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New Representations for G/G/1 Waiting Times

2014/12/03 by Michael L. Wenocur, Wenocur, Michael L.
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #math.PR #msc:45E10

paper · pdf · doi:10.48550/arxiv.1412.1203

47 pages, 1 algorithm

arxiv created 2014/12/03 · arxiv updated 2014/12/04

Abstract

We obtain an explicit representation for the Laplace transform of the waiting time for a wide class of distributions by solving the Wiener-Hopf factorization problem via the Hadamard product theorem. Under broad conditions it is shown that this representation is invertible by an infinite partial fraction expansion. Computational schema illustrated by a variety of examples demonstrate the feasibility of numerically solving a rich class of G/G/1 queue possessing either bounded service or arrival times. In particular very tractable computations are derived for the M/M/1 queue with gated arrivals.

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