Admission and termination control of a two class loss system - Ulukuş, Mehmet Yasin. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009)
In this thesis, we consider admission and termination control policies in a Markovian loss system with two classes of jobs. A class is characterized by the arrival and service rates, in addition to a fixed reward and termination cost. There are three possible decisions upon an arrival: admitting or rejecting the arriving job, or admitting him/her by terminating a job which is already in the system. The aim is to maximize total expected discounted profit over a finite or infinite horizon. We build a Markov decision model to analyze the structure of optimal policies. We prove that when there is an idle server in the system, it is never optimal to terminate a job. In addition, we prove that there exists an optimal threshold policy for admission and termination. The threshold levels depend on the jobs of both classes already being served in the system. Furthermore, under certain conditions, we can ensure that a job class is “preferred” or “strongly-preferred”. Preferred jobs are always admitted to the system if there are free servers. On the other hand, a strongly-preferred job is always admitted to the system even when the system is full, so that a job of the other class is terminated by incurring the termination cost. We show that both job types cannot be strongly preferred, although it is possible that one of them is strongly-preferred, and the other one is preferred.
Keywords: Markov processes.