Deadline Scheduling as Restless Bandits

Zhe Yu, Yunjian Xu, Lang Tong

Published 2016-10-03Version 1

The problem of stochastic deadline scheduling is considered. A constrained Markov decision process model is introduced in which jobs arrive randomly at a service center with stochastic job sizes, rewards, and completion deadlines.The service provider faces random processing costs, convex non-completion penalties, and a capacity constraint that limits the simultaneous processing of jobs. Formulated as a restless multi-armed bandit problem, the stochastic deadline scheduling problem is shown to be indexable. A closed-form expression of the Whittle's index is obtained for the case when the processing costs are constant. An upper bound on the gap-to-optimality of the Whittle's index policy obtained and is shown converge to zero super exponentially as the number of available processors increases.