SCHEDULING JOBS SUBJECT TO NON-HOMOGENEOUS POISSON SHOCKS

Consider n tasks which must be attempted in some order. To successfully complete any given task requires a random amount of time. However, 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. The authors consider such problems as maximizing: (i) The expected number of successful tasks; (ii) The length of time until no tasks remain; (iii) The expected total reward earned; where a reward R//i is obtained upon successful completion of task i.