MULTIPLE SERVER PREEMPTIVE SCHEDULING WITH IMPATIENCE. Issue 2 (31st May 2016) - Cao, Yang
Abstract : There are n customers that need to be served by m parallel servers ( n ≥ m ). Customer i will only wait in queue for an exponentially distributed time with rate λ i before departing the system. The service time on server j is exponentially distributed with rate μ j for all customers, and upon completion of service of customer i a positive reward r i is earned. The non-preemptive problem is to choose, after each service completion, which currently in queue customer to serve next. The preemptive problem is to decide when to preempt a service, and to choose, after each service completion or preemption, which currently in queue customer to serve next. The objective of both problems is to maximize the expected total return. We give conditions under which a list policy is optimal for both problems.