A model for the M/M/1 queue and its applications in communication networks

Abstract

In this work, a continuous differential equation model describing the evolution of the mean number in an M/M/1 queue has been developed. The validity of this approximation has been established by comparisons with work by Stern {23} and with the results of extensive simulation studies. In an effort to extend the model to the prediction of the behavior of a network of queues, such as found in a packet switched communication network, the technique was successfully applied to a series of queues in tandem. This approximation scheme was next applied to a simple network which incorporated alternate routes between the source and destination. The existance of alternate routes necessitated, of course, the use of a control mechanism for choosing which route to use for a particular customer. In view of recent trends towards control based on averages, it was decided to implement a scheme based on such. It was found that the model accurately predicted the behavior of the network under this form of control. Finally, the model was used to describe a general N node ring network with distributed control.