交互环境下带有启动时间的清空排队系统分析

Analysis of a Clearing Queueing System with Setup Times in Alternating Environment

研究了一个交互环境下带有启动时间的马尔可夫清空排队系统。在指数服务循环结束时刻,服务员瞬时服务完系统中所有顾客;该系统在交替的环境中运作,环境的交替会影响顾客的到达率及交通工具的到达率(即服务员的服务速率);刚到达的顾客会基于简单线性"收益-成本"结构,决定是否进入系统。依据系统的不同状态,得到顾客的止步策略、系统状态的稳态分布、平均队长以及社会最优收益,最后给出了一些数值实例。

This paper studies a Markovian clearing queuing system with setup times in alternating environment. At the completion of exponential service cycles,the server removes all present customers. The system operates in an alternating environment which may influences the arrival rate of the customers and the transportation facility（ i.e.,service rate）. Upon their arrivals,customers decide whether to join or balk the system based on a natural linear ＂reward-cost＂structure. According to the different states of system,we derive the balking strategies of customers,the stationary distribution of system state,the mean queue length and the social optimal benefit.Finally,some numerical examples are presented.