Queueing Systems with Service Interruptions

Awi Federgruen · Linda Green

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

In many queueing systems, the service process is subject to interruptions resulting from breakdowns, scheduled off-periods or the arrival of customers with preemptive priority. We consider a single server, first-come, first-served queueing system that alternates between periods when service is available (“on-periods”) and periods when the server is unavailable (“off-periods”). We consider the case of Poisson arrivals and general service, on- and off-time distributions and derive bounds and approximations for the mean waiting time, probability of delay and steady-state distribution of the number in system. These results are exact for the case of exponentially distributed on-times. Computational results are reported.

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References

1977Fundamentals of Queueing Theory.1984Matrix-Geometric Solutions to Stochastic Models 1975Theory, Volume 1, Queueing Systems 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1982Approximating a Point Process by a Renewal Process, I: Two Basic Methods 1962A Waiting Line with Interrupted Service, Including Priorities 1975Utilization of Idle Time in an M / G /1 Queueing System 1958Queuing with Preemptive Priorities or with Breakdown

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