 1.Orange Labs,Lannion,France;2.Department of Mathematics and Computer Science,Eindhoven University of Technology,Eindhoven,The Netherlands |
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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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