An inversion algorithm for 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 non-complete-sharing policies involving upper-limit and guaranteed-minimum bounds for the different classes, but here we consider both bounds simultaneously. Major features of the algorithm are: dimension reduction by conditional decomposition based on special structure, an effective scaling algorithm to control errors in the inversion, the efficient treatments of multiple classes with identical parameters and the truncation of large sums