Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

Abstract

Bandwidth-sharing networks provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers in computer and communication systems, and can be used to develop traffic pricing/charging mechanisms. At the same time, such models are exciting from an operations research perspective because their analysis requires techniques from stochastic modeling and optimization. In this paper, we develop a framework to approximate bandwidth-sharing networks under the assumption that the number of users as well as the capacities of the system are large, and the assumption that the traffic that each user is allowed to submit is bounded above by some rate, which is standard in practice. We also assume that customers on each route in the network abandon according to exponential patience times. Under Markovian assumptions, we develop fluid and diffusion approximations, which are quite tractable: for most parameter combinations, the invariant distribution is multivariate normal, with mean and diffusion coefficients that can be computed in polynomial time as a function of the size of the network.