Open-loop routeing to M parallel servers with no buffers

Open-loop routeing to M parallel servers with no buffers

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Article ID: iaor2004681
Country: United States
Volume: 37
Issue: 3
Start Page Number: 668
End Page Number: 684
Publication Date: Sep 2000
Journal: Journal of Applied Probability
Authors: , , ,
Keywords: decision theory
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 expression for the cost for MMPP and MAP processes. Finally we present an application to optimal robot scheduling for Web search engines.

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