An invariance principle for semimartingale reflecting Brownian motions in an orthant
Queueing Systems: Theory and Applications
Short communication: Short-term fairness and long-term QoS in the Internet
Performance Evaluation
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We consider a flow-level model of Internet congestion control introduced by Massoulié and Roberts [2]. We assume that bandwidth is shared amongst elastic documents according to a weighted proportional fair bandwidth sharing policy. With Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. In [1], under a mild local traffic condition, we establish a diffusion approximation for the workload process (and hence for the flow count process) in this model. We first recall that result in this paper. We then state results showing that when all of the weights are equal (proportional fair sharing) the diffusion has a product form invariant distribution with a strikingly simple interpretation in terms of dual random variables, one for each of the resources of the network. This result can be extended to the case where document sizes are distributed as finite mixtures of exponentials, and to models that include multi-path routing (these extensions are not described here, but can be found in [1]).