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The steady-state appearance of the M/G/1 queue under the discipline of shortest remaining processing time

Published online by Cambridge University Press:  01 July 2016

R. Schassberger
R. Schassberger*
Affiliation:
Technische Universität Braunschweig
*
∗Postal address: Institut für Mathematische Stochastik, Technische Universität Braunschweig, Postfach 3329, D-3300 Braunschweig, W. Germany.
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Abstract

For the queue M/G/1 under the discipline SRPT (shortest remaining processing time) the system state is taken to be the counting measure N which assigns to each Borel set A of R+ the number N(A) of customers present with residual service times taking values in A. A steady-state analysis is given for the corresponding Laplace functional. As a corollary, the steady-state number in queue is obtained in terms of its generating function.

Keywords

QUEUE DISCIPLINELAPLACE FUNCTIONALS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 456 - 479
Copyright
Copyright © Applied Probability Trust 1990 

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References

[1] Baccelli, F. and Bremaud, P. (1987) Palm Probabilities and Stationary Queues. Lecture Notes in Statistics 41, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[2] Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[3] Flipo, D. (1981) Comparaison des disciplines de service des files d'attente G/G/l. Ann. Inst. H. Poincaré XVII, 191–212.Google Scholar
[4] Kallenberg, O. (1976) Random Measures. Academic Press, London.Google Scholar
[5] Schassberger, R. (1973) Warteschlangen. Springer-Verlag, Wien.CrossRefGoogle Scholar
[6] Schassberger, R. (1984) A new approach to the M/G/1 processor sharing queue. Adv. Appl. Prob. 16, 202–213.CrossRefGoogle Scholar
[7] Schrage, L. E. (1968) A proof of the optimality of the shortest remaining processing time discipline. Operat. Res. 16, 687–690.CrossRefGoogle Scholar
[8] Schrage, L. E. and Miller, L. W. (1966) The queue M/G/1 with the shortest remaining processing time discipline. Operat. Res. 14, 670–684.CrossRefGoogle Scholar