Exponential Queues with Server Vacations

B. Vinod

36 citations0/0 files storedJournal of the Operational Research Society

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

Abstract

In this paper, we analyse a queueing system where the server may take a vacation. The customers arrive at the service facility according to a Poisson process, and are served if the server is available (not on vacation). We consider two models: when the server vacation cycle is independent of and dependent on the number of customers in the system. The infinitesimal generators of the underlying Markov processes have a block tri-diagonal structure, and we provide a matrix geometric solution. When the vacation cycle is independent of the customer queue length, we present a simple load-dependent approximation that is fairly accurate.

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References

1977Fundamentals of Queueing Theory.1984Matrix-Geometric Solutions to Stochastic Models 1978Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector 1981Computation of Steady-State Probabilities for M/M/1 Priority Queues 1969The Solution Of Quasi Birth And Death Processes Arising From Multiple Access Computer Systems.1977The M/M/1 Queue with Randomly Varying Arrival and Service Rates.1982Explicit Steady-State Solutions to Some Elementary Queueing Models

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