A multiobjective control approach to priority queues

Abstract.

This paper introduces a multiobjective control formulation of the priority assignment (PA) problem for a discrete-time single-server queueing system with q competing classes of customers, and the discounted cost criterion. A multiobjective priority assignment (MPA) problem is presented, which is analyzed from the viewpoint of both Pareto and lexicographic optimality. The cμ-rule, which is a well known optimal control policy for the PA problem, is shown to be Pareto optimal, strong Pareto optimal with respect to a certain norm on ℝ^q, and also lexicographically optimal for MPA. These results are used to study a constrained PA problem.