Abstract
In this paper, we present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite numberS of waiting places and a batch service capacityb. A service period is initialized when a service starting thresholda of waiting customers has been reached. The model is denoted accordingly byM/G [a,b]/1−S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.
Similar content being viewed by others
References
M.F. Neuts, A general class of bulk queues with Poisson input, Ann. Math. Stat. 38 (1967) 759–770.
M.F. Neuts, Queues solvable without Rouchés, Oper. Res. 27 (1979) 767–781.
M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models — An Algorithmic Approach (Johns Hopkins University Press, Baltimore, 1981).
M.L. Chaudhry, B.R. Madill and G. Brié, Computational Analysis of steady-state probabilities ofM/G a,b/1 and related nonbulk queues, Queueing Systems 2 (1987) 93–114.
N.T.J. Bailey, On queueing process with bulk service, J. Roy. Stat. Soc. B16 (1954) 80–87.
F. Downton, Waiting time in bulk service queues, J. Roy. Stat. Soc. B17 (1955) 256–261.
B.W. Gnedenko and D. König,Handbuch der Bedienungstheorie II (Akademie-Verlag Berlin, 1984) pp. 203–204.
D. Gross and C.M. Harris, Fundamentals of queueing theory (Wiley, New York, 1985) pp. 163–170.
P.J. Kuehn, Approximate analysis of general queueing networks by decomposition, IEEE Trans. Comm. COM-27 (1979) 113–126.
P. Tran-Gia and T. Raith, Performance analysis of finite capacity polling systems with nonexhaustive service, Performance Evaluation 9 (1988) 1–16.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gold, H., Tran-Gia, P. Performance analysis of a batch service queue arising out of manufacturing system modelling. Queueing Syst 14, 413–426 (1993). https://doi.org/10.1007/BF01158876
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01158876