Performance Analysis Using a Hierarchical Loss Network Model

In this paper we present a hierarchical loss network model for estimating the end-to-end blocking probabilities of large networks. As networks grow in size, nodes tend to form clusters geographically and hierarchical routing schemes are more commonly used. Loss network and reduced load models are often used to approximate end-to-end call blocking probabilities and hence throughput. However so far all work being done in this area is for flat networks with flat routing schemes. We aim at developing a more efficient approximation method for networks that have a natural hierarchy and/or when some form of hierarchical routing policy is used. We present two hierarchical models in detail for fixed hierarchical routing and dynamic hierarchical routing policies, respectively, via the notion of network abstraction, route segmentation, traffic segregation and aggregation. Computation is done separately within each cluster (local) and among clusters (global), and the fixed point is obtained by iteration between local and global computations. We present results from both numerical experiments and discrete event simulations.