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.
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This work was supported by the Euro-Ngi network of excellence.
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Altman, E., Yechiali, U. Analysis of customers’ impatience in queues with server vacations. Queueing Syst 52, 261–279 (2006). https://doi.org/10.1007/s11134-006-6134-x
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DOI: https://doi.org/10.1007/s11134-006-6134-x