We consider a multiclass single-server queueing network as a model of a packetswitching network. The rates packets are sent into this network are controlledby queues which act as congestion windows. By considering a sequence ofcongestion controls, we analyse a sequence of stationary queueing networks. Inthis asymptotic regime, the service capacity of the network remains constantand the sequence of congestion controllers act to exploit the network'scapacity by increasing the number of packets within the network. We show thatthe stationary throughput of routes on this sequence of networks converges toan allocation that maximises aggregate utility subject to the network'scapacity constraints. To perform this analysis, we require that our utilityfunctions satisfy an exponential concavity condition. This family of utilitiesincludes weighted α-fair utilities for α > 1.
"Utility optimization in congested queueing networks." J. Appl. Probab. 48 (1) 68 - 89, March 2011. https://doi.org/10.1239/jap/1300198137