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The non-renewal nature of the quasi-input process in the M/G/1/∞ queue

Published online by Cambridge University Press:  14 July 2016

Jeffrey J. Hunter
Jeffrey J. Hunter*
Affiliation:
University of Auckland
*
∗Postal address: Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

Falin (1984) examined the quasi-input process (the flow of service starting times) in the M/G/1/∞ queue and raised the question as to whether this process is a renewal process. We show that, except in the trivial case of instantaneous service, the quasi-input process is never renewal.

Keywords

QUEUEING THEORYRANDOM FLOWSMARKOV RENEWAL PROCESSESRENEWAL PROCESSESSTATIONARY DISTRIBUTIONS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 803 - 811
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Burke, P. J. (1956) The output of a queueing system. Operat. Res. 4, 699–704.Google Scholar
[2] Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
[3] Daley, D. J. and Shanbhag, D. N. (1975) Independent inter-departure times in M/G/1/N queues. J.R. Statist. Soc. B37, 259–263.Google Scholar
[4] Disney, R. L. and De Morais, P. R. (1976) Covariance properties for the departure process of M/Ek/1/N queues. AIIE Trans. 8, 169–175.CrossRefGoogle Scholar
[5] Disney, R. L., Farrell, R. L. and De Morais, P. R. (1973) A characterisation of M/G/1 queues with renewal departure processes. Management Sci. 19, 1222–1228.Google Scholar
[6] Falin, G. I. (1984) Quasi-input process in the M/G/1/8 queue. Adv. Appl. Prob. 16, 695–696.Google Scholar
[7] Simon, B. (1979) Equivalent Markov-renewal processes. Technical Report VTR 8001, Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg.Google Scholar
[8] Simon, B. and Disney, R. L. (1984) Markov renewal processes and renewal processes: some conditions for equivalence. NZ Operat. Res. 12, 19–29.Google Scholar