具有部分备用服务员的M/M/c休假排队

M/M/c vacation queue with partial spare servers

顾客到达是泊松过程,模型具有c个服务员A和d个备用服务员B,1≤d<c.A服务员在岗工作时B服务员备用,上岗服务员若因某种原因休假,备用服务员立即替换上岗,B服务员不休假,A,B服务员的服务时间均服从负指数分布.用拟生灭过程和矩阵几何解的方法得到了稳态队长的分布,在此基础上证明了在服务台全忙条件下的队长和等待时间的条件随机分解,给出了附加队长的母函数和附加延迟的拉普拉斯变换,通过数值例子分析了参数对平均附加队长和平均附加延迟的影响.

Customer arrival is Poisson process with c waiter A and d waiter B,and d is not less than 1,but less than c.When waiter A work,waiter B are spare.If waiter A are on vacation for some reasons,the spare waiter B should replace immediately.Waiter B have no vacation.The service time of waiter A and B show negative exponential distribution.Based on quasi birth and death（QBD） process and matrix geometric solution method,the steady state distribution for queue length was obtained.The conditional stochastic decomposition structures for queue length and waiting time were proved when all the servers are busy.The parent function of additional captain and Laplace transform of additional delay were obtained.The effects of the parameters on the average additional captain and the average additional delay were analyzed by numerical examples.