具有不耐烦顾客和可变服务率的可修M/M/1/N-G排队系统（英文）

A repairable M / M /1 / N-G queue with impatient customers and variant service rates

给出容量有限的具有不耐烦和可变服务率的排队系统,其中服务率可变是因负顾客的到达而引起的。若负顾客在正常服务期间到达,它不仅删除正在服务的正顾客,而且或以概率p使服务台的服务速率降低,或以概率1-p使服务台失效。若负顾客在服务台低服务期到达,则它在删除正在服务的正顾客同时,还使服务台失效。若负顾客在服务台闲期或修理期到达,则它对系统不产生影响。服务台失效时,立即进行修理且修复如新。在服务台低服务期或修理期间,顾客是不耐烦的。利用马尔科夫过程理论,研究稳态概率方程,给出系统性能测度。在性能分析的基础上给出数值例子,说明不同参数对系统行为的影响。

A finite-buffer queueing system with impatient and variant service rate is presented due to the arrival of negative customers. Assume that if a negative customer arrives during normal service period, it not only eliminates the positive customer being served, but also with probability p causes the server to slow down its service rate or with probability 1-p causes the server＇ s breakdown. If a negative customer arrives during lower service period, it eliminates the customer being served and makes the server break- down. If a negative customer arrives when the server is idle or in repair period, it has no effect on the system. When the server＇ s breakdown occurs, it is sent immediately for repair and it is as well as new after repair. The customers are impatient during the server＇ s lower service period and repair period. By using the Markov process method, the equations of the steady state probabilities are first developed, and then some performance measures of the system are given. Based on the performance analysis, some numeri- cal examples are presented to illustrate the effect of the various parameters on the behavior of the system.