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The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

Published online by Cambridge University Press:  14 July 2016

Do Le Minh
Do Le Minh*
Affiliation:
The New South Wales Institute of Technology
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Abstract

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution.

All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

Keywords

QUEUEINGDISCRETE-TIMETIME-INHOMOGENEOUSEMPTINESSVIRTUAL WAITING TIMEDEPARTURE PROCESSEXPECTED WAITING TIMEEXPECTED NUMBER IN THE SYSTEMRESIDUAL SERVICE TIMEPERIODIC ARRIVAL FUNCTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 590 - 601
Copyright
Copyright © Applied Probability Trust 1978 

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References

Bagchi, T. P. and Templeton, J. G. C. (1972) Numerical Methods in Markov Chains and Bulk Queues. Lecture Notes in Economics and Mathematical Systems No. 72, Springer-Verlag, New York.Google Scholar
Brockmeyer, E., HalstrøM, H. L. and Jensen, A. (1960) The Life and Works of A. K. Erlang. Acta Polytechnica Scandinavica, Mathematics and Computing Machinery Series No. 6, Copenhagen.Google Scholar
Dafermos, S. C. and Neuts, M. F. (1971) A single server queue in discrete time. Cahiers Centre Études Recherche Opér. 13, 23–40.Google Scholar
Hasofer, A. M. (1964) On the single-server queue with non-homogeneous Poisson input and general service time. J. Appl. Prob. 1, 369–384.Google Scholar
Heimann, D. and Neuts, M. F. (1973) The single server queue in discrete time-Numerical analysis IV. Naval Res. Logist. Quart. 20, 753–766.CrossRefGoogle Scholar
Keilson, J. and Kooharian, A. (1960) On time dependent queuing processes. Ann. Math. Statist. 31, 104–112.Google Scholar
Keilson, J. and Kooharian, A. (1962) On the general time dependent queue with a single server. Ann. Math. Statist. 33, 767–791.CrossRefGoogle Scholar
Kendall, D. G. (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math. Statist. 24, 338–354.Google Scholar
Klimko, E. M. and Neuts, M. F. (1973) The single server queue in discrete time-Numerical analysis II. Naval Res. Logist. Quart. 20, 305–319.Google Scholar
Leese, E. L. and Boyd, D. W. (1966) Numerical methods of determining the transient behaviour of queues with variable arriving rates. J. Canad. Opns Res. Soc. 4, 1–13.Google Scholar
Minh, D. L. (1977) A discrete time, single server queue from a finite population. Management Sci. 23, 756–767.CrossRefGoogle Scholar
Minh, D. L. and Blunden, W. R. (1977) Time-inhomogeneous signalized intersection as a discrete infinite dam. Proc. Seventh Internat. Symp. Transportation and Traffic Theory, ed. Sasaki, T. and Yamaoka, T. Institute of Systems Science Research, Kyoto, 271–280.Google Scholar
Moore, S. C. (1975) Approximating the behaviour of non-stationary single server queues. Opns Res. 23, 1011–1033.Google Scholar
Takács, L. (1955) Investigation of waiting time problems by reduction to Markov processes. Acta Math. Hungar. 6, 101–129.Google Scholar
Yevdokimova, G. S. (1974) The distribution of waiting time in the case of a periodic input flow. Engineering Cybernetics 12, 81–85.Google Scholar