Abstract： 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.
2011, Vol. 32 
