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http://dx.doi.org/10.1214/ss/1177010131

has been cited by the following article:

• TITLE: Mathematical Modeling in Heavy Traffic Queuing Systems

  AUTHORS: Sulaiman Sani, Onkabetse A. Daman

  KEYWORDS: Queuing Process, Brownian Process, Martingale, Regularly Varying Functions

  JOURNAL NAME: American Journal of Operations Research, Vol.4 No.6, November 17, 2014

  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.