Online algorithms for the provision of quality of service in networks

Abstract

New Internet applications require the underlying network to provide different levels of more reliable service. The concept of Quality of Service (QoS) was designed to meet this demand. A number of algorithmic issues arise in the provision of QoS, and in this study we consider three related online scheduling problems for QoS. These three problems, besides having practical applications, are also of considerable theoretical interest. The first problem is an online preemptive scheduling problem, in which a set of jobs with varying release times, deadlines, processing times and weights must be scheduled so as to maximize the total value obtained. Unlike classical scheduling problems, partially completed jobs can obtain partial values proportional to their amounts processed. This problem has applications in multimedia QoS provisioning in networks as well as other practical applications. The second problem is a packet scheduling problem for network switches supporting QoS. Packets with different QoS values arrive at a network switch and are to be sent along an outgoing link. Due to overloading conditions, some packets have to be dropped. The objective is to maximize the total value of packets that are sent. We formulate this as an online unit job scheduling problem, where each job is specified by its release time, deadline, and weight. In the third problem, a set of pages is to be broadcasted to clients on demand. Requests asking for the same page can be satisfied in a single broadcast. Each request is associated with a deadline, and the objective is to maximize the profit on requests satisfied before their deadlines. We provide new and improved online algorithms and lower bounds on the competitive ratios for these problems. In some cases the bounds are tight. Some major contributions include: (1) a 1.58-competitive timesharing algorithm for the scheduling of jobs with partial values, and a 1.618 lower bound on the competitive ratio of non-timesharing algorithms; (2) a randomized lower bound of 1.25 which applies simultaneously to the scheduling of partial value jobs, unit jobs,' and broadcasts with deadlines, as well as their variations; (3) optimal and improved algorithms for some special cases of unit job scheduling; and (4) extension of the scheduling problems to the multiprocessor case, including a new multiprocessor algorithm for unit job scheduling. We also show that the three problems have interesting connections, and that some of the techniques we have developed can be applied to more than one of these problems.