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Some comments on the simple queue

Published online by Cambridge University Press:  01 July 2016

N. Ravichandran  and
A. Gravey
N. Ravichandran*
Affiliation:
Indian Institute of Management, Ahmedabad
A. Gravey*
Affiliation:
Centre National d'Etudes des Télécommunications
*
∗Postal address: Indian Institute of Management, Vastrapur, Ahmedabad-380 015, India.
∗∗ Postal address: CNET/EVP, BP 40, 22301 Lannion Cedex, France.
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Abstract

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This communication provides an explicit expression for the joint probability of exactly i arrivals and j service completions in a duration of length t for the simple queue. The impossibility of a similar expression for the queue-length distribution is explained.

Keywords

MARKOVIAN QUEUES: BUSY PERIOD: ARRIVAL PROCESS: DEPARTURE PROCESS: QUEUE-LENGTH DISTRIBUTION
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 933 - 935
Copyright
Copyright © Applied Probability Trust 1984 

References

[1] Cooper, R. B. (1972) Introduction to Queuing Theory. Macmillan, London.Google Scholar
[2] Feller, W. (1968) An Introduction to Probability Theory and its Applications. Wiley, New York.Google Scholar
[3] Pegden, C. D. and Rosenshine, M. (1982) Some new results for the M/M/l queue. Management Sci. 28, 821–828.Google Scholar