Online Scheduling of Equal-Length Jobs: Randomization and Restarts Help

We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor, non-preemptive schedule of these jobs that maximizes the number of completed jobs. In the online version, each job arrives at its release time. We give two online algorithms with competitive ratios below 2 and show several lower bounds on the competitive ratios. First, we give a -competitive randomized algorithm. Our algorithm needs only one fair random bit, as it chooses one of two (nearly identical) deterministic algorithms, each with probability . We also show a lower bound of for barely random algorithms, that (with arbitrary probability) choose one of two deterministic algorithms. Next, we give a deterministic -competitive algorithm in the model that allows restarts, and we show that in this model the ratio is optimal. For randomized algorithms with restarts we show a lower bound of

Online scheduling of equal-length jobs: Randomization and restarts help

We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor, non-preemptive schedule that maximizes the number of completed jobs. In the online version, each job arrives at its release time. We give two online algorithms with competitive ratios below 2 and show several lower bounds on the competitive ratios. First, we give a barely random 5/3-competitive algorithm that uses only one random bit. We also show a lower bound of 3/2 on the competitive ratio of barely random algorithms that randomly choose one of two deterministic algorithms. If the two algorithms are selected with equal probability, we can further improve the bound to 8/5. Second, we give a deterministic 3/2-competitive algorithm in the model that allows restarts, and we show that in this model the ratio 3/2 is optimal. For randomized algorithms with restarts we show a lower bound of 6/5

Improved Online Algorithms for Buffer Management in QoS Switches

We consider the following buffer management problem arising in QoS networks: packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total value of forwarded packets is maximized. If a packet is not forwarded before its deadline, it is lost and brings no profit. The main result of the paper is an online 64/3

Preemptive Scheduling in Overloaded Systems

The following scheduling problem is studied: We are given a set of tasks with release times, deadlines, and profit rates. The objective is to determine a 1-processor preemptive schedule of the given tasks that maximizes the overall profit. In the standard model, each completed task brings profit, while non-completed tasks do not. In the metered model, a task brings profit proportional to the execution time even if not completed. For the metered task model, we..

Online Competitive Algorithms for Maximizing Weighted Throughput of Unit Jobs

We study an online bu#er management problem for networks supporting Quality-of-Service (QoS) applications. Packets with di#erent 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 scheduling problem for unit-length jobs, where each job is specified by its release time, deadline, and a nonnegative weight (QoS value). The goal is to maximize the weighted throughput, that is the total weight of scheduled jobs