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The single-server queue with random service output

Published online by Cambridge University Press:  14 July 2016

O. J. Boxma
O. J. Boxma*
Affiliation:
Mathematical Institute, University of Utrecht
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Abstract

In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate.

Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.

Keywords

QUEUEINGPROCESSES WITH STATIONARY INDEPENDENT INCREMENTSINFINITE DAMSPOLLACZEK INTEGRAL EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 763 - 778
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Boxma, O. J. (1974) The single-server queue with varying service intensity. Master's Thesis, Delft University of Technology, Delft (In Dutch).Google Scholar
[2] Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[3] Cohen, J. W. (1974) Regenerative processes and stationary distributions in queueing theory. Report, Mathematical Institute, Utrecht.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and its Applications , Vol. II. Wiley, New York.Google Scholar
[5] Gani, J. and Pyke, R. (1960) The content of a dam as the supremum of an infinitely divisible process. J. Math. Mech. 9, 639–651.Google Scholar
[6] Grinstein, J. and Rubinovitch, M. (1974) Queues with random output — the case of Poisson arrivals. J. Appl. Prob. 11, 771–784.CrossRefGoogle Scholar
[7] Prabhu, N. U. and Rubinovitch, M. (1971) On a continuous time extension of Feller's lemma. Z. Wahrscheinlichkeitsth. 17, 220–226.Google Scholar
[8] Stidham, S. (1972) Regenerative processes in the theory of queues, with applications to the alternating-priority queue. Adv. Appl. Prob. 4, 542–577.CrossRefGoogle Scholar
[9] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar