Scheduling Jobs Subject to Nonhomogeneous Poisson Shocks

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Abstract
Consider n tasks which must be attempted in some order. To successfully complete any given task requires a random amount of time. However, we suppose that there are external events, called shocks, which occur according to a nonhomogeneous Poisson process. If no shocks occur while a task is being performed, then that task is considered a success. If a shock does occur, then work on that task ends and work on the next one begins. We consider such problems as maximizing The expected number of successful tasks; The length of time until no tasks remain; The expected total reward earned; where a reward R1 is obtained upon successful completion of task i.

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