Utility optimization in congested queueing networks: invited presentation, extended abstract

We consider a multi-class single server queueing network as a model of a packet switching network. We discuss how such networks perform a proportionally fair optimization when congested. We discuss the connections between product form queueing networks, insensitivity and proportional fairness. We prove that stationary throughput of a closed multi-class single server queueing network converges to a proportionally fair allocation as the number of packets across routes increases. We then let the rate packets enter different routes of the network be controlled by congestion windows, which record the number of sent but not yet acknowledged packets on each route of the network. By considering a sequence of such congestion windows we allow the network to become congested. We show that these networks maximize aggregate utility subject to the networks capacity constraints. To perform this analysis we require our utility functions to satisfy an exponential concavity assumption. This family of utility functions includes the weighted α-fair family of utilities for parameter α > 1.