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Pseudo-conservation laws in cyclic-service systems

Published online by Cambridge University Press:  14 July 2016

O. J. Boxma  and
W. P. Groenendijk
O. J. Boxma
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
W. P. Groenendijk*
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
*
∗Postal address: Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands.
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Abstract

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a ‘pseudo-conservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.

Keywords

QUEUEING SYSTEMSWITCH-OVER TIMESMEAN WAITING TIMECONSERVATION LAW
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 949 - 964
Copyright
Copyright © Applied Probability Trust 1987 

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References

[1] Boxma, O. J. (1984) Two symmetric queues with alternating service and switching times. In Performance '84 , ed. Gelenbe, E., North-Holland, Amsterdam, 409–431.Google Scholar
[2] Boxma, O. J. (1986) Models of two queues: a few new views. In Teletraffic Analysis and Computer Performance Evaluation , eds. Boxma, O. J., Cohen, J. W. and Tijms, H. C., North-Holland, Amsterdam, 75–98.Google Scholar
[3] Boxma, O. J. and Meister, B. (1986) Waiting-time approximations for cyclic-service systems with switch-over times. Performance Eval. Rev. 14, 254–262.CrossRefGoogle Scholar
[4] Bux, W. and Truong, H. L. (1983) Mean-delay approximations for cyclic-service queueing systems. Performance Eval. 3, 187–196.CrossRefGoogle Scholar
[5] Cohen, J. W. (1987) A two-queue model with semi-exhaustive alternating service. Performance '87. To appear.Google Scholar
[6] Ferguson, M. J. and Aminetzah, Y. J. (1985) Exact results for nonsymmetric token ring systems. I.E.E.E. Trans. Communications 33, 223–231.CrossRefGoogle Scholar
[7] Fuhrmann, S. W. (1985) Symmetric queues served in cyclic order. Operat. Res. Letters 4, 139–144.Google Scholar
[8] Fuhrmann, S. W. and Cooper, R. B. (1985) Stochastic decompositions in the M/G/1 queue with generalised vacations. Operat. Res. 33, 1117–1129.Google Scholar
[9] Kleinrock, L. (1976) Queueing Systems , Vol. 2. Wiley, New York.Google Scholar
[10] Ott, T. J. (1984) On the M/G/1 queue with additional inputs. J. Appl. Prob. 21, 129–142.CrossRefGoogle Scholar
[11] Schrage, L. (1970) An alternative proof of a conservation law for the queue G/G/1. Operat. Res. 18, 185–187.Google Scholar
[12] Takagi, H. (1984) Mean message waiting time in a symmetric polling system. In Performance '84 , ed. Gelenbe, E., North-Holland, Amsterdam, 293–302.Google Scholar
[13] Takagi, H. (1986) Analysis of Polling Systems. The MIT Press, Cambridge, Mass.Google Scholar
[14] Watson, K. S. (1984) Performance evaluation of cyclic service strategies — a survey. In Performance '84 , ed. Gelenbe, E., North-Holland, Amsterdam, 521–533.Google Scholar
[15] Wolff, R. W. (1982) Poisson arrivals see time averages. Operat. Res. 30, 223–231.CrossRefGoogle Scholar