In a loss system customers arrive in attempt to seize some of the available system resources. At the time of arrival, a customer finding insufficient available resources leaves the system, hence the term loss system. Otherwise, the customer seizes the required amount of resources for a random holding time and then leaves the system, thereby making available the previously held resources. In this chapter the authors investigate a class of loss systems known as product-form loss networks, which are generalizations of the classical Erlang and Engset loss models. Loss networks can provide a mathematical model for various resources sharing systems including circuit-switched networks and other types of connection-oriented communication networks. The authors develop basic properties of loss networks related to the product-form stationary distribution by generalizing the classical loss models. They find analogies between loss networks and the well-studied product-form queueing networks, which suggest that the parallel methods of analysis can be applied to both types of models. Blocking probabilities and other quantities of interest for loss networks are expressible in terms of a normalization constant, which is analogous to the normalization constant of queueing networks. Evaluation of the normalization constant usually poses significant computational challenges even for simple loss networks with special structure. The authors discuss state-of-the-art computational methods and asymptotic approximations for evaluating the normalization constant and blocking probabilities in product-form loss networks. In conclusion they discuss open problems and related areas of research.
