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On the stability of a class of non-monotonic systems of parallel queues

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Abstract

We investigate, under general stationary e‘rgodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p + 1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions for the existence of a stationary workload, which indicate a “splitting” of the system in heavy traffic, into a loss system of p servers (that is, a system with p servers and no waiting room), plus a FCFS system of S − p servers. To prove this result, we show en route an original sufficient condition for the existence and uniqueness of a stationary workload for a multiple-server loss system.

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Authors and Affiliations

  1. Department of Industrial Engineering & Management Sciences, Northwestern University, Mc Cormick School of Engineering, 2145 Sheridan Road, Evanston, IL, 60208, USA

    Pascal Moyal

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  1. Pascal Moyal
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Correspondence to Pascal Moyal.

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Moyal, P. On the stability of a class of non-monotonic systems of parallel queues. Discrete Event Dyn Syst 27, 85–107 (2017). https://doi.org/10.1007/s10626-016-0230-9

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  • DOI: https://doi.org/10.1007/s10626-016-0230-9

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