An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates

The algorithm developed in Choudhury et al. (1994) for computing (exact) steady-state blocking probabilities for each class in product-form loss networks is extended to cover general state-dependent arrival and service rates. This generalization allows 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, the authors consider noncomplete-sharing policies involving upper-limit and guaranteed-minimum bounds for the different classes, but in the present paper both bounds are discussed simultaneously. These bounds are important for providing different grades of service with protection against overloads by other classes. The algorithm is based on numerically inverting the generating function of the normalization constant, which is derived in the present paper. 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. The authors show that the computational complexity of the inversion approach is usually significantly lower than the alternative recursive approach