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Analysis of customers’ impatience in queues with server vacations. (English) Zbl 1114.90015
Summary: 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.

MSC:
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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