Queues with waiting time dependent service

R. Bekker, G.M. Koole, B. Nielsen, T. Nielsen

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Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples. © 2011 The Author(s).
Original languageEnglish
Pages (from-to)61-78
JournalQueueing Systems
Issue number1
Publication statusPublished - 2011


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