Dispatching Discrete-Size Jobs with Multiple Deadlines to Parallel Heterogeneous Servers.

Esa Hyytiä, Rhonda Righter, Olivier Bilenne, Xiaohu Wu

Abstract: We study the M/D/1 queue and its generalization, the M/iD/1 queue, when jobs have firm deadlines for waiting (or sojourn) time. If a deadline is not met, a job-specific deadline violation cost is incurred. The M/iD/1 queue enables us to model both varying jobs sizes and batch arrival processes. We derive explicit value functions for these M/D/1-type of queues that enable the development of efficient cost-aware dispatching policies to parallel servers.