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

  • R. Schassberger (a1)

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.

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Postal address: Institut für Mathematische Stochastik, Technische Universität Braunschweig, Postfach 3329, D-3300 Braunschweig, W. Germany.

References

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[1] Baccelli, F. and Bremaud, P. (1987) Palm Probabilities and Stationary Queues. Lecture Notes in Statistics 41, Springer-Verlag, Berlin.
[2] Cohen, J. W. (1982) The Single Server Queue. North-Holland, Amsterdam.
[3] Flipo, D. (1981) Comparaison des disciplines de service des files d'attente G/G/l. Ann. Inst. H. Poincaré XVII, 191212.
[4] Kallenberg, O. (1976) Random Measures. Academic Press, London.
[5] Schassberger, R. (1973) Warteschlangen. Springer-Verlag, Wien.
[6] Schassberger, R. (1984) A new approach to the M/G/1 processor sharing queue. Adv. Appl. Prob. 16, 202213.
[7] Schrage, L. E. (1968) A proof of the optimality of the shortest remaining processing time discipline. Operat. Res. 16, 687690.
[8] Schrage, L. E. and Miller, L. W. (1966) The queue M/G/1 with the shortest remaining processing time discipline. Operat. Res. 14, 670684.

Keywords

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

  • R. Schassberger (a1)

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