Admission Control to M/G/1 Subject to General Class-Specific Admission and Rejection Costs

We consider the M/G/1 queue where job sizes become known upon arrival subject to a general cost structure. More specifically, we are interested in determining the optimal admission policy to the (size-aware) system with multiple job-classes each having its own admission and rejection costs. The cost for admitting a job is a class-specific function of the waiting time. As a special case, we consider a deadline cost structure where admitting a job that will be late has a smaller cost than rejecting it. We analyse the system within the framework of Markov decision processes, and derive expressions that enable us to determine the size-aware value function, and the optimal class-specific admission control, as well as the resulting mean cost. The availability of the value function allows one to develop efficient dispatching policies for a system with heterogeneous parallel servers.