On a single server queue with negative arrivals and request repeated

J.R. Artalejo · Antonio Gómez‐Corral

34 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.

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References

1963Introduction to the Theory of Queues.1997Retrial Queues 1991Product-form queueing networks with negative and positive customers 1990A survey of retrial queues 1987A survey on retrial queues 1989A survey on retrial queues 1990Numerical investigation of a multiserver retrial model 1994G-networks: a unifying model for neural and queueing networks

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