Longest Wait First for Broadcast Scheduling

We consider online algorithms for broadcast scheduling. In the pull-based broadcast model there are $n$ unit-sized pages of information at a server and requests arrive online for pages. When the server transmits a page $p$, all outstanding requests for that page are satisfied. The longest-wait-first} (LWF) algorithm is a natural algorithm that has been shown to have good empirical performance. In this paper we make two main contributions to the analysis of LWF and broadcast scheduling. \begin{itemize} \item We give an intuitive and easy to understand analysis of LWF which shows that it is O(1/\eps^2)-competitive for average flow-time with (4+\eps) speed. Using a more involved analysis, we show that LWF is O(1/\eps^3)-competitive for average flow-time with $(3.4+\epsilon)$ speed. \item We show that a natural extension of LWF is O(1)-speed O(1)-competitive for more general objective functions such as average delay-factor and $L_k$ norms of delay-factor (for fixed $k$). \end{itemize

Online Scheduling to Minimize the Maximum Delay Factor

In this paper two scheduling models are addressed. First is the standard model (unicast) where requests (or jobs) are independent. The other is the broadcast model where broadcasting a page can satisfy multiple outstanding requests for that page. We consider online scheduling of requests when they have deadlines. Unlike previous models, which mainly consider the objective of maximizing throughput while respecting deadlines, here we focus on scheduling all the given requests with the goal of minimizing the maximum {\em delay factor}.We prove strong lower bounds on the achievable competitive ratios for delay factor scheduling even with unit-time requests.For the unicast model we give algorithms that are (1 + \eps)-speed O({1 \over \eps})-competitive in both the single machine and multiple machine settings. In the broadcast model we give an algorithm for similar-sized pages that is (2+ \eps)-speed O({1 \over \eps^2})-competitive. For arbitrary page sizes we give an algorithm that is (4+\eps)-speed O({1 \over \eps^2})-competitive

Equivalence of Two Linear Programming Relaxations for Broadcast Scheduling

Samir Khuller and Yoo-Ah Kim Abstract. A server needs to compute a broadcast schedule for n pages whose request times are known in advance. Outputting a page satisfies all outstanding requests for the page. The goal is to minimize the average waiting time of a client. In this paper we show the equivalence of two apparently different relaxations that have been considered for this problem. Key words: scheduling, broadcasting, approximation algorithms, linear programming 1 Introduction The informal description of the problem is as follows. There are n data items, 1; : : : ; n, called pages. Time is broken into "slots". A time slot is defined as the unit of time to transmit one page on the wireless channel. A request for a page j arrives at time t and then waits. When page j has been transmitted, this request has been satisfied. Arrival times of requests for pages are known, and we wish to find a broadcast schedule that minimizes the average waiting time