Analysis of customers’ impatience in queues with server vacations |
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Authors: | Eitan Altman Uri Yechiali |
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Institution: | (1) INRIA, 2004 route des Lucioles, B.P. 93, 06902 Sophia Antipolis, France;(2) Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel |
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Abstract: | Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always
been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival.
In this paper we consider systems with servers vacations where customers’ impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never
been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and
M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show
that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation
discipline.
This work was supported by the Euro-Ngi network of excellence. |
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Keywords: | Queueing Single and multiple vacations Impatience Abandonment M/M/1 M/G/1 M/M/c |
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