Bounds on the performance of admission control and routing policies for general topology networks with multiple call classes

We consider the problem of obtaining non-trivial lower bounds on the the lost revenue under any routing and admission control scheme in a multi-class loss network. First, we use the following simple idea to bound the performance of any coordinate-convex admission policy on a single link: the blocking probability of any call class is lower bounded by considering just this class in isolation and replacing the available bandwidth (a random quantity) by its mean. Then, following the methods of Kelly (1994) and Gibbens and Kelly (see IEEE Journal on Selected Areas in Communications, p.100-10, 1995), we use this single link bound to obtain linear programs which give bounds in the case of sparsely-connected networks with multiple bandwidth classes and alternate routing