带有抢占优先权和重试的排队系统的优化分析

Optimization Analysis of Queueing Systems with Preemptive Priority and Retrial

摘要: 本文研究了带有抢占优先权和重试的M/M/1排队系统。首先，采用概率生成函数的方法，得到了系统的稳态概率和主要性能指标。然后考虑了双目标优化的问题，旨在同时最小化系统成本和顾客逗留时间，借助NSGA-II算法来寻找Pareto最优解集。最后建立了以最优成本为因变量，非优先权顾客的到达率、最优逗留时间以及最优逗留时间的负指数为自变量建立了回归模型，进行了回归分析及模型的显著性检验。本文的分析能够使系统在提高服务质量的同时最小化成本，研究结论对系统管理者来说具有一定的参考价值。

Abstract: In this paper, the M/M/1 queueing system with preemption priority and retrial is studied. First, the steady state probability and main performance measures of the system are obtained by using probability generating function method. Then, the problem of Bi-objective optimization is consid-ered to minimize both system cost and customer’ sojourn time, and NSGA-II algorithm is used to find the optimal solution set of Pareto. Finally, a regression model is established with the optimal cost as the dependent variable, the arrival rate of non-priority customers, the optimal sojourn time and the negative index of the optimal sojourn time as independent variables, the regression analy-sis and the significance test of the model are carried out. The analysis of this paper can improve the service quality of the system while minimizing the cost, and the research conclusion has a certain reference value for system managers.