Approximating Large Scale Queueing System: An Overview and Directions for Further Research

Source abstract

Queueing systems are very well studied in the literature. There are a good collection of mathematical tools for studying a variety of queueing related problems. Occasionally, however, researchers doubt the applicability of some of the existing mathematical models to complex and/or large scale queueing systems they encounter in practical situations, such as in communication networks. This has led to the use of simulations and other types of approximation models for dealing with large scale systems. When approximate solutions are presented, purists often state that such solutions do not quite capture all the nuances of the real system. The question is when does a queueing system become large and require approximations, given the abundant literature on exact mathematical methods for analyzing them, and which approximation methods are appropriate to use? Is there a clear approach to readily determine whether a queuing system is large and/or complex? Thus, there is a need for an understanding of how to determine when a system of queues is deemed large and/or complex, and the need for approximation techniques in their analyses. In this paper, we briefly address this issue by providing an overview of existing tools that can be applied in analyzing any queueing problems that are deemed large and/or complex, while also focusing on approximation techniques for systems that are modeled as Markov Chains. In addition, we show that deriving a specific measure for categorizing a queueing system as large and/or complex can be an arduous task to achieve, and we propose the foundations for investigating such measures in future works. Finally, we conclude with open questions and problems with respect to modeling large scale and/or complex queueing systems and their approximations, to promote further research of effective approximation techniques for practitioners and analysts.