带启动时间的Geom／Geom／1多重工作休假排队

摘要

A Geo/Geo/1 queue model with Set - up Time and Working Vacations is studied. The server works at a lower rate rather than completely stops service during the vacation time. Using quasi - birth - death and matrix - geometric solution method, the steady - state distributions for queue size is given. Additionally, we obtain the average number of the customers and the average sojourn time of a customer in the stationary state.%本文中研究了一个带有启动时间的Geom／Geom／1多重工作休假排队模型。服务台在休假期间，不停止服务，而是以较低的服务率为顾客提供服务。运用拟生灭过程和矩阵几何解的方法，给出了该模型的稳态队长分布，并求出了平均队长以及顾客的平均逗留时间。