Analysis of some simple policies for dynamic resource allocation

Abstract

Complexity-performance trade-offs are investigated for dynamic resource allocation in load sharing networks with Erlang-type statistics. The emphasis is on the performance of simple allocation strategies that can be implemented on-line. The resource allocation problem is formulated as a stochastic optimal control problem. Variants of a simple least load routing policy are shown to lead to a fluid type limit and to be asymptotically optimal. Either finite capacity constraints or migration of load can be incorporated into the setup.

Three policies, namely optimal repacking, least load routing, and Bernoulli splitting, are examined in more detail. Large deviations principles are established for the three policies in a simple network of three consumer types and two resource locations and are used to identify the network overflow exponents. The overflow exponents for networks with arbitrary topologies are identified for optimal repacking and Bernoulli splitting policies, and conjectured for the least load routing policy.

Finally, a process-level large deviations principle is established for Markov processes in the Euclidean space with a discontinuity in the transition mechanism along a hyperplane. The transition mechanism of the process is assumed to be continuous on one closed half-space and also continuous on the complementary open half-space. A similar result was recently obtained by Dupuis and Ellis for lattice-valued Markov processes satisfying a mild communication/controllability condition. The proof presented here relies on the work of Blinovskii and Dobrushin, which in turn is based on an earlier work of Dupuis and Ellis.