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Open-loop routeing to M parallel servers with no buffers

Part of: Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Eitan Altman ,
Sandjai Bhulai ,
Bruno Gaujal  and
Arie Hordijk
Eitan Altman*
Affiliation:
INRIA
Sandjai Bhulai*
Affiliation:
Vrije Universiteit Amsterdam
Bruno Gaujal*
Affiliation:
LORIA
Arie Hordijk*
Affiliation:
Leiden University
*
∗Postal address: INRIA B.P. 93, 2004 Route des Lucioles, 06902 Sophia Antipolis Cedex, France. Email address: altman@sophia.inria.fr
∗∗Postal address: Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
∗∗∗Postal address: LORIA B.P. 102, 54602 Villers-les-Nancy, France
∗∗∗∗Postal address: Leiden University, 2300 RA Leiden, The Netherlands
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Abstract

In this paper we study the assignment of packets to M parallel heterogeneous servers with no buffers. The controller does not have knowledge on the state of the servers and bases all decisions on the number of time slots ago that packets have been sent to the different servers. The objective of the controller is to minimize the expected average cost. We consider a general stationary arrival process, with no independence assumptions. We show that the problem can be transformed into a Markov Decision Process (MDP). We further show under quite general conditions on cost functions that only a finite number of states have to be considered in this MDP, which then implies the optimality of periodic policies. For the case of two servers we obtain a more detailed structure of the cost and optimal policies. In particular we show that the average cost function is multimodular, and we obtain expressions for the cost for MMPP and MAP processes. Finally we present an application to optimal robot scheduling for Web search engines.

Keywords

Markov decision processesmultimodularityoptimal open-loop controlrouteing

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 90C40: Markov and semi-Markov decision processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 668 - 684
Copyright
Copyright © Applied Probability Trust 2000 

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