Individual, class-based, and social optimal admission policies in two-priority queues

This paper considers the admission control problem for an M/M/1 queueing system serving two classes of customers. Class 1 customers have preemptive resume priority over class 2 customers. Within each class, the service is provided on a first-come, first-served basis. The system is controlled by accepting or rejecting arriving customers. There is a class-dependant reward and holding cost associated with each each accepted customer. The goal is to minimize the expected total discounted net cost. We analyze and compare the optimal control under three criteria: individual optimization, class optimization, and social optimization. We show (i) the optimal policy is of either critical-number or switching-curve form under each optimization criterion, (ii) the class-optimal policy accepts more class 1 customers but less class 2 customers than the socially optimal policy, which has interesting socioeconomic implication, (iii) the individual optimal policy accepts more class 1 customers tahn the class-optimal policy, while it can accept either more or less class 2 customers than either of the two optimal policies.