Recensione dell'articolo: (Dieker, A. B.; Shin, J.- " From local to global stability in stochastic processing networks through quadratic Lyapunov functions." - Math. Oper. Res. 38 (2013), no. 4, 638–664.)

This paper deals with the design and analysis of scheduling policies for stochastic networks, and specifically with the search for tools that can characterize the stability region of scheduling policies, i.e., the exact conditions on the arrival and service rates under which a network is stabilized by a policy. The authors introduce the class of stochastic processing networks that they study in this paper. They define, also, a randomized scheduling policy for stochastic processing networks that requires coordination within local components (e.g. service stations), and which is computationally attractive because it is a kind of priority policy. This policy, called the ε-least routed first served policy, prioritizes, with high probability, jobs that have been the least routed. Here ε≥0 is a small number that helps to make the meaning of “high probability” precise. In this context the authors prove a theorem which establishes global stability using a local quadratic Lyapunov function.