Stability of a queue with discriminatory random order service discipline and heterogeneous servers

We consider a queueing system with two classes of customers, two heterogeneous servers, and discriminatory random order service (DROS) dis cipline. The two servers may have either the same or different DROS weights for each class. Customers of each class arrive according to a Poisson process and the service times of each class of customers are assumed to be exponen tially distributed with service rate depending on both the customer's class and the servers. We provide stability and instability conditions for this two-class two-server queue with DROS discipline.