Analysis of a priority polling system with group services

We consider a priority polling system consisting of two queues attended by a single server. Type i customers arrive to queue i according to a homogeneous Poisson process with rate λ i . Queue i has its own buffer of finite capacity K i for i= 1 2. Customers are served in groups, with the group service time distributed according to distribution with mean . The distribution is assumed to be independent of the group size. The service discipline is as follows: at the completion of a service (of any type) the server polls queue 1 and serves all waiting customers at the same time. If there are no customers waiting in queue 1, the server polls queue 2 and serves the group that it finds upon its arrival to queue 2. If the system is empty, the server waits for the first arrival. Customers who arrive during a service wait until the server becomes free. The steady-state analysis of the model is carried out by deriving expressions for the distribution of the number of type i customers in the queue and the waiting tim...