Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T09:46:50.190Z Has data issue: false hasContentIssue false
  • English
  • Français

The Power-Series Algorithm for Polling Systems with Time Limits

Published online by Cambridge University Press:  27 July 2009

J. P. C. Blanc
J. P. C. Blanc
Affiliation:
Tilburg University, Center for Economic Research, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with evaluation and optimization of polling systems with time limits. Performance measures are evaluated with the power-series algorithm, a flexible technique for computing performance measures for multiqueue systems. The constant time limits are approximated by Erlang distributed variables. The algorithm is extended to compute derivatives of performance measures. This allows for optimization of cost functions with respect to the mean values of the time limits by gradient methods. Several properties of the optimal time limits are revealed by the numerical solution of various optimization problems.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 2 , April 1998 , pp. 221 - 237
Copyright
Copyright © Cambridge University Press 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Baker, J.E. & Rubin, I. (1987). Polling with a general-service order table. IEEE Transactions on Communications 35: 283–288.CrossRefGoogle Scholar
2.Blanc, J.P.C. (1992). Performance evaluation of polling systems by means of the power-series algorithm. Annals of Operations Research 35: 155–186.CrossRefGoogle Scholar
3.Blanc, J.P.C. (1993). Performance analysis and optimization with the power-series algorithm. In Donatiello, L. & Nelson, R. (eds.), Performance evaluation of computer and communication systems. Berlin: Springer-Verlag, pp. 53–80.CrossRefGoogle Scholar
4.Blanc, J.P.C. (1996). Optimization of periodic polling systems with non-preemptive, time-limited service. CentER Discussion paper 9663, Tilburg University.Google Scholar
5.Blanc, J.P.C. & Van der Mei, R.D. (1995). Optimization of polling systems with Bernoulli schedules. Performance Evaluation 22: 139–158.CrossRefGoogle Scholar
6.Blanc, J.P.C. & Van der Mei, R.D. (1996). Computation of derivatives by means of the power-series algorithm. INFORMS Journal on Computing 8: 45–54.CrossRefGoogle Scholar
7.Borst, S.C., Boxma, O.J., & Levy, H. (1995). The use of service limits for efficient operation of multistation single-medium communication systems. IEEEJACM Transactions on Networking 3: 602–612.CrossRefGoogle Scholar
8.Coffman, E. Jr, Mitrani, I., & Fayolle, G. (1988). Two queues with alternating service periods. In Courtois, P.-J. & Latouche, G. (eds.), Performance '87. Amsterdam: North-Holland, pp. 227–239.Google Scholar
9.Fricker, C. & Jaïbi, M.R. (1994). Monotonicity and stability for periodic polling models. Queueing Systems 15: 211–238.CrossRefGoogle Scholar
10.Leung, K.K. (1994). Cyclic-service systems with nonpreemptive, time-limited service. IEEE Transactions on Communications 42: 2521–2524.CrossRefGoogle Scholar
11.Resing, J.A.C. (1993). Polling systems and multitype branching processes. Queueing Systems 13: 409–426.CrossRefGoogle Scholar
12.Takagi, H. (1986). Analysis of polling systems. Cambridge, MA: The MIT Press.Google Scholar
13.Van den Hout, W.B. & Blanc, J.P.C. (1995). The power-series algorithm for Markovian queueing networks. In Stewart, W.J. (ed.), Computations with Markov chains. Boston: Kluwer, pp. 321–338.CrossRefGoogle Scholar