Optimal scheduling of two competing queues with blocking

Consideration is given to the problem of optimal scheduling for two queues competing for service at a single station, where the queues have finite capacities and the service rate is class-dependent. The cost structure is linear in the number of holding customers in the queues, combined with blocking costs incurred whenever arrivals encounter a full queue. It is shown that the optimal policy minimizing this criterion is of the switching type if the blocking cost is larger than the holding cost for each queue. Under certain conditions on the cost parameters, the optimal policy is shown to become a fixed-priority rule, whereas in an extreme but useful case it becomes threshold-based. Numerical computations are included to validate the analytical findings. Finally, the authors consider a practically tractable performance criterion and develop an adaptive control adjustment scheme for the threshold-based policy, using online performance sensitivity estimation