mathematics for networking y.c. tay national university of singapore
TRANSCRIPT
Mathematics for Networking
Y.C. TayNational University of Singapore
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
your favourite mathematical
topic
your favourite networking
topicexamples (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, DiotTraffic matrix estimation: existing techniques and new directions
SIGCOMM 2002
your favourite mathematical
topic
your favourite networking
topicexamples (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, DiotTraffic matrix estimation: existing techniques and new directions
SIGCOMM 2002stochasticanalysis QoS
mobility
JiangA basic stochastic network calculus
SIGCOMM 2006
Grossglauser and Tse,Mobility increases the capacity of ad hoc wireless networks
INFOCOM 2001
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
JiangA basic stochastic network calculus
SIGCOMM 2006
Grossglauser and Tse,Mobility increases the capacity of ad hoc wireless networks
INFOCOM 2001
markovchains
sensors
wireless
BianchiPerformance analysis of the IEEE 802. 11
distributed coordination functionJSAC 2000
Shah, Roy, Jain, BrunetteData Mules: Modeling and analysis of a three-tier
architecture for sparse sensor networksAd Hoc Networks 2003
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
BianchiPerformance analysis of the IEEE 802. 11
distributed coordination functionJSAC 2000
Shah, Roy, Jain, BrunetteData Mules: Modeling and analysis of a three-tier
architecture for sparse sensor networksAd Hoc Networks 2003
queueingtheory
Menth, Martin, CharzinskiCapacity overprovisioning for networks with
resilience requirementsSIGCOMM 2006
Wu, RegitEffective capacity: A wireless link model for support of
quality of serviceIEEE Trans. Wireless Comm. 2003
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
Menth, Martin, CharzinskiCapacity overprovisioning for networks with
resilience requirementsSIGCOMM 2006
Wu, RegitEffective capacity: A wireless link model for support of
quality of serviceIEEE Trans. Wireless Comm. 2003
scheduling
switches
Iyer, McKeownAnalysis of the parallel packet switch architecture
IEEE/ACM Trans. Networking 2003
Kansal, Potter, SrivastavaPerformance aware tasking for environmentally powered sensors
SIGMETRICS 2004
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
Iyer, McKeownAnalysis of the parallel packet switch architecture
IEEE/ACM Trans. Networking 2003
Kansal, Potter, SrivastavaPerformance aware tasking for environmentally powered sensors
SIGMETRICS 2004
(non)linear programming
KellyCharging and rate control for elastic traffic
European Trans. on Telecom. 1997
Kodialam, NandagopalCharacterizing the capacity region in multi-radio
multi-channel wireless mesh networksMobicom 2005
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
(non)linear programming
KellyCharging and rate control for elastic traffic
European Trans. on Telecom. 1997
Kodialam, NandagopalCharacterizing the capacity region in multi-radio
multi-channel wireless mesh networksMobicom 2005
gametheory
TCP
routingAkella, Seshan, Karp, Shenker, PapadimitriouSelfish behavior and stability of the Internet:
a game-theoretic analysis of TCPSIGCOMM 2002
Roughgarden, TardosHow bad is selfish routing?
JACM 2002
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
(non)linear programming
gametheory
TCP
routingAkella, Seshan, Karp, Shenker, PapadimitriouSelfish behavior and stability of the Internet:
a game-theoretic analysis of TCPSIGCOMM 2002
Roughgarden, TardosHow bad is selfish routing?
JACM 2002
control theory
security
multimedia
Kaafar, Mathy, Barakat, Salamatian, Turletti, DabbousSecuring Internet coordinate embedding systems
SIGCOMM 2007
He, Nahrstedt, LiuEnd-to-end delay control of multimedia
applications over multihop wireless linksACM TOMCCAP 2008
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
(non)linear programming
gametheory
TCP
routing
control theory
security
multimedia
Kaafar, Mathy, Barakat, Salamatian, Turletti, DabbousSecuring Internet coordinate embedding systems
SIGCOMM 2007
He, Nahrstedt, LiuEnd-to-end delay control of multimedia
applications over multihop wireless linksACM 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 NetworksSIGCOMM 2004
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
(non)linear programming
gametheory
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 NetworksSIGCOMM 2004
coding theory
multicast
Byers, Luby, Mitzenmacher, Rege.A digital fountain approach to reliable distribution of bulk data
SIGCOMM 98
Ahlswede, Cai, Li, YeungNetwork information flow
IEEE Trans. Information Theory 2000
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
(non)linear programming
gametheory
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, YeungNetwork information flow
IEEE Trans. Information Theory 2000
graphtheory
KleinbergThe small-world phenomenon: an algorithm perspective
STOC 2000
Li, Alderson, Willinger, DoyleA first-principles approach to understanding the
Internet's router-level topologySIGCOMM 2004
your favourite mathematical
topic
your favourite networking
topicexamples (recent or well-cited papers)
statistics
traffic engineering
stochasticanalysis QoS
mobility
markovchains
sensors
wireless
queueingtheory
scheduling
switches
(non)linear programming
gametheory
TCP
routing
control theory
security
multimedia
differential equations
P2P
coding theory
multicast
graphtheory
KleinbergThe small-world phenomenon: an algorithm perspective
STOC 2000
Li, Alderson, Willinger, DoyleA first-principles approach to understanding the
Internet's router-level topologySIGCOMM 2004
logic
BGP
Wang, Jia, Liu, Loo, Sokolsky, Basu Formally verifiable networking
HotNets 2009
Karsten, Keshav, Prasad,BegAn axiomatic basis for communication
SIGCOMM 2007
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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?
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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
your favourite mathematical
topic
your favourite networking
topicsome issues
stochasticanalysis
markovchains
queueingtheory
scheduling
(non)linear programming
control theory
differential equations
logic
graphtheory
coding theory
gametheory
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
Mathematics for Networking
Y.C. TayNational University of Singapore
http://www.math.nus.edu.sg/~mattyc/NetMaths.ppt