INVERSION ALGORITHM TO COMPUTE BLOCKING PROBABILITIES IN LOSS NETWORKS WITH STATE-DEPENDENT RATES

We extend our recently developed algorithm for computing (exact) steady-state blocking probabilities for each class in product-form loss networks to cover general state-dependent arrival and service rates, This generalization allows us to consider, for the first time, a wide variety of buffered and unbuffered resource-sharing models with non-Poisson traffic, as may arise with overflows in the context of alternative routing, As before, we consider noncomplete-sharing policies involving upper-limit and guaranteed-minimum bounds for the different classes, but here we consider both bounds simultaneously, These bounds are important for providing different grades of service with protection against overloads by other classes, Our algorithm is based on numerically inverting the generating function of the normalization constant, which we derive here, Major features of the algorithm are: dimension reduction by elimination of nonbinding resources and by conditional decomposition based on special structure, an effective scaling algorithm to control errors in the inversion, efficient treatment of multiple classes with identical parameters and truncation of large sums, We show that the computational complexity of our inversion approach is usually significantly lower than the alternative recursive approach.