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Mathematics for Networking Y.C. Tay National University of Singapore.

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Presentation on theme: "Mathematics for Networking Y.C. Tay National University of Singapore."— Presentation transcript:

1 Mathematics for Networking Y.C. Tay National University of Singapore

2 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers)

3 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering Leland, Taqqu, Willinger, Wilson: On the self-similar nature of Ethernet traffic. SIGCOMM 1993 Medina, Taft, Salamatian, Bhattacharyya, Diot Traffic matrix estimation: existing techniques and new directions SIGCOMM 2002

4 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering Leland, Taqqu, Willinger, Wilson: On the self-similar nature of Ethernet traffic. SIGCOMM 1993 Medina, Taft, Salamatian, Bhattacharyya, Diot Traffic matrix estimation: existing techniques and new directions SIGCOMM 2002 stochastic analysis QoS mobility Jiang A basic stochastic network calculus SIGCOMM 2006 Grossglauser and Tse, Mobility increases the capacity of ad hoc wireless networks INFOCOM 2001

5 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility Jiang A basic stochastic network calculus SIGCOMM 2006 Grossglauser and Tse, Mobility increases the capacity of ad hoc wireless networks INFOCOM 2001 markov chains sensors wireless Bianchi Performance analysis of the IEEE 802. 11 distributed coordination function JSAC 2000 Shah, Roy, Jain, Brunette Data Mules: Modeling and analysis of a three-tier architecture for sparse sensor networks Ad Hoc Networks 2003

6 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless Bianchi Performance analysis of the IEEE 802. 11 distributed coordination function JSAC 2000 Shah, Roy, Jain, Brunette Data Mules: Modeling and analysis of a three-tier architecture for sparse sensor networks Ad Hoc Networks 2003 queueing theory Menth, Martin, Charzinski Capacity overprovisioning for networks with resilience requirements SIGCOMM 2006 Wu, Regit Effective capacity: A wireless link model for support of quality of service IEEE Trans. Wireless Comm. 2003

7 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory Menth, Martin, Charzinski Capacity overprovisioning for networks with resilience requirements SIGCOMM 2006 Wu, Regit Effective capacity: A wireless link model for support of quality of service IEEE Trans. Wireless Comm. 2003 scheduling switches Iyer, McKeown Analysis of the parallel packet switch architecture IEEE/ACM Trans. Networking 2003 Kansal, Potter, Srivastava Performance aware tasking for environmentally powered sensors SIGMETRICS 2004

8 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches Iyer, McKeown Analysis of the parallel packet switch architecture IEEE/ACM Trans. Networking 2003 Kansal, Potter, Srivastava Performance aware tasking for environmentally powered sensors SIGMETRICS 2004 (non)linear programming Kelly Charging and rate control for elastic traffic European Trans. on Telecom. 1997 Kodialam, Nandagopal Characterizing the capacity region in multi-radio multi-channel wireless mesh networks Mobicom 2005

9 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches (non)linear programming Kelly Charging and rate control for elastic traffic European Trans. on Telecom. 1997 Kodialam, Nandagopal Characterizing the capacity region in multi-radio multi-channel wireless mesh networks Mobicom 2005 game theory TCP routing Akella, Seshan, Karp, Shenker, Papadimitriou Selfish behavior and stability of the Internet: a game-theoretic analysis of TCP SIGCOMM 2002 Roughgarden, Tardos How bad is selfish routing? JACM 2002

10 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches (non)linear programming game theory TCP routing Akella, Seshan, Karp, Shenker, Papadimitriou Selfish behavior and stability of the Internet: a game-theoretic analysis of TCP SIGCOMM 2002 Roughgarden, Tardos How bad is selfish routing? JACM 2002 control theory security multimedia Kaafar, Mathy, Barakat, Salamatian, Turletti, Dabbous Securing Internet coordinate embedding systems SIGCOMM 2007 He, Nahrstedt, Liu End-to-end delay control of multimedia applications over multihop wireless links ACM TOMCCAP 2008

11 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches (non)linear programming game theory TCP routing control theory security multimedia Kaafar, Mathy, Barakat, Salamatian, Turletti, Dabbous Securing Internet coordinate embedding systems SIGCOMM 2007 He, Nahrstedt, Liu End-to-end delay control of multimedia applications over multihop wireless links ACM TOMCCAP 2008 differential equations P2P Zou, Gong, Towsley. Code red worm propagation modeling and analysis CCS 2002 Qiu, Srikant. Modeling and performance analysis of BitTorrent-like Peer-to-Peer Networks SIGCOMM 2004

12 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches (non)linear programming game theory TCP routing control theory security multimedia differential equations P2P Zou, Gong, Towsley. Code red worm propagation modeling and analysis CCS 2002 Qiu, Srikant. Modeling and performance analysis of BitTorrent-like Peer-to-Peer Networks SIGCOMM 2004 coding theory multicast Byers, Luby, Mitzenmacher, Rege. A digital fountain approach to reliable distribution of bulk data SIGCOMM 98 Ahlswede, Cai, Li, Yeung Network information flow IEEE Trans. Information Theory 2000

13 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches (non)linear programming game theory TCP routing control theory security multimedia differential equations P2P coding theory multicast Byers, Luby, Mitzenmacher, Rege. A digital fountain approach to reliable distribution of bulk data SIGCOMM 98 Ahlswede, Cai, Li, Yeung Network information flow IEEE Trans. Information Theory 2000 graph theory Kleinberg The small-world phenomenon: an algorithm perspective STOC 2000 Li, Alderson, Willinger, Doyle A first-principles approach to understanding the Internet's router-level topology SIGCOMM 2004

14 your favourite mathematical topic your favourite networking topic examples (recent or well-cited papers) statistics traffic engineering stochastic analysis QoS mobility markov chains sensors wireless queueing theory scheduling switches (non)linear programming game theory TCP routing control theory security multimedia differential equations P2P coding theory multicast graph theory Kleinberg The small-world phenomenon: an algorithm perspective STOC 2000 Li, Alderson, Willinger, Doyle A first-principles approach to understanding the Internet's router-level topology SIGCOMM 2004 logic BGP Wang, Jia, Liu, Loo, Sokolsky, Basu Formally verifiable networking HotNets 2009 Karsten, Keshav, Prasad,Beg An axiomatic basis for communication SIGCOMM 2007

15 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed?

16 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed? feedback -- retransmissions: dropped packets collisions

17 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed? feedback -- retransmissions: dropped packets collisions -- congestion-induced user behavior: aborted transfers shortened sessions

18 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed? feedback -- retransmissions: dropped packets collisions -- congestion-induced user behavior: aborted transfers shortened sessions wireless interference: not pairwise not binary

19 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed? feedback -- retransmissions: dropped packets collisions -- congestion-induced user behavior: aborted transfers shortened sessions wireless interference: not pairwise not binary optimality: wireless sensitivity human rationality

20 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed? feedback -- retransmissions: dropped packets collisions -- congestion-induced user behavior: aborted transfers shortened sessions wireless interference: not pairwise not binary optimality: wireless sensitivity human rationality closed form expressions: iterative solutions implicit solutions

21 your favourite mathematical topic your favourite networking topic some issues stochastic analysis markov chains queueing theory scheduling (non)linear programming control theory differential equations logic graph theory coding theory game theory statistics security QoS multimedia P2P traffic engineering multicast BGP TCP switches routing mobility sensors wireless timescale (milliseconds or seconds or hours): steady state? independent, identically distributed? feedback -- retransmissions: dropped packets collisions -- congestion-induced user behavior: aborted transfers shortened sessions wireless interference: not pairwise not binary optimality: wireless sensitivity human rationality closed form expressions: iterative solutions implicit solutions

22 Mathematics for Networking Y.C. Tay National University of Singapore http://www.math.nus.edu.sg/~mattyc/NetMaths.ppt

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