Fixed-Point Approximations of Bandwidth-Sharing Networks with Rate Constraints

Bandwidth-sharing networks are important flow level models of communication networks. We focus on the fact that it takes a signicant number of users to saturate a link, necessitating the inclusion of individual rate constraints. In particular we extend work of Reed & Zwart on fluid models of bandwidth sharing with rate constraints under Markovian assumptions: we consider a bandwidth sharing network with rate constraints, where job sizes and deadlines have a general joint distribution. We introduce a fluid model and investigate several of its properties. In particular we show that its invariant point approximates the invariant distribution of the bandwidth sharing network if capacities are large.