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A transient solution to an M/M/1 queue: a simple approach

Published online by Cambridge University Press:  01 July 2016

P. R. Parthasarathy*
Affiliation:
Indian Institute of Technology, Madras
*
Postal address: Department of Mathematics, Indian Institute of Technology, Madras 600–036, India.
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Abstract

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A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1987 

References

Champernowne, D. G. (1956) An elementary method of solution of the queueing problem with a single server and continuous parameter. J. R. Statist. Soc. B 18, 125128.Google Scholar
Conolly, B. W. (1958) A difference equation technique applied to a simple queue with arbitrary arrival interval distribution. J. R. Statist. Soc. B 21, 168175.Google Scholar
Karlin, S. and Mcgregor, J. (1959) Many server queueing processes with Poisson input and exponential service times. Pacific J. Math. 8, 87118.CrossRefGoogle Scholar
Ledermann, W. and Reuter, , (1956) Spectral theory for the differential equations of simple birth and death equations of simple birth and death process. Phil. Trans. R. Soc. London A 246, 321369.Google Scholar
Pegden, C. D. and Rosenshine, M. (1982) Some new results for the M/M/1 queue. Management Sci. 28, 821828.CrossRefGoogle Scholar