Approximation of the queue-length distribution of an M/GI/s queue by the basic equations

Masakiyo Miyazawa

42 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

We give a unified way of obtaining approximation formulas for the steady-state distribution of the queue length in theM/GI/squeue. The approximations of Hokstad (1978) and Case A of Tijms et al. (1981) are derived again. The main interest of this paper is in considering the theoretical meaning of the assumptions given in the literature. Having done this, we derive new approximation formulas. Our discussion is based on one version of the steady-state equations, called the basic equations in this paper. The basic equations are derived forM/GI/s/kwith finite and infinitek.Similar approximations are possible forM/GI/s/k(k< +∞).

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References

1978Approximations in finite-capacity multi-server queues by Poisson arrivals 1978Approximations for the M/G/m Queue 1979Approximations of the Mean Waiting Time in an M/G/s Queueing System 1981Approximations for the steady-state probabilities in theM/G/cqueue 1983Diffusion Approximation for an M / G / m Queue 1979Heavy traffic theory for queues with several servers. II 1971A relation between stationary queue and waiting time distributions 1983The derivation of invariance relations in complex queueing systems with stationary inputs

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2008BALKING AND RENEGING IN M/G/s SYSTEMS EXACT ANALYSIS AND APPROXIMATIONS 1995Approximations for the delay probability in the M/G/s queue 2005A Two-Moment Approximation for the GI/G/c Queue with Finite Capacity 2006An algorithm for repairable item inventory system with depot spares and general repair time distribution

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