Stabilization Techniques for Load-dependent Queueing Networks Algorithms

Product-Form (PF) queueing networks are one of the most popular modelling techniques for evaluating the performances of computing and telecommunication infrastructures. Several computational algorithms have been developed for their exact solution. Unlike the algorithms for load-independent models, the ones for models with queue-dependent servers, either with single class or multiclass workloads, are numerically unstable. Furthermore, existing numerical stabilization technique for multiclass load-dependent models are not always efficient. The search for such result is motivated by the complexity of nowadays systems, which often require the use of load-dependent models. In this work we review numerical instabilities of computational algorithms for product-form queueing networks. Then, we propose a general solution to the problem based on arbitrary precision arithmetics. Finally, we discuss a new specialized stabilization technique for two class load-dependent models.