Online Maximizing Weighted Throughput in a Fading Channel

Abstract

We consider online scheduling weighted packets with time constraints over a fading channel. Packets arrive at the transmitter in an online manner. Each packet has a value and a deadline by which it should be sent. The fade state of the channel determines the throughput obtained per unit of time and the channel's quality may change over time. In this paper, we design online algorithms to maximize weighted throughput, defined as the total value of the packets sent by their respective deadlines. Competitive ratio is employed to measure an online algorithm's performance. For this problem and one of its variants, we present two online algorithms with competitive ratios 2.618 and 2 respectively. IntroductionTime-varying signal strength is a fundamental characteristic of wireless channels. Scheduling packets over fading wireless channels has received much attention (see [9,5,8,10, 2] and the references therein). A scheduling algorithm can significantly improve the communication performance by taking advantages of the changing channel states. In this paper, we consider scheduling weighted packets with time constraints in an online manner.Resource allocation for fading channels has been a well-studied topic in the area of information theory. The quantity to maximize is often the Shannon capacity, defined as the tightest upper bound of the amount of information (the total number of packets) that can be reliably transmitted over a communication channel. Tse and Hanly [9] have found capacity limits and optimal resource allocation policies for such fading channels. In [5], the authors applied a dynamic programming approach to get the optimal solution for scheduling uniform-value packets under both time and energy constraints. A polynomial-time optimal offline solution of scheduling packets with deadlines was given in [8,10]. In their problem settings, energy is minimized under the assumption that all arriving packets are successfully delivered. An optimal offline algorithm maximizing throughput and a heuristic online approach of scheduling uniform-value packets with possibly different deadlines were given in [2]. No theoretical analysis has been provided for the heuristic online solution. The first work considering scheduling weighted packets is [7], in which an optimal offline algorithm is provided but theoretical analysis of the proposed online algorithm is missing.Note that in previous studies, packets have uniform values (except in [7]) and their arrivals at the transmitter are usually modeled by a Poisson distribution. However, packets from different users and