Consecutive customer losses in oscillating GIX/M//n systems with state dependent services rates

Consecutive customer losses in oscillating GIX/M//n systems with state dependent services rates

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Article ID: iaor20091428
Country: Netherlands
Volume: 162
Issue: 1
Start Page Number: 143
End Page Number: 158
Publication Date: Sep 2008
Journal: Annals of Operations Research
Authors: ,
Keywords: GI/M/c queues
Abstract:

We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GIX/M//n systems with state dependent services rates, also denoted as GIX/M(m)–M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear system of equations. The results derived are illustrated for specific sets of parameters.

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