Dynamic server assignment in a two-queue model |
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Institution: | 1. CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;2. Tilburg University, Faculty of Economics, P.O. Box 90153, 5000 LE Tilburg, The Netherlands |
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Abstract: | We consider a polling model of two M/G/1 queues, served by a single server. The service policy for this polling model is of threshold type. Service at queue 1 is exhaustive. Service at queue 2 is exhaustive unless the size of queue 1 reaches some level T during a service at queue 2; in the latter case the server switches to queue 1 at the end of that service. Both zero- and nonzero switchover times are considered. We derive exact expressions for the joint queue length distribution at customer departure epochs, and for the steady-state queue-length and sojourn time distributions. In addition, we supply a simple and very accurate approximation for the mean queue lengths, which is suitable for optimization purposes. |
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