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On the busy period distribution of the M/G/2 queueing system

Published online by Cambridge University Press:  14 July 2016

Douglas P. Wiens*
Affiliation:
University of Alberta
*
Postal address: Department of Statistics and Applied Probability, University of Alberta, Edmonton, Canada T6G 2G1.

Abstract

Equations are derived for the distribution of the busy period of the GI/G/2 queue. The equations are analyzed for the M/G/2 queue, assuming that the service times have a density which is an arbitrary linear combination, with respect to both the number of stages and the rate parameter, of Erlang densities. The coefficients may be negative. Special cases and examples are studied.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada.

References

Bhat, U. N. (1966) The queue GI/M/2 with service rate depending on the number of busy servers. Ann. Inst. Statist. Math. 18, 211221.CrossRefGoogle Scholar
Cohen, J. W. (1982) On the M/G/2 queueing model. Stoch. Proc. Appl. 12, 231248.CrossRefGoogle Scholar
De Smit, J. H. A. (1973a) Some generai results for many server queues. Adv. Appl. Prob. 5, 153169.CrossRefGoogle Scholar
De Smit, J. H. A. (1973b) On the many server queue with exponential service times. Adv. Appl. Prob. 5, 170182.CrossRefGoogle Scholar
De Smith, J. H. A. (1983) The queue GI/M/s with customers of different types or the queue GI/Hm/s. Adv. Appl. Prob. 15, 392419.CrossRefGoogle Scholar
Heffer, J. C. (1969) Steady-state solution of the M/Ek/c(8, FIFO) queueing system. CORS J. 7, 1630.Google Scholar
Hokstad, P. (1978) Approximations for the M/G/m queue. Operat. Res. 26, 511523.CrossRefGoogle Scholar
Karlin, S. and Mcgregor, J. (1958) Many server queueing processes with Poisson input and exponential service times. Pacific J. Math. 8, 87118.CrossRefGoogle Scholar
Pollaczek, F. (1961) Théorie Analytique des Problèmes Stochastiques Relatifs à un Groupe de Lignes Téléphoniques avec Dispositif d'Attente. Gauthier, Paris.Google Scholar
Tijms, H. C., Van Horn, M. H. and Federgruen, A. (1981) Approximations for the steady-state probabilities in the M/G/c queue. Adv. Appl. Prob. 13, 186206.CrossRefGoogle Scholar
Wiens, D. P. (1987) On the busy period distribution of the M/G/2 queueing system. University of Alberta, Department of Statistics and Applied Probability, Technical Report 87.03.Google Scholar