Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling

We consider online algorithms for pull-based broadcast scheduling. In this setting there are n pages of information at a server and requests for pages arrive online. When the server serves (broadcasts) a page p, all outstanding requests for that page are satisfied. We study two related metrics, namely maximum response time (waiting time) and maximum delay-factor and their weighted versions. We obtain the following results in the worst-case online competitive model. We show that FIFO (first-in first-out) is 2-competitive even when the page sizes are different. Previously this was known only for unit-sized pages [10] via a delicate argument. Our proof differs from [10] and is perhaps more intuitive. We give an online algorithm for maximum delay-factor that is O(1/e 2)-competitive with (1 + e)-speed for unit-sized pages and with (2 + e)-speed for different sized pages. This improves on the algorithm in [13] which required (2 + e)-speed and (4 + e)-speed respectively. In addition we show that the algorithm and analysis can be extended to obtain the same results for maximum weighted response time and delay factor. We show that a natural greedy algorithm modeled after LWF (Longest-Wait-First) is not O(1)-competitive for maximum delay factor with any constant speed even in the setting of standard scheduling with unit-sized jobs. This complements our upper bound and demonstrates the importance of the tradeoff made in our algorithm.

[1]  Rajmohan Rajaraman,et al.  Improved algorithms for stretch scheduling , 2002, SODA '02.

[2]  Benjamin Moseley,et al.  Online scheduling to minimize the maximum delay factor , 2008, SODA.

[3]  J. Wong,et al.  Broadcast Delivery , 1988, Proc. IEEE.

[4]  Kirk Pruhs,et al.  Multicast Pull Scheduling: When Fairness Is Fine , 2003, Algorithmica.

[5]  Prudence W. H. Wong,et al.  New Results on On-Demand Broadcasting with Deadline via Job Scheduling with Cancellation , 2004, COCOON.

[6]  Kirk Pruhs,et al.  A maiden analysis of longest wait first , 2005, TALG.

[7]  Joseph Y.-T. Leung,et al.  Handbook of Scheduling: Algorithms, Models, and Performance Analysis , 2004 .

[8]  Rajiv Gandhi,et al.  Algorithms for Minimizing Response Time in Broadcast Scheduling , 2002, IPCO.

[9]  Nikhil Bansal,et al.  Improved approximation algorithms for broadcast scheduling , 2006, SODA '06.

[10]  Michael A. Bender,et al.  Flow and stretch metrics for scheduling continuous job streams , 1998, SODA '98.

[11]  Joseph Naor,et al.  Approximating the average response time in broadcast scheduling , 2005, SODA '05.

[12]  Benjamin Moseley,et al.  Longest Wait First for Broadcast Scheduling , 2009, ArXiv.

[13]  Bala Kalyanasundaram,et al.  Scheduling Broadcasts in Wireless Networks , 2000, ESA.

[14]  Michael A. Bender,et al.  Scheduling algorithms for procrastinators , 2008, J. Sched..

[15]  Kirk Pruhs,et al.  A Comparison of Multicast Pull Models , 2002, ESA.

[16]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[17]  Rajiv Gandhi,et al.  Algorithms for Minimizing Response Time in Broadcast Scheduling , 2002, Algorithmica.

[18]  Marek Chrobak,et al.  A Note on Scheduling Equal-Length Jobs to Maximize Throughput , 2006, J. Sched..

[19]  Rajiv Gandhi,et al.  Dependent rounding and its applications to approximation algorithms , 2006, JACM.

[20]  Jae-Hoon Kim,et al.  Scheduling Broadcasts with Deadlines , 2003, COCOON.

[21]  Jacques Carlier,et al.  Handbook of Scheduling - Algorithms, Models, and Performance Analysis , 2004 .

[22]  Samir Khuller,et al.  Broadcast scheduling: Algorithms and complexity , 2008, TALG.

[23]  Stanley B. Zdonik,et al.  Dissemination-based data delivery using broadcast disks , 1995, IEEE Wirel. Commun..

[24]  Nikhil Bansal,et al.  Improved approximation algorithms for broadcast scheduling , 2006, SODA 2006.

[25]  Thomas Erlebach,et al.  NP-Hardness of Broadcast Scheduling and Inapproximability of Single-Source Unsplittable Min-Cost Flow , 2002, SODA '02.

[26]  Feifeng Zheng,et al.  Improved on-line broadcast scheduling with deadlines , 2008, J. Sched..

[27]  Michael J. Franklin,et al.  On-Demand Broadcast Scheduling , 1999 .

[28]  Feifeng Zheng,et al.  Improved On-Line Broadcast Scheduling with Deadlines , 2006, COCOON.

[29]  Benjamin Moseley,et al.  Longest Wait First for Broadcast Scheduling [Extended Abstract] , 2009, WAOA.

[30]  Kirk Pruhs.  Competitive online scheduling for server systems , 2007, PERV.

[31]  Michael J. Franklin,et al.  R × W: a scheduling approach for large-scale on-demand data broadcast , 1999, TNET.

[32]  S. Muthukrishnan,et al.  Minimizing maximum response time in scheduling broadcasts , 2000, SODA '00.