具有不耐烦顾客和PH分布休假的M/M/1排队系统  

Analysis of M/M/1 Queueing System with Impatient Customers and PH Distributed Vacation

作　　者：李单单[1] 岳德权[1] 赵冰[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《数学的实践与认识》2017年第3期198-205,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301458)

摘　　要：研究了具有不耐烦顾客的M/M/1休假排队系统,其中休假时间服从位相分布.当顾客在休假时间到达系统,顾客则会因为等待变得不耐烦.服务员休假结束后立刻开始工作.如果在顾客不耐烦时间段内,系统的休假还没有结束,顾客就会离开系统不再回来.建立的模型为水平相依QBD拟生灭过程,通过利用BrightTaylor算法得到系统的稳态概率解.同时还得到一些重要的性能指标.最后通过数据实例验证了我们的结论.In this paper, we study an M/M/1 queueing system with impatient customers and vacation, where the vacation time follows a phase type distribution. When customers arrive at the system during a vacation, they may be impatient due to waiting. The server comes back to start working immediately after vacation completion. If the vacation has not been completed before the customer＇s timer expires, the customer abandons the queue, never to return. We formulate the model as a level dependent Quasi-Birth-Death process and then compute the steady state probability by using Bright-Taylor algorithm. We also obtain some key performance measures. Numerical results are presented to illustrate our results.

关 键 词：排队系统 水平相依QBD拟生灭过程 不耐烦顾客 PH分布 休假 

分 类 号：O226[理学—运筹学与控制论]