休假M/G/1排队系统离去过程的进一步分析

对具有多重和单重服务员假期的M/G/1排队系统,进一步分析了其离去过程,得到在(0,t]时间内离去平均数的LS变换表达式;证明了在t=0时刻系统中无顾客且服务员也开始休假的条件下,如果服务时间和休假时间均服从负指数分布,则(0,t]时间内离去平均数的LS变换表达式在到达率和服务率交换时是不变的:讨论了(0,t]时间内离去平均数的渐近展开,给出了便于计算的近似公式,具有重要的应用价值。

Further Analysis of Expected Number of Departures in M/G/1 Queues with Server Vacations

In this paper, the departure processes of M/G/1 queueing systems with single server vacation and multiple server vacations are analyzed. The expressions of the LS transform of the expected number of departures during the time interval (0, t] are obtained. It is shown that the LS transform of the expected number of departures during (O, t] is invariant under the interchange of arrival and service rates in the initially empty M/M/1 queue in which the server begins vacations at t=0 and the length of each vacation has an exponential distribution. Simultaneously the asymptotic expansions of the expected number of departures during (0, t] are also discussed. It is given that the asymptotic formula are convenient in application.