On product form tandem structures (Q811989)

In order to characterize the existence of a product form solution, the author and \textit{A. Hordijk} introduced the concept of adjoint (artificial) Markov chain [see e.g. Bull. Int. Stat. Inst. 50, No. 2, 776--789 (1983; Zbl 0585.60089)]. Following this concept the paper investigates the existence of product form solution for the generic example of two interdependent service stations and two interdependent job classes. It shows that there exists a solution satisfying the station-class balance relation if and only if the introduced adjoint Markov chain is reversible. It checks the existence of a product form solution by means of reversibility despite the fact that the system itself is non-reversible. Three special cases are considered which show the possibility of product forms in presence of 1. intermediate blocking and delays; 2. load dependent service sharing over the stations; 3. job-class interdependent access (and departure) blocking.