AN OPTIMAL POLICY TO MINIMIZE EXPECTED TARDINESS COST DUE TO WAITING TIME IN THE QUEUE

摘要

We consider a discrete time queueing system. The service time and the interarrival time have geometric distributions. We assume that there is a single decision maker (DM) who has a task (Task A (TA)) which need to be processed by the server of the queueing system and another task (Task B (TB)) which is processed outside the queue and need a constant time. While processing TB, DM observes the queue at every unit time and can interrupt TB to join the queue, but DM cannot process TB while in the queueing system. After TA is finished, DM resumes TB. There is a deadline to process both tasks and if the both tasks are finished beyond the deadline, a tardiness cost is incurred. We aim at minimizing the tardiness cost and show the properties of the optimal policy.