Optimal Routing Problems and Multimodularity

In this paper we study the static assignment of packets to M parallel heterogeneous servers with no buffers. Blocked packets are lost and the objective is to minimize the average number of lost packets. The paper is divided into three parts. In the first part we formulate the problem as a Markov Decision Problem with partial observation and we derive an equivalent full observation problem. From this full observation problem we derive some structural results. We establish, in particular, the existence of an optimal periodic policy. The second part of the paper deals with computational aspects of the problem. We use multimodularity to derive an algorithm to compute optimal policies and show that for two servers the cost function is multimodular. In the third part we consider the same problem with well known arrival processes, such as the Poisson Process, the Markov Modulated Poisson Process and the Markovian Arrival Process.

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