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Mathematical Problems in Engineering
Volume 2014, Article ID 767651, 16 pages
http://dx.doi.org/10.1155/2014/767651
Research Article

Product-Form Solutions for Integrated Services Packet Networks and Cloud Computing Systems

Department of Mathematics and State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing 210093, China

Received 25 February 2014; Revised 26 August 2014; Accepted 27 August 2014; Published 13 October 2014

Academic Editor: Joao B. R. Do Val

Copyright © 2014 Wanyang Dai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We iteratively derive the product-form solutions of stationary distributions for a type of preemptive priority multiclass queueing networks with multiserver stations. This type of queueing systems can typically be used to model the stochastic dynamics of some large scale backbone networks with multiprocessor shared-memory switches or local (edge) cloud computing centers with parallel-server pools. The queueing networks are Markovian with exponential interarrival and service time distributions. The obtained iterative solutions can be used to conduct performance analysis or as comparison criteria for approximation and simulation studies. Numerical comparisons with existing Brownian approximating model (BAM) related to general interarrival and service times are provided to show the effectiveness of our current designed algorithm and our previous derived BAM. Furthermore, based on the iterative solutions, we can also give some analysis concerning network stability for some cases of these queueing systems, which provides some insight for more general study.