earticle

영어

We consider a single server queue in which multi-class customers arrive ac-cording to Poisson process and service times are exponentially distributed. The server works following a gate mechanism in which arriving customers do not en-ter service immediately and wait to form a batch. This batch of customers get service after the completion of service to the previous batch. We also assume that after the service time of all customers, a customer of one class may join the next batch to get the service of another or the same class. The number of customers in a batch, duration of service time to a batch and the probability for the busy period to end in ¯nite time are obtained. Elegant expressions are obtained when there are only two classes. These results are extended to multi-class customers in a varying environment. The connections between queues and branching processes is exploited to obtain these results. Numerical illustrations are presented.