A Tandem BMAP/G/1 → •/M/N/0 Queue with Group Occupation of Servers at the Second Station

We consider a two-stage tandem queue with single-server first station and multiserver second station. Customers arrive to Station 1 according to a batch Markovian arrival process BMAP . A batch may consist of heterogeneous customers. The type of a customer is determined upon completion of a service at Station 1. The customer’s type is classified based on the number of servers required to process the request of the customer at Station 2. If the required number of servers is not available, the customer may leave the system forever or block Station 1 by waiting for the required number of servers. We determine the stationary distribution of the system states at embedded epochs and derive the Laplace-Stieltjes transform of the sojourn time distribution. Some key performance measures are calculated, and illustrative numerical results are presented.