Institute for Systems Research

As networks grow in size, nodes tendto form clusters geographically and hierarchical routing schemes are morecommonly used. Loss network and reduced load models are often used toapproximate end-to-endcall blocking probabilities, and hence, throughput. However so far all workbeing done in this area is for flat networks with flat routing schemes.

We aim at developing a more efficient approximation method for networksthat have a natural hierarchy and/or when some form of hierarchical routingpolicy is used. We present two hierarchical models in detail for fixedhierarchical routing and dynamic hierarchical routing policies,respectively, via the notion of network abstraction, route segmentation, traffic segregationand aggregation. Computation is done separately within each cluster (local)and among clusters (global), and the fixed point is obtained by iterationbetween local and global computations. We also present numerical resultsfor the first case.

The performance metric of interest is the end-to-end call blockingprobability. Blocking probabilities in a loss network have been studiedquite extensively but very few considered multiple traffic classes andrates together with adaptive/state dependent routing.

We propose a fixed-point method, a.k.a. reduced load approximation,to estimate the end-to-end blocking probability in a multihop, multirateloss network with adaptive routing. Simulation results are provided tocompare with that of approximations. The approximation scheme is shownto be asymptotically correct in a natural limiting regime, and it givesconservative estimates of blocking probabilities under heavy trafficload.