Blocking probabilities in multitraffic loss systems: insensitivity, asymptotic behavior, and approximations

It is known that, under any sharing policy, the state describing the number of calls established for each class of traffic in steady state has a product-form distribution when the connection time distribution has a rational Laplace transform. The product-form property further holds for arbitrary holding time distribution under coordinate convex sharing policies. For the complete sharing policy case, an aggregate state describing the number of occupied circuits is shown to maintain the product-form property under asymptotic behavior, when the capacity and traffic intensities go to infinity on a comparable scale. Two theorems relative to the asymptotic behavior of the blocking probabilities which provide some insight into the nature of the blocking phenomenon are given. An approximation which reduces the numerical complexity of evaluating the blocking probabilities for the different classes of service to the computation of a single Erlang formula and the determination of the root of a monotonous polynomial function is proposed