Dispatching fixed-sized jobs with multiple deadlines to parallel heterogeneous servers

We study the M/D/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. We derive explicit value functions for this M/D/1 queue that enable the development of efficient cost-aware dispatching policies to parallel servers. The performance of the resulting dispatching policies is evaluated by means of simulations.