No abstract

The objective pursued in this paper is two-fold. The first part addresses the following combinatorial problem: is it possible to construct an infinite sequence over n letters where each letter is distributed as "evenly" as possible and appears with a given rate? The second objective of the paper is to use this construction in the framework of optimal routing in queuing networks. We show under rather general assumptions that the optimal deterministic routing in stochastic event graphs is such a sequence.

In this paper we investigate the properties of multimodular functions. In doing so we give elementary proofs for properties already established by Hajek and we generalize some of his results. In particular, we extend the relation between convexity and multimodularity to some convex subsets of ℤm. We also obtain general optimization results for average costs related to a sequence of multimodular functions rather than to a single function. Under this general context, we show that the expected average cost problem is optimized by using regular sequences. We finally illustrate the usefulness of this theory in admission control into a D/D/1 queue with fixed batch arrivals, with no state information. We show that the regular policy minimizes the average queue length for the case of an infinite queue, but not for the case of a finite queue. When further adding a constraint on the losses, it is shown that a regular policy is also optimal for the finite queue case.

In this paper we show that for a finite Markov decision process an average optimal policy can be found by solving only one linear programming problem. Also the relation between the set of feasible solutions of the linear program and the set of stationary policies is analyzed.dynamic programming: Markov, finite stage, programming: infinite horizon

Consider a queueing model in which arriving customers have to choose between m parallel servers, each with its own queue. We prove for general arrival streams that the policy which assigns to the shortest queue is stochastically optimal for models with finite buffers and batch arrivals.