Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines

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• 作者：Jianyu Cao ; Weixin Xie
• 关键词：Polling system ; Stability ; Batch Markovian arrival process ; Gated service ; State ; dependent time ; limited service ; Preemptive repeat different
• 刊名：Queueing Systems
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：85
• 期：1-2
• 页码：117-147
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Operation Research/Decision Theory; Computer Communication Networks; Probability Theory and Stochastic Processes; Supply Chain Management; Systems Theory, Control;
• 出版者：Springer US
• ISSN：1572-9443
• 卷排序：85

文摘

The stability of a cyclic polling system, with a single server and two infinite-buffer queues, is considered. Customers arrive at the two queues according to independent batch Markovian arrival processes. The first queue is served according to the gated service discipline, and the second queue is served according to a state-dependent time-limited service discipline with the preemptive repeat-different property. The state dependence is that, during each cycle, the predetermined limited time of the server’s visit to the second queue depends on the queue length of the first queue at the instant when the server last departed from the first queue. The mean of the predetermined limited time for the second queue either decreases or remains the same as the queue length of the first queue increases. Due to the two service disciplines, the customers in the first queue have higher service priority than the ones in the second queue, and the service fairness of the customers with different service priority levels is also considered. In addition, the switchover times for the server traveling between the two queues are considered, and their means are both positive as well as finite. First, based on two embedded Markov chains at the cycle beginning instants, the sufficient and necessary condition for the stability of the cyclic polling system is obtained. Then, the calculation methods for the variables related to the stability condition are given. Finally, the influence of some parameters on the stability condition of the cyclic polling system is analyzed. The results are useful for engineers not only checking whether the given cyclic polling system is stable, but also adjusting some parameters to make the system satisfy some requirements under the condition that the system is stable.