Asymptotically Optimal Lagrangian Priority Policy for Deadline Scheduling with Processing Rate Limits

Abstract

We study the deadline scheduling problem for multiple deferrable jobs that arrive in a random manner and are to be processed before individual deadlines. The processing of the jobs is subject to a time-varying limit on the total processing rate at each stage. We formulate the scheduling problem as a restless multi-armed bandit (RMAB) problem. Relaxing the scheduling problem into multiple independent single-arm scheduling problems, we define the Lagrangian priority value as the greatest tax under which it is optimal to activate the arm, and establish the asymptotic optimality of the proposed Lagrangian priority policy for large systems. Numerical results show that the proposed Lagrangian priority policy achieves 22%-49% higher average reward than the classical Whittle index policy (that does not take into account the processing rate limits).