一类M/G/1排队系统的最优控制

Optimal Control of a Type of M/G/1 Queueing System

研究一类排队系统容量有限,服务规则是先到先服务的M/G/1排队系统 服务台在一定的顾客数目下启动,在系统空闲时关闭 采用补充变量法和L变换分析,得到了稳态条件下的概率母函数 采用N策略,研究了这类排队系统的最优控制策略,得到了一种最优控制方法 控制目标是根据系统的状态,动态地确定最优服务台启动策略以保证系统平均利润最大 通过给出的目标函数确定服务台启动的最佳顾客数。

This paper discusses a type of queuing system with finite capacity. Service discipline is first come first service. The server turns on when a certain number of customers are present and turns off in idle period. By use of supplemental variables method and L transform analyses, we get the generating function of equilibrium distribution. By using N policies, we then study the optimal control policy of this queuing system. Method of optimal control is obtained. The objective is to dynamically determine the optimal number of customers based on the state of system, so as to maximize the average profit. In order to determine the optimal number of customers when the server turns on, we present the object function. Thereby, we can gain the optimal economic profit.