Optimal QoS control of interacting service stations

¹ Faculté des Sciences et Techniques, Département de Mathématiques et Informatique, route de Casablanca, BP. 577, Settat, Maroc; haqiq@netscape.net.
² Carleton University, Department of Systems and Computer Engineering, 1125 Colonel By Drive, Ottawa, Ontario, K1 S5 B6, Canada
³ Faculté des Sciences Mirande, Laboratoire Informatique de Recherche sur les Systèmes Intelligents et leurs Applications, BP. 47870, 21078 Dijon Cedex, France
⁴ University of Ottawa, School of Information, Technology and Engineering, 161 Louis Pasteur, Ottawa, Ontario, K1 N6 N5, Canada

Received: May 2001

Abstract

We consider a system of three queues and two types of packets. Each packet arriving at this system finds in front of it a controller who either sends it in the first queue or rejects it according to a QoS criterion. When the packet finishes its service in the first queue, it is probabilistically routed to one of two other parallel queues. The objective is to minimize a QoS discounted cost over an infinite horizon. The cost function is composed of a waiting cost per packet in each queue and a rejection cost in the first queue. Subsequently, we generalize this problem by considering a system of (m+1) queues and n types of packets. We show that an optimal policy is monotonic.