Stability of a G I / G / 1 Queue: A Survey

Stability of queues is of fundamental importance in the application of queueing models. To establish the stability of a queue, one has to utilize a mathematical model to describe the evolution of the queue and then defines stability on the model. However, the types of stability are various according to their underlying processes. In this study, we survey the different underlying processes of a GI/G/1 queue, classify the various types of stability and study the relations among them. Furthermore, from the viewpoint of sample-path, we propose a new result regarding the growth rate of the queue time when the traffic intensity equals 1.