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The M/G/∞ system revisited: finiteness, summability, long range dependence, and reverse engineering

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Abstract

We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated.

We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied to various examples, including ones with infinite queues and non-summable workloads.

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  1. School of Mathematics & School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Iddo Eliazar

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  1. Iddo Eliazar
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Correspondence to Iddo Eliazar.

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AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10

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Eliazar, I. The M/G/∞ system revisited: finiteness, summability, long range dependence, and reverse engineering. Queueing Syst 55, 71–82 (2007). https://doi.org/10.1007/s11134-006-9005-6

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  • DOI: https://doi.org/10.1007/s11134-006-9005-6

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