Technical Note—Stochastic Scheduling with Abandonment: Necessary and Sufficient Conditions for the Optimality of a Strict Priority Policy

We consider a stochastic scheduling problem in clearing systems with two types of jobs, each characterized by a general service time distribution, an exponentially distributed lifetime, and a reward. A job abandons the system if its waiting time in the queue is larger than its lifetime. Preemption is not allowed. The objective is to maximize the total expected reward. When service times are homogeneous, we provide a set of necessary and sufficient conditions for the optimality of a strict priority policy. When service times are heterogeneous and exponentially distributed, we conjecture a set of necessary conditions, which would also be sufficient when one parameter is identical (reward or lifetime rate) for the two types of jobs.