Criteria for local stability and rate of convergence are completely characterized for a single resource, single user system. Stability criteria are also described for networks where all users share the same roundtrip delay.
Numerical experiments investigate extensions to more general networks.
Finally, through simulations, we are able to evaluate the relative importance of queueing delays and propagation delays on network stability. This is joint work with David Tan and Frank Kelly at the University of Cambridge Statistical Laboratory. We compare the unfinished work in this queue to the work in a queue with a constant server rate equal to the average value of the time varying process. Our lower bound is shown to be tight as the timescale of variation in the linespeed process tends to infinity. In the other direction, we compute a limiting value for the unfinished work as the linespeed process changes more and more slowly, and conjecture that this value is in fact an upper bound on unfinished work for any timescale.