Exact and asymptotic solutions for models of new telecommunication services

A new product-form, finite capacity network model is described for the blocking analysis of modern telecommunication services such as automatic redial, video on demand, interactive TV and video telephony. It allows multiple finite sources requiring random routes and a random number of resource units from one or several resource types. We obtain a simple closed-form expression for the generating partition function and from that derive three computational methods based on numerical inversions, asymptotic approximations and recursion relations. The main concepts from the asymptotic method are also used in the numerical inversion method to justify speed-up of this method for large models. Numerical examples are presented to illustrate the effectiveness of the procedures.