We consider the problem of dynamic admission control in a Markovian loss queueing system with two classes of jobs with different service rates and random revenues. We establish the existence of an optimal monotone policy. We also show that under certain conditions there exist preferred jobs from either class.

In this paper we are going to develop group replacement policies for a service system by considering the number of customers dynamically in the queue. We consider a service system with multiple independent servers operating in parallel and a single queue. Customers arrive in accordance with a Poisson process, and the service time for each customer follows an exponential distribution. The servers are unreliable with identically exponentially distributed failure times and the repair time is assumed negligible. We formulate this model as a continuous time Markov decision process, and prove the optimal group replacement policy has a threshold structure.