Strong Stability of Queueing Systems and Networks: a Survey and Perspectives

The analysis of the stability of queueing models aims at determining the conditions under which the mathematical model is a good representation of the real system despite approximation and estimation errors. In this chapter, the authors review the application of the strong stability method to queues and queueing networks and provide directions for future research. They introduce the notations and the basic definitions and theorems of the strong stability theory. Queueing systems are among the first and most studied stochastic systems in the context of the strong stability theory. Many types of queues and queueing networks have been analyzed and their stability established. The authors also review the use of non‐parametric density estimation method in the study of those systems.