Stochastic networks with product form equilibrium (Q2734968)

This is a survey article on queueing networks of the type for which the state evolution in time can be described by a continuous-time Markov chain possessing a stationary distribution of a so-called product form. The classical examples are the Jackson and Gordon-Newell networks. After describing these the author reports on rather general models, stating theorems on the existence of a product form stationary distribution, monotonicity and correlation properties of the state process, the distribution of the state seen by a customer arriving at a station, sojourn time distributions, and an insensitivity property (whereby the stationary distribution of the numbers of customers present at a station depends on certain service time distributions only through their expected values). No proofs are given. Loss networks, diffusion and fluid approximations, networks in discrete time, and networks with negative customers are covered only by references. The list of references is impressive.NEWLINENEWLINEFor the entire collection see [Zbl 0961.60001].