An algorithm for product-form loss networks based on numerical inversion of generating functions

摘要

We consider a family of product-form loss networks with multiple classes of calls, each of which requires multiple trunks. The calls call use multiple circuits on each trunk (the multi-rate case). There can be upper-limit and guaranteed-minimum sharing policies as well as the standard complete-sharing policy. If all the requirements of a call cannot be met upon arrival, then the call is blocked. We develop an algorithm for computing the (exact) steady-state blocking probability of each traffic class. The algorithm is based on the numerical inversion of generating functions of the normalization constants and a scaling approach for error control. The computational complexity can often be reduced dramatically by exploiting conditional decomposition based on special structure and by appropriately truncating large finite sums. We show that the proposed algorithm is effective by several numerical examples.