Queueing Networks - Insensitivity and a Heuristic Approximation

The Baskett-Chandy-Muntz-Palacios theorem on insensitivity of queueing networks with respect to the form of d.f.'s of service times in case of fixed means is true under more general assumptions as in the original paper [1]. (i) The d.f.'s of service times can have arbitrary forms and must not have a rational Laplace-Stieltjes transform. (ii) The number of servers in nodes with pre-emptive resume LIFO discipline can be greater than one. The proof in [5] is based on the method of Bedienungsprozesse of K6nig, Matthes and Nawrotzki [2], [3] and no continuity arguments are needed. Furthermore, a heuristic approximation for state probabilities and waiting times is suggested which is based on the approximation of nodes with FIFO discipline by nodes with pre-emptive resume LIFO discipline, as is done in [4] for MIGIs. The accuracy of the approximation is similar to that of diffusion approximation.