具有备用服务员和不耐烦顾客的排队模型及其仿真

Simulation of a queuing model with backup waiters and impatient customers

影响排队系统性能的因素有很多,在某些假设条件下,服务员的数量决定服务效率,而不耐烦顾客的存在会影响服务收益.传统的排队理论主要是针对不同时间分布类型的排队模型分别进行分析的,而蒙特卡洛仿真模型可以同时适应多种时间分布类型的排队过程.本文构建了几种常见条件下的排队模型,并利用蒙特卡洛仿真方法对其进行了模拟,特别是分析了若干常用指标.通过对这些模型的仿真结果比较分析,表明:若根据顾客排队的情况及时调整服务员数量,则既可以提高服务效率,又可避免过多资源闲置浪费以及顾客流失;同时,仿真结果的各项指标可以作为设置排队类型及其模型参数的依据,为有关决策提供参考.

There are many factors that affect the performance of a queuing system.Under certain assumptions,the number of waiters determines the service efficiency while the presence of impatient customers will affect the service earnings.Traditional queuing theory primarily analyzes queuing models with different time distribution types,while a Monte Carlo simulation model can adapt to the queuing processes of different time distribution types simultaneously.In this paper,several queuing models under common conditions were constructed and simulated by a Monte Carlo simulation;in particular,some commonly used indicators were analyzed.Through a comparison and analysis of the simulation results from these models,it is shown that if the number of waiters is adjusted based on the customer queuing circumstances,it can not only improve service efficiency,but also avoid excessive waste of idle resources and loss of customers.Meanwhile,the simulation results can be used as the basis for setting up queue types and model parameters,as well as a reference for decision making.