Queues with waiting time dependent service |
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Authors: | R Bekker G M Koole B F Nielsen T B Nielsen |
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Institution: | 1.Dept. Mathematics,VU University Amsterdam,Amsterdam,The Netherlands;2.Dept. Informatics and Mathematical Modelling,Technical University of Denmark,Kgs. Lyngby,Denmark |
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Abstract: | 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. |
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