Abstract
In anM/M/1 queueing model, a decision maker can choosem pairs of arrival- and service rates. He can change his action at any time epoch, a ‘switch’ of action costs an amount depending on the size of the switch. Besides that there are continuously incurring costs. Over a finite time horizon, there exists an optimal monotone hysteretic Markov policy. This is shown essentially by the technique of time discretization.
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References
Hordijk A, Van der Duyn Schouten FA (1984) Discretization and weak convergence in Markov decision drift processes. Math O R 9(1):112–141
Hordijk A, Van der Duyn Schouten FA (1985) Markov decision drift processes: Conditions for optimality obtained by discretization. Math O R 10:160–173
Lu FV, Serrozo RF (1984)M/M/1 queueing decision processes with monotone hysteretic optimal policies. Math O R 32(1):1116–1132
Plum HJ (1984) Diskretisierung des Zeitparameters in einem Modell gesteuerter Markoffscher Sprungprozesse mit Impulskontrollen. Dissertation, Univ Bonn
Plum HJ (1987) Impulsive and continuously acting control of jump processes — time discretization. To appear in Stochastics
Plum HJ (1986) Optimal monotone hysteretic policies in anM/M/1 queueing problem with switching costs. Report 02. Institute of Applied Mathematics and Computer Science. University of Leiden, The Netherlands
Van der Duyn Schouten FA (1983) Markov decision processes with continuous time parameter. Math Centre Tract 164, Amsterdam
Van Dijk N (1984) Controlled Markov processes-time discretization. CWI Tract 11, Amsterdam
Yushkevich AA (1983) Continuous time Markov decision processes with interventions. Stochastics 9:235–274
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The work producing this article was done during a half year stay at the University of Leiden, The Netherlands, with Prof. Arie Hordijk. A technical report (a more detailled version of this article) was written there [6]. The opportunity for this stay was given by the University of Bonn, Germany, where the author, at that time, worked as scientific assistant of Prof. M. Schäl.
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Plum, H.J. Optimal monotone hysteretic Markov policies in anM/M/1 queueing model with switching costs and finite time horizon. ZOR - Methods and Models of Operations Research 35, 377–399 (1991). https://doi.org/10.1007/BF01498330
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DOI: https://doi.org/10.1007/BF01498330