Phase Transitions in Multiserver Queuing Systems

Abstract

In this paper synergetic effects in queuing systems and networks are investigated. In the systems M|M|n|0 with failures phase transition is established in cases when competition between servers for customers is present and when it is absent. In the systems \(M|M|n|\infty \) and \(M|G|n|\infty \) with heavy traffic, where distribution of service times are hyperexponential, for some stationary characteristics phase transitions are established. The critical parameters of these phase transitions are defined by load coefficients. The obtained results are spread onto queuing networks with nodes which have the type \(M|G|n|\infty \) and the effect of a queue disappearence is investigated. The main approach of these systems and networks analysis is their transformation into Jackson networks.