Mehmet Yasin Ulukuş, Refik Güllü and Lerzan Örmeci. ADMISSION AND TERMINATION CONTROL OF A TWO-CLASS LOSS SYSTEM

Abstract. In this talk, we consider admission and termination control policies in
a Markovian loss system with two classes of jobs. Each class has a
different arrival and service rate, as well as a different fixed reward
and termination cost. There are three possible decisions upon an
arrival: admitting or rejecting the arriving customer, or admitting
him/her by terminating a customer who 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 customer. In
addition, we prove that there exists an optimal threshold policy. The
threshold levels depend on the customers of both classes already being
served in the system. Furthermore, under certain conditions, we can
ensure that a customer class is *preferred* or
*strongly-preferred*.  Preferred customers are always admitted to
the system if there are free servers. On the other hand, a
strongly-preferred customer is always admitted to the system even if the
system is full, so that a customer of the other class is terminated by
incurring the termination cost. We show that both customer types cannot
be strongly preferred, although it is possible that one of them is
strongly-preferred, and the other one is preferred. Computational
results will be presented to illustrate some of the analytical results.