Waiting time analysis for a queueing system with time‐limited service and exponential timer
研究了单队列中受定时器控制的时限服务（耗尽型或门限型）和服务器休假，推导了M/G/1系统在四种抢占/非抢占服务规则下的等待时间和逗留时间的拉普拉斯-斯蒂尔杰斯变换及矩公式。
We consider a single-queue with exhaustive or gated time-limited services and server vacations, in which the length of each service period at the queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes empty, whichever occurs first, and then takes vacations. The customer whose service is interrupted due to the timer expiration may be attended according to nonpreemptive or preemptive service disciplines. For the M/G/1 exhaustive/gated time-limited service queueing system with an exponential timer and four typical preemptive/nonpreemptive service disciplines, we derive the Laplace—Stieltjes transforms and the moment formulas for waiting times and sojourn times through a unified approach, and provide some new results for these time-limited service disciplines. © John Wiley & Sons, Inc. Naval Research Logistics 48: 638–651, 2001.