延迟控制休假的M／M／1排队系统

本文研究带有延迟休假的 Ｍ／Ｍ／１排队系统，服务员在空闲了一段时间（称做延迟时间）后才正式开始休假，每次休假的时间长度有指数分布．若一次休假结束时系统中的顾客数目低于某一水平Ｋ，则服务员开始另一次休假；否则转为投入服务，这时系统开始一个新的忙期。对于延迟时间有指数分布和是确定的情形分别求得系统的稳态分布的精确表示及某些性能指标．文章还讨论了系统优化问题，给出使得单位时间平均总成本最小的Ｋ值．证明在泊松到达的情形最优延迟时间是０（无延迟）或无穷（无休假）

M/M/1 Queueing System with Delayed Controlled Vacation

An M/M/1 queue with delayed vacation is studied. If the server has been idle for a period of time (called the delay time), the server begins an exponentially distributed vacation which is repeated as long as the number of customers in the system remains less than some number K. For the cases of exponential and deterministic delay time, exact expressions for the steady state probability distribution are obtained, together with associated performance measures. System optimization is also considered; values of K are given which minimize the average total cost per unit time, and it is shown that the optimal delay period is either 0 (no delay) or infinite (no vacation), in case of Poisson arrivals.