Teletraffic engineering for product-form circuit-switched networks

We develop a performance modeling methodology for product-form circuit-switched networks. These networks allow for: arbitrary topology and link capacities; Poisson and finite population arrivals; multiple classes of calls, each class with a different route and bandwidth requirement; conference as well as point-to-point calls. The methodology is first applied to generalized tree networks, which consist of multiple access links feeding into a common link. Each access link may support multiple ‘long-distance' classes (requiring circuits only on the access link and on the common link) and multiple ‘local' classes (requiring circuits only on the access link). For generalized tree networks an efficient algorithm is given to determine the blocking probabilities. The methodology is then applied to hierarchical tree networks, where traffic is repeatedly merged in the direction of a root node. We also establish a ‘Norton' theorem for product-form circuit-switched networks. This theorem implies that for any given calling class, the entire network can be replaced by an Erlang loss system with a state-dependent arrival rate, without modifying the equilibrium probabilities for the particular calling class.