Fixed Point Approximation for Multirate Multihop Loss Networks with Adaptive

In this paper, we consider a class of loss networks where multiple tra c classes are present, each has di erent bandwidth requirement, and each tra c stream is routed according to an adaptive routing scheme. The performance metric of interest is the end-to-end call blocking probability. Blocking probabilities in a loss network have been studied quite extensively but very few considered multiple tra c classes and rates together with adaptive/state dependent routing. We propose a xed-point method, a.k.a. reduced load approximation, to estimate the end-to-end blocking probability in a multihop multirate loss network with adaptive routing. Simulation results are provided to compare with that of approximations. The approximation scheme is shown to be asymptotically correct in a natural limiting regime, and it gives conservative estimates of blocking probabilities under heavy tra c load. This work was supported by the Center for Satellite and Hybrid Communication Networks, under NASA cooperative agreement NCC3-528