具有两类平行顾客的灾难清空排队系统均衡分析

Equilibrium analysis of queueing system with two types of parallel customers and disaster

研究了具有两类平行顾客、不完全可靠服务台即带有灾难清空的排队系统中顾客的均衡进队策略.在该排队系统中,两种不同类型的顾客独立到达,且该过程分别形成不同参数的泊松过程.系统是不完全可靠的,系统内所有顾客因灾难发生而被全部清空,且未接受服务被迫退队的顾客可得到一定的补偿.基于顾客的收益-损失函数,在系统信息完全可见和几乎可见两种情形下,分析了两类顾客的均衡阈值策略和系统平均社会收益.最后给出数值案例,得到了系统参数对顾客策略的影响.

This paper studies the equilibrium strategies of two classes of parallel customers in a queueing system which has disaster arrival.In this queueing system,the arrival processes of two types of customers are mutually independent and form a Poisson process with different parameters respectively.The system is not completely reliable,all customers in the system are emptied due to the arrival of disaster,so that customers who have not finished the service are forced to withdraw from the queue and receive certain compensation.According to the benefit-loss function,the paper analyzes the equilibrium balking strategies of customers and the average social benefit of the system at the two cases of fully observable and almost observable system information level,respectively.Finally,the influence of system parameters on these strategies is analyzed through numerical examples.