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Correlation functions in the G/M/1 system

Published online by Cambridge University Press:  01 July 2016

S. K. Srinivasan  and
C. Chudalaimuthu Pillai
S. K. Srinivasan*
Affiliation:
Indian Institute of Technology, Madras
C. Chudalaimuthu Pillai*
Affiliation:
Indian Institute of Technology, Madras
*
∗Postal address: Department of Mathematics, Indian Institute of Technology, Madras-600 036, India.
∗Postal address: Department of Mathematics, Indian Institute of Technology, Madras-600 036, India.
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Abstract

The G/G/1 queueing system is studied by means of the regeneration point method, exploiting the concept of busy cycles. Recurrence relations are set-up for the distribution of the queue length at the arrival epochs. The same method is used to obtain the correlation structure of arrivals and departures for the G/M/1 queue.

Keywords

REGENERATION POINTBUSY CYCLEQUEUE LENGTHPRODUCT DENSITYCORRELATION FUNCTIONPOWER SPECTRUM
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 2 , June 1980 , pp. 530 - 540
Copyright
Copyright © Applied Probability Trust 1980 

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References

Burke, P. J. (1956) The output of queueing systems. Operat. Res. 4, 699–704.Google Scholar
Cohen, J. W. (1969) The Single Server Queue. North Holland, Amsterdam.Google Scholar
Conolly, B. (1975) Lecture Notes in Queueing Systems. Ellis Horwood Ltd., Chichester.Google Scholar
Craven, B. D. (1965) Serial dependence of a Markov process. J. Austral. Math. Soc. 3, 503–512.CrossRefGoogle Scholar
Daley, D. J. (1968a) The correlation structure of the output process of some single server queueing systems. Ann. Math. Statist. 39, 1007–1019.Google Scholar
Daley, D. J. (1968b) The serial correlation coefficients of waiting times in a stationary single server queue. J. Austral. Math. Soc. 8, 683–699.Google Scholar
Pakes, A. G. (1971) The serial correlation coefficients of waiting times in the stationary GI/M/1 queue. Ann. Math. Statist. 42, 1727–1734.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
Ramakrishnan, A. (1950) Stochastic processes relating to particles distributed in an infinity of states. Proc. Camb. Phil. Soc. 46, 595–602.Google Scholar
Reynolds, J. F. (1967) On the auto-correlation function of a queue. Proc. A.F.I.R.O. Congress, Nancy, May 1967. Google Scholar
Reynolds, J. F. (1972) On linearly regressive processes. J. Appl. Prob. 9, 208–213.CrossRefGoogle Scholar
Reynolds, J. F. (1975) The covariance structure of queues and related processes—A survey of recent work. Adv. Appl. Prob. 7, 383–415.CrossRefGoogle Scholar
Srinivasan, S. K. (1974) Stochastic Point Processes and their Applications. Griffin, London.Google Scholar
Srinivasan, S. K. and Subramanian, R. (1969) Queueing theory and imbedded renewal processes. J. Math. Phys. Sci. 3, 221–244.Google Scholar
Srinivasan, S. K., Subramanian, R. and Vasudevan, R. (1972) Correlation functions in queueing theory. J. Appl. Prob. 9, 604–616.Google Scholar