Abstract
In this paper we will consider two-person zero-sum games and derive a general approach for solving them. We apply this approach to a queueing problem. In section 1 we will introduce the model and formulate the Key-theorem. In section 2 we develop the theory that we will use in section 3 to prove the Key-theorem. This includes a general and useful result in Lemma 2.1 on the sufficiency of stationary policies.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Altman E (1994) A Markov game approach for optimal routing into a queueing network. Technical Report 2178, INRIA, Submitted
Altman E, Hordijk A (1994) Zero-sum Markov games and worst-case optimal control of queueing systems. To appear in Questa
Altman E, Hordijk A, Spieksma F (1994) Contraction conditions for average and α-discount optimality in countable state markov games with unbounded rewards. Technical Report TW-93-16, Leiden University, Submitted to MOR
Hajek B (1984) Optimal control of two interacting service stations. IEEE Transactions on Automatic Control 29(6):491–499
Hernández-Lerma O, Lasserre JB (1994) Lineaire programming and Markov control processes. SIAM Journal on Control and Optimization 32(2):480–500
Kurano M (1989) The existence of a minimum pair of state and policy for Markov decision processes under the hypothesis of Doeblin. SIAM Journal on Control and Optimisation 27:296–307
Lasserre JB (1994) Average optimal stationary policies and linear programming in countable space Markov decision processes. Journal of mathematical analysis and applications 183:233–249.
Lippman SA (1975) Appling a new device in the optimization of exponential queueing systems. Operations Research 23:687–710
Raghavan TES, Tijs SH, Vrieze OJ (1985) On stochastic games with additive reward and transition structure. Journal of Optimization Theory and Applications 47(4):451–464
Sennott LI (1989) Average cost optimal stationary policies in infinite state Markov decision processes with unbounded costs. Operations Research 37(4):626–633
Sennott LI (1994) Zero-sum stochastic games with unbounded costs: discounted and average cost cases. ZOR 40:145–162
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hordijk, A., Passchier, O. & Spieksma, F. Optimal service control against worst case admission policies: A multichained stochastic game. Mathematical Methods of Operations Research 45, 281–301 (1997). https://doi.org/10.1007/BF01193866
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01193866