Exclusion in a priority queue

We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally asymmetric exclusion process with a dynamically varying lattice length. We calculate exact local density profiles for an unbounded queue by deriving domain wall dynamics from the microscopic transition rules. The structure of the unbounded queue carries over to bounded queues where, although no longer exact, we find the domain wall theory is in very good agreement with simulation results. Within this approximation we calculate average waiting times for queueing customers.