Hierarchical Space Merging Algorithm for the Analysis of Open Tandem Queueing Networks

详细信息    查看全文

• 作者：A. Z. Melikov ; L. A. Ponomarenko ; A. M. Rustamov
• 关键词：open tandem queueing ; feedback ; three ; dimensional Markov chain ; hierarchical space merging algorithm
• 刊名：Cybernetics and Systems Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：52
• 期：6
• 页码：867-877
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Artificial Intelligence (incl. Robotics); Processor Architectures; Software Engineering/Programming and Operating Systems;
• 出版者：Springer US
• ISSN：1573-8337
• 卷排序：52

文摘

The Markov model of a two-stage queueing network with feedback is proposed. Poisson flows arrive to both stages from outside. A part of already serviced calls at the first node instantaneously enter the second node (if there is free space here) while the other calls leave the network. After the service is completed at the second node, there are three possibilities: (i) the call leaves the network; (ii) it instantaneously feeds back to the first node (if there is free space here); (iii) it feeds back to the first node after some delay in orbit. All feedbacks are determined by known probabilities. Both nodes have finite capacities. The mathematical model of the investigated network is a three-dimensional Markov chain, and a hierarchical space merging algorithm is developed to calculate its steady-state probabilities. The results of numerical experiments are demonstrated.