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CONVEXITY IN TANDEM QUEUES

Published online by Cambridge University Press:  22 January 2004

Ger Koole
Ger Koole
Affiliation:
Department of Mathematics, Vrije Universiteit Amsterdam, The Netherlands, E-mail: koole@cs.vu.nl
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Abstract

We derive convexity results and related properties for the value functions of tandem queuing systems. The results for standard multiserver queues are new. For completeness, we also prove and generalize existing results on tandems of controllable queues. The results can be used to compare queuing systems. This is done for systems with and without batch arrivals and for systems with different numbers of on–off sources.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 1 , January 2004 , pp. 13 - 31
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Altman, E., Gaujal, B., & Hordijk, A. (2000). Multimodularity, convexity and optimization properties. Mathematics of Operations Research 25: 324–347.Google Scholar
Altman, E. Jiménez, T.,, &Koole, G.M. (2001). On the comparison of queueing systems with their fluid limits. Probability in the Engineering and Informational Sciences 15: 165–178.Google Scholar
Altman, E. & Koole, G.M. (1998). On submodular value functions and complex dynamic programming. Stochastic Models 14: 1051–1072.Google Scholar
Asmussen, S. & Koole, G.M. (1993). Marked point processes as limits of Markovian arrival streams. Journal of Applied Probability 30: 365–372.Google Scholar
Chang, C.S., Chao, X., Pinedo, M., & Weber, R.R. (1992). On the optimality of LEPT and cμ-rules for machines in parallel. Journal of Applied Probability 29: 667–681.Google Scholar
Hajek, B. (1985). Extremal splitting of point processes. Mathematics of Operations Research 10: 543–556.Google Scholar
Hordijk, A. & Koole, G.M. (1992). On the assignment of customers to parallel queues. Probability in the Engineering and Informational Sciences 6: 495–511.Google Scholar
Koole, G.M. (1998). Structural results for the control of queueing systems using event-based dynamic programming. Queueing Systems 30: 323–339.Google Scholar
Koole, G.M. & Liu, Z. (1997). Stochastic bounds for queueing systems with multiple on–off sources. Probability in the Engineering and Informational Sciences 12: 25–48.Google Scholar
Lippman, S.A. (1975). Applying a new device in the optimization of exponential queueing systems. Operations Research 23: 687–710.Google Scholar
Liyanage, L. & Shanthikumar, J.G. (1992). Second-order properties of single-stage queueing systems. In U.N. Bhat and I.S. Basawa (eds.), Queueing and related models. Oxford: Oxford University Press, pp. 129–160.
Meester, L.E. (1990). Contributions to the theory and applications of stochastic convexity. Ph.D. thesis, University of California at Berkeley.
Puterman, M.L. (1994). Markov decision processes. New York: Wiley.
Shaked, M. & Shanthikumar, J.G. (1990). Parametric stochastic convexity and concavity of stochastic processes. Annals of the Institute of Statistical Mathematics 42: 509–531.Google Scholar
Stidham, S., Jr. & Weber, R.R. (1993). A survey of Markov decision models for control of networks of queues. Queueing Systems 13: 291–314.Google Scholar
Weber, R.R. & Stidham, S., Jr. (1987). Optimal control of service rates in networks of queues. Advances in Applied Probability 19: 202–218.Google Scholar