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Transient solution to the many-server Poisson queue: a simple approach

Published online by Cambridge University Press:  14 July 2016

P. R. Parthasarathy  and
M. Sharafali
P. R. Parthasarathy*
Affiliation:
Indian Institute of Technology, Madras
M. Sharafali*
Affiliation:
Government Arts College, Nandanam, Madras
*
∗Postal address: Department of Mathematics, Indian Institute of Technology, Madras 600 036, India.
∗∗Postal address: Department of Mathematics, Government Arts College, Nandanam, Madras 600 035, India.
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Abstract

An elegant time-dependent solution for the number in the M/M/c queueing system is derived in a direct way.

Keywords

SYSTEM SIZEALMOST LOWER TRIANGLESSTEADY-STATE PROBABILITIESBUSY PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 584 - 594
Copyright
Copyright © Applied Probability Trust 1989 

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References

Chaudhury, M. L. and Templeton, J. G. C. (1973) A note on the distribution of a busy period for M/M/c queueing system, Math. Operationsforsch. Statist. 4, 75–79.CrossRefGoogle Scholar
Ledermann, W. and Reuter, G. E. H. (1954) Spectral theory for the differential equations of simple birth and death processes, Phil. Trans. R. Soc. London 246, 321–369.Google Scholar
Parthasarathy, P. R. (1987) A transient solution to a M/M/1 queue — a simple approach. Adv. Appl. Prob. 19, 997–998.Google Scholar
Raju, S. N. and Bhat, U. N. (1982) A computationally oriented analysis of the G/M/1 queue. Opsearsh 19, 67–83.Google Scholar
Saaty, T. L. (1960) Time-dependent solution of the many server Poisson queue. Operat. Res. 8, 755–771.Google Scholar
Saaty, T. L. (1961) Elements of Queueing Theory, with Applications. McGraw-Hill, New York.Google Scholar