The Finite Capacity GI/M/1 Queue with Server Vacations

Fikri Karaesmen · Surendra M. Gupta

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

Abstract

We consider the GI/M/1/K queue where the server takes exponentially distributed vacations when there are no customers left to serve in the queue. We obtain the queue length distribution at arrival epochs and random epochs for the multiple vacation case. We present heuristic algorithms to compute the blocking probability for this system. Several numerical examples are presented to analyze the behaviour of the blocking probability and to test the performance of the heuristics.

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References

1984Matrix-Geometric Solutions to Stochastic Models 1982Approximating a Point Process by a Renewal Process, I: Two Basic Methods 1984Approximating a Point Process by a Renewal Process, II: Superposition Arrival Processes to Queues 1997Machine interference problem with warm spares, server vacations and exhaustive service 1989Blocking Probability for M/G/1 Vacation Systems with Occupancy Level Dependent Schedules 1991Finite capacity vacation models with non-renewal input 1980The M/G/1 Finite Capacity Queue with Delays 1992Heuristics for Finite-Buffer Queues

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2014Optimization analysis of the machine repair problem with multiple vacations and working breakdowns 2010Optimal management of remanufacturing systems with server vacations 2010Analysis of a discrete-time GI/Geo/1/N queue with multiple working vacations 2013Profit optimisation of the multiple-vacation machine repair problem using particle swarm optimisation 2006Analysis of finite capacity discrete-time GI/Geo/1 queueing system with multiple vacations

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