具有可利用服务员的M／G／1排队模型(英文)

M/G/1 Queue with an Available Server

本文考虑了具有可利用服务员的M／G／1有有限容量的排队模型．当工作量超过k(k是常数或者随机变量),可利用服务员参与工作,一直到工作量少于或等于k．可利用服务员的速率依赖于目前工作量．应用Level-crossing方法,获得了工作量的平稳分布．应用Kolmogorov向后微分方程方法,构造更新方程以获得忙期的Laplace变换．

We consider M/G/1 queue with an available server, which is infinite capacity with Poisson arrivals. When the workload exceeds k （k 〉 0 is a constant or a random variable）, an available server attends and works with initial server until the workload is less than or equal to k. The available server＇s rate depends on the workload present. Applying the level-crossing argument, we show the steady-state distribution of the workload. Also using the Kolmogorov＇s backward differential equation, we construct renewal equations to get the Laplace transform of the busy period.