On Packet Scheduling with Adversarial Jamming and Speedup

In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes. Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these properties in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of $\phi+1\approx 2.618$ on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in $[1,4)$ and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al. and the lower bound by Anta et al.Comment: Appeared in Proc. of the 15th Workshop on Approximation and Online Algorithms (WAOA 2017

Tians scheduling: Using partial processing in best-effort applications

Abstract-To service requests with high quality, interactive services such as web search, on-demand video and online gaming keep average server utilization low. As servers become busy, queuing delays increase, and requests miss their deadlines, resulting in degraded quality of service with poor user experience and potential revenue loss. In this paper, we propose Tians scheduling, a group of scheduling algorithms for interactive services that can produce partial answers during overload. A Tians scheduler allocates processing time to each request based on system load with the objective of maximizing overall quality of responses. We propose three Tians scheduling algorithms -offline, online clairvoyant and online nonclairvoyant. For interactive applications with concave quality profile, we prove that the offline algorithm is optimal. We show the effectiveness of the online algorithms by conducting a simulation study modeling important applications -a web search engine and video-ondemand (VOD) system. Simulation results show a significant improvement of Tians over traditional server models: average response quality improves and the variance of responses decreases. Keywords-interactive services, best-effort applications, offline, online clairvoyant, online nonclairvoyant, partial results, quality profile, scheduling, VOD bandwidth allocation, web search engine

On-Line Scheduling with Tight Deadlines

This paper is concerned with the on-line problem of scheduling jobs with tight deadlines in a single-processor system. It has been known for long that in such a setting, no on-line algorithm is optimal (or 1-competitive) in the sense of matching the optimal o-line algorithm on the total value of jobs that meet the deadline

On-line Scheduling with Tight Deadlines

This paper is concerned with the on-line problem of scheduling jobs with tight deadlines in a uni-processor system. It has been known for long that in such a setting, no on-line algorithm is 1-competitive (i.e., optimal) in the sense of matching the optimal off-line algorithm on the total value of jobs that meet the deadlines; indeed, no algorithm can be better than k-competitive, where k is the importance ratio of the jobs. Recent work, however, reveals that the competitive ratio can be improved to a constant if the on-line scheduler is equipped with a processor O(1) times faster [9], and further to one when using a processor O(log k) times faster [13]. This paper presents a new on-line algorithm for scheduling jobs with tight deadlines and shows that it is 1-competitive when using a processor that is only O(1) times faster