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An upper bound on the performance of queues with returning customers. (English) Zbl 0626.60092

The authors consider a stationary queueing system with Poisson arrival and exponential service time depending on the queue length. They discuss the following orbit system: Customers who cannot be served immediately join the queue once again with probability \(r_ 1\) for the first time and \(r_ 2\) for further times. They derive properties of the expected number of reentering customers and bounds on the performance of geometric \((r_ 2=r_ 1<1)\) and infinite \((r_ 2=1)\) orbit systems.
Reviewer: W.Schlee-Kossler

MSC:

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