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Queueing Systems

, Volume 55, Issue 1, pp 71–82 | Cite as

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

  • Iddo Eliazar
Article

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.

Keywords

M/G/∞ systems Poisson point processes Infinite arrival rates Lévy inflows Workload processes Long Range Dependence (LRD) Reverse engineering 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.School of Mathematics & School of ChemistrySackler Faculty of Exact Sciences, Tel Aviv UniversityTel AvivIsrael

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