Abstract
In this article, modeling in queuing systems with heavy traffic customer flows is reviewed. Key areas include their limiting distributions, asymptotic behaviors, modeling issues and applications. Heavy traffic flows are features of queuing in modern communications, transportation and computer systems today. Initially, we reviewed the onset of asymptotic modeling for heavy traffic single server queuing systems and then proceeded to multi server models supporting diffusion approximations developed recently. Our survey shows that queues with heavy traffic customer flows have limiting distributions and extreme value maximum. In addition, the diffusion approximation can conveniently model performance characters such as the queue length or the waiting time distributions in these systems.
Highlights
There are times when queueing systems behave like fluid
The motivation leading to the above results and many others came from the works of Kingman and others on the asymptotic behaviors of queuing systems under heavy traffic
The diffusion approximation in heavy traffic queuing systems came to light in the works of Iglehart [12], Gaver [13] and Newell [14]
Summary
There are times when queueing systems behave like fluid. A good scenario is when customers of a busy bus station experience rush hour. Our objective in this paper is to survey works on heavy traffic queueing systems generally in the light of both mathematical and statistical realities with emphasis on those queues supporting the diffusion approximation. This includes their distributions, analyses, modeling and application. It is anticipated that a survey of this kind will provide an excellent background in heavy traffic studies especially in packets and internet traffic prevalent in computers, communications and telecommunications systems. Recent studies have shown that the Poisson based models are relevant and could be used to describe the internet traffic central in this controversy.
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