离散时间闸门式多级门限服务的两级优先级轮询排队系统分析

An Exact Analysis of Discrete Time Two-Level Priority Polling System Based on Multi-times Gated Service Policy

本文提出了一种基于闸门式多级门限服务的两级优先级轮询系统.论文先构建了系统的排队分析模型,然后把模型中各个站点内的等待顾客数合起来设定为系统状态变量,对系统状态变量的概率母函数求二阶偏导后组成迭代方程组,联立求解后得到了站点的平均排队队长、顾客平均等待时间以及服务器查询周期等关键指标的完整数学解析表达式.最后,对该模型进行了仿真实验分析,实验结果与理论结果相一致.系统性能分析表明该轮询系统满足了周期性系统服务资源分配过程中业务多样性和弹性服务的发展需求,使得轮询控制策略应用方面更为广泛.

This paper proposed a new system of two-class priority polling based on multi-times gated service policy. A queuing model of the polling system is constructed, in which the number of waiting customers in each site is set together as random variables of the system state. Moreover,iterative equations are set up by taking second-order partial derivatives of the generating function, and then the integral mathematical analytical expressions of the key indexes are derived via simulta- neous solution, concerning the mean queue length, the mean waiting time of the key queue and common queues, and the mean polling period time of the server. Finally, computer simulations are conducted on the system and it is found that theo- retical and simulation results are identical. The analysis shows that this new polling system satisfies the demand of service diversity and flexible service in the process of resource allocation in a periodic system, and demonstrates that the polling con- trol protocol has wider applications.