Fluid models of congestion collapse in overloaded switched networks

We consider a switched network (i.e. a queueing network in which there are constraints on which queues may be served simultaneously), in a state of overload. We analyse the behaviour of two scheduling algorithms for multihop switched networks: a generalized version of max-weight, and the α-fair policy. We show that queue sizes grow linearly with time, under either algorithm, and we characterize the growth rates. We use this characterization to demonstrate examples of congestion collapse, i.e. cases in which throughput drops as the switched network becomes more overloaded. We further show that the loss of throughput can be made arbitrarily small by the max-weight algorithm with weight function f(q) = q as α → 0.