Steady-state analysis of shortest expected delay routing

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Abstract

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with non-identical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product-forms that can be determined recursively. The resulting series expression is directly amenable for numerical calculations and it also provides insight in the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.
Original languageEnglish
Pages (from-to)309–354
Number of pages46
JournalQueueing Systems: Theory and Applications
Volume84
Issue number3
Early online date11 Aug 2016
DOIs
Publication statusPublished - 1 Dec 2016

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