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The workload in the M/G/1 queue with work removal. (English) Zbl 1095.60510

Summary: We consider an M/G/1 queue with the special feature of additional negative customers, who arrive according to a Poisson process. Negative customers require no service, but at their arrival a stochastic amount of work is instantaneously removed from the system. We show that the workload distribution in this M/G/1 queue with negative customers equals the waiting time distribution in a GI/G/1 queue with ordinary customers only; the effect of the negative customers is incorporated in the new arrival process.

MSC:

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

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