Data Traffic Dynamics and Saturation on a Single Link
The dynamics of User Datagram Protocol (UDP) traffic
over Ethernet between two computers are analyzed using nonlinear
dynamics which shows that there are two clear regimes in the data
flow: free flow and saturated. The two most important variables
affecting this are the packet size and packet flow rate. However,
this transition is due to a transcritical bifurcation rather than phase
transition in models such as in vehicle traffic or theorized large-scale
computer network congestion. It is hoped this model will help lay
the groundwork for further research on the dynamics of networks,
especially computer networks.
[1] D.J. Watts and S.H. Strogatz, "Collective dynamics of -small-world-
networks", Nature, vol. 393, pp.440-442, 1998
[2] R. Albert, H. Jeong, and A.L. Barab'asi, "Diameter of the World-Wide
Web", Nature, vol. 401, pp.130-131, 1999
[3] M.E.J. Newman, "Scientific collaboration networks. I. Network construction
and fundamental results", Phys. Rev. E, vol. 64, 016131, 2001
[4] M.E.J. Newman, "Scientific collaboration networks. II. Shortest paths,
weighted networks, and centrality", Phys. Rev. E, vol. 64, 016132, 2001
[5] S.N. Dorogovtsev and J.F.F. Mendes, "Exactly solvable small-world
network" Europhys. Lett. vol. 50, pp. 1-7, 2000
[6] M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On power-law relationships
of the Internet topology", Comp. Comm. Rev., vol. 29, pp.251-262, 1999
[7] R. Pastor-Satorras R and A. Vespignani, "Epidemic spreading in scalefree
networks", Phys. Rev. Lett., vol. 86, pp.3200-3203, 2001
[8] T. Ohira and R. Sawatari, "Phase transition in a computer network traffic
model", Phys. Rev. E, vol. 58, pp.193-195, 1998
[9] M. Takayasu, H. Takayasu, and K. Fukuda, "Dynamic phase transition
observed in the Internet traffic flow", Physica A, vol. 277, pp.248-255,
2000
[10] R.V. Sol'e and S. Valverde, "Information transfer and phase transitions
in a model of internet traffic ", Physica A, vol. 289, pp.595-605, 2001
[11] L. Zhao, Y.C. Lai, K.H. Park, and N. Ye, "Onset of traffic congestion
in complex networks", Phys. Rev. E, vol. 71, 026125, 2005
[12] L. Lago-Fern'andez, R. Huerta, F. Corbacho, and J. Sig'-uenza, "Fast
Response and Temporal Coherent Oscillations in Small-World Networks",
Phys. Rev.Lett., vol. 84, pp.2758-2761, 2000
[13] S.F. Wang and G.R. Chen, "Synchronization in small-world dynamical
networks", Intl J. of Bifurcation and Chaos, vol. 12, pp.187-192, 2002
[14] H. Hong, Y.M. Choi, and B.J. Kim, "Synchronization on small-world
networks", Phys. Rev. E, vol. 65, 026139, 2002
[15] M. Barahona and L.M. Pecora, "Synchronization in Small-World Systems",
Phys. Rev. Lett., vol. 89, 054101, 2002
[16] E. Almaas, A.N. Oltvai, and A.L. Barab'asi, "The activity reaction core
and plasticity of metabolic networks" PLoS Comp. Bio., vol. 1, pp.557-
563, 2005
[17] R. Guimera and L. Nunes-Amaral, "Functional cartography of complex
metabolic networks" Nature, vol. 433, pp.895-900, 2005
[18] B.S. Kerner and H. Rehborn, "Experimental properties of phase transitions
in traffic flow", Phys. Rev. Lett., vol. 79, pp.4030-4033, 1997
[19] C.F. Daganzo, M.J. Cassidy, and R.L. Bertini, "Causes And Effects Of
Phase Transitions In Highway Traffic (Research Report)", University of
California, Berkeley Institute of Transportation Studies Research Report,
Report No. UCB-ITS-RR-97-8, 1997
[20] D. Chowdhury, L. Santen, and A. Schadschneider, "Statistical Physics
of Vehicular Traffic and Some Related Systems" Phys. Rep., vol. 329,
pp.199-329, 2000
[21] S. G'abor and I. Csabai, "The analogies of highway and computer
network traffic", Physica A, vol. 307, pp.516-526, 2002
[22] Widely Integrated Distributed Environment (WIDE) Project, Kanagawa,
Japan, MAWI Working Group Traffic Archive (WIDE Backbone traffic
traces)[Online]. Available: http://mawi.wide.ad.jp/mawi/
[23] Stanford Linear Accelerator Center (SLAC) PingER End-to-End
Performance Measuring Project [Online]. Available: http://wwwiepm.
slac.stanford.edu/pinger/
[24] H. Chang, S. Jamin, Z.M. Mao, and W. Willinger, "An Empirical
Approach to Modeling Inter-AS Traffic Matrices" in Proc. of the 5th
ACM SIGCOMM Conference on Internet Measurement, Berkeley, CA
2005, pp.139-152
[25] M. Mathis, J. Semke, J. Mahdavi, and T. Ott, "The macroscopic behavior
of the TCP congestion avoidance", Comp. Comm. Rev., vol. 27, no. 3,
pp.67-82, 1997
[26] A. Veres and M. Boda, "The Chaotic Nature of TCP Congestion
Control-, in. Proc. of INFOCOM 2000, vol. 3, Tel Aviv, Israel, 2000,
pp. 1715-1723
[27] W.E. Leland, M.S. Taqqu, W. Willinger, and D.V. Wilson, "On the Self-
Similar Nature of Ethernet Traffic (Extended Version)", IEEE/ACM Trans.
on Networking, vol. 2, pp.1-15, 1994
[28] A. Feldmann, A. Gilbert, and W. Willinger, "Data networks as cascades:
Investigating the multifractal nature of Internet WAN traffic", Proc. of
ACM SIGCOMM -98, Vancouver, Canada, 1998, pp.42-55
[29] S. Uhlig, "Non-stationarity and high-order scaling in TCP flow arrivals:
a methodological analysis", Comp. Comm. Rev., vol. 34, no. 2, pp.9-24,
2004
[30] K. Fukuda, H. Takayasu, and M. Takayasu, "Origin of Critical Behavior
in Ethernet Traffic", Physica A, vol. 287, pp.289-301, 2000
[31] W. Fang and L. Peterson, "Inter-AS traffic patterns and their implications"
in Proc. Of the Global Telecommunications Conference, GLOBECOM
-99, Rio de Janeiro, Brazil, vol. 3, 1999, pp.1859-1868
[32] T. Mori, R. Kawahara, S. Naito, and S. Goto, "On the Characteristics of
Internet Traffic Variability: Spikes and Elephants", in Proc. of the 2004
International Symposium on Applications and the Internet, Tokyo, Japan,
2004, pp.99-106
[33] C. Dovrolis, P. Ramanathan, and D. Moore, "What Do Packet Dispersion
Techniques Measure?" in Proc. of INFOCOM 2001 Anchorage, AL, vol.
2, 2001, pp.905-914
[34] J. Cowie and A. Ogielski, "Global Routing Instabilities during Code Red
2 and Nimda Worm Propagation (conference report)", CAIDA Internet
Statistics and Metrics Analysis Workshop, San Diego, CA, December
2001
[35] D. Moore, C. Shannon, D.J. Brown, G.M. Voelker, and S. Savage,
"Inferring Internet Denial-of-Service Activity" ACM Trans. on Comp.
Sys., vol.24, no. 2, pp.115-139, 2006
[36] X.M. He, C. Papadopoulos, J. Heidemann, and A. Hussain, "Spectral
Characteristics of Saturated Links (research report)", University of Southern
California USC/CS Report, Los Angeles, CA, 2004
[37] K. Papagiannaki, N. Taft, Z.L. Zhang, and C. Diot, "Long-term forecasting
of Internet backbone traffic: observations and initial models" in Proc.
of INFOCOM 2003, San Francisco, CA, vol. 2, 2003, pp.1178-1188
[38] M. Barth'elemy, B. Gondran, and E. Guichard, "Large scale crosscorrelations
in internet traffic", Phys. Rev. E, vol. 66, 056110, 2002
[39] M. Mathis, "Pushing up the Internet MTU (conference report)", Joint-
Techs Workshop, Miami, FL, 2003
[1] D.J. Watts and S.H. Strogatz, "Collective dynamics of -small-world-
networks", Nature, vol. 393, pp.440-442, 1998
[2] R. Albert, H. Jeong, and A.L. Barab'asi, "Diameter of the World-Wide
Web", Nature, vol. 401, pp.130-131, 1999
[3] M.E.J. Newman, "Scientific collaboration networks. I. Network construction
and fundamental results", Phys. Rev. E, vol. 64, 016131, 2001
[4] M.E.J. Newman, "Scientific collaboration networks. II. Shortest paths,
weighted networks, and centrality", Phys. Rev. E, vol. 64, 016132, 2001
[5] S.N. Dorogovtsev and J.F.F. Mendes, "Exactly solvable small-world
network" Europhys. Lett. vol. 50, pp. 1-7, 2000
[6] M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On power-law relationships
of the Internet topology", Comp. Comm. Rev., vol. 29, pp.251-262, 1999
[7] R. Pastor-Satorras R and A. Vespignani, "Epidemic spreading in scalefree
networks", Phys. Rev. Lett., vol. 86, pp.3200-3203, 2001
[8] T. Ohira and R. Sawatari, "Phase transition in a computer network traffic
model", Phys. Rev. E, vol. 58, pp.193-195, 1998
[9] M. Takayasu, H. Takayasu, and K. Fukuda, "Dynamic phase transition
observed in the Internet traffic flow", Physica A, vol. 277, pp.248-255,
2000
[10] R.V. Sol'e and S. Valverde, "Information transfer and phase transitions
in a model of internet traffic ", Physica A, vol. 289, pp.595-605, 2001
[11] L. Zhao, Y.C. Lai, K.H. Park, and N. Ye, "Onset of traffic congestion
in complex networks", Phys. Rev. E, vol. 71, 026125, 2005
[12] L. Lago-Fern'andez, R. Huerta, F. Corbacho, and J. Sig'-uenza, "Fast
Response and Temporal Coherent Oscillations in Small-World Networks",
Phys. Rev.Lett., vol. 84, pp.2758-2761, 2000
[13] S.F. Wang and G.R. Chen, "Synchronization in small-world dynamical
networks", Intl J. of Bifurcation and Chaos, vol. 12, pp.187-192, 2002
[14] H. Hong, Y.M. Choi, and B.J. Kim, "Synchronization on small-world
networks", Phys. Rev. E, vol. 65, 026139, 2002
[15] M. Barahona and L.M. Pecora, "Synchronization in Small-World Systems",
Phys. Rev. Lett., vol. 89, 054101, 2002
[16] E. Almaas, A.N. Oltvai, and A.L. Barab'asi, "The activity reaction core
and plasticity of metabolic networks" PLoS Comp. Bio., vol. 1, pp.557-
563, 2005
[17] R. Guimera and L. Nunes-Amaral, "Functional cartography of complex
metabolic networks" Nature, vol. 433, pp.895-900, 2005
[18] B.S. Kerner and H. Rehborn, "Experimental properties of phase transitions
in traffic flow", Phys. Rev. Lett., vol. 79, pp.4030-4033, 1997
[19] C.F. Daganzo, M.J. Cassidy, and R.L. Bertini, "Causes And Effects Of
Phase Transitions In Highway Traffic (Research Report)", University of
California, Berkeley Institute of Transportation Studies Research Report,
Report No. UCB-ITS-RR-97-8, 1997
[20] D. Chowdhury, L. Santen, and A. Schadschneider, "Statistical Physics
of Vehicular Traffic and Some Related Systems" Phys. Rep., vol. 329,
pp.199-329, 2000
[21] S. G'abor and I. Csabai, "The analogies of highway and computer
network traffic", Physica A, vol. 307, pp.516-526, 2002
[22] Widely Integrated Distributed Environment (WIDE) Project, Kanagawa,
Japan, MAWI Working Group Traffic Archive (WIDE Backbone traffic
traces)[Online]. Available: http://mawi.wide.ad.jp/mawi/
[23] Stanford Linear Accelerator Center (SLAC) PingER End-to-End
Performance Measuring Project [Online]. Available: http://wwwiepm.
slac.stanford.edu/pinger/
[24] H. Chang, S. Jamin, Z.M. Mao, and W. Willinger, "An Empirical
Approach to Modeling Inter-AS Traffic Matrices" in Proc. of the 5th
ACM SIGCOMM Conference on Internet Measurement, Berkeley, CA
2005, pp.139-152
[25] M. Mathis, J. Semke, J. Mahdavi, and T. Ott, "The macroscopic behavior
of the TCP congestion avoidance", Comp. Comm. Rev., vol. 27, no. 3,
pp.67-82, 1997
[26] A. Veres and M. Boda, "The Chaotic Nature of TCP Congestion
Control-, in. Proc. of INFOCOM 2000, vol. 3, Tel Aviv, Israel, 2000,
pp. 1715-1723
[27] W.E. Leland, M.S. Taqqu, W. Willinger, and D.V. Wilson, "On the Self-
Similar Nature of Ethernet Traffic (Extended Version)", IEEE/ACM Trans.
on Networking, vol. 2, pp.1-15, 1994
[28] A. Feldmann, A. Gilbert, and W. Willinger, "Data networks as cascades:
Investigating the multifractal nature of Internet WAN traffic", Proc. of
ACM SIGCOMM -98, Vancouver, Canada, 1998, pp.42-55
[29] S. Uhlig, "Non-stationarity and high-order scaling in TCP flow arrivals:
a methodological analysis", Comp. Comm. Rev., vol. 34, no. 2, pp.9-24,
2004
[30] K. Fukuda, H. Takayasu, and M. Takayasu, "Origin of Critical Behavior
in Ethernet Traffic", Physica A, vol. 287, pp.289-301, 2000
[31] W. Fang and L. Peterson, "Inter-AS traffic patterns and their implications"
in Proc. Of the Global Telecommunications Conference, GLOBECOM
-99, Rio de Janeiro, Brazil, vol. 3, 1999, pp.1859-1868
[32] T. Mori, R. Kawahara, S. Naito, and S. Goto, "On the Characteristics of
Internet Traffic Variability: Spikes and Elephants", in Proc. of the 2004
International Symposium on Applications and the Internet, Tokyo, Japan,
2004, pp.99-106
[33] C. Dovrolis, P. Ramanathan, and D. Moore, "What Do Packet Dispersion
Techniques Measure?" in Proc. of INFOCOM 2001 Anchorage, AL, vol.
2, 2001, pp.905-914
[34] J. Cowie and A. Ogielski, "Global Routing Instabilities during Code Red
2 and Nimda Worm Propagation (conference report)", CAIDA Internet
Statistics and Metrics Analysis Workshop, San Diego, CA, December
2001
[35] D. Moore, C. Shannon, D.J. Brown, G.M. Voelker, and S. Savage,
"Inferring Internet Denial-of-Service Activity" ACM Trans. on Comp.
Sys., vol.24, no. 2, pp.115-139, 2006
[36] X.M. He, C. Papadopoulos, J. Heidemann, and A. Hussain, "Spectral
Characteristics of Saturated Links (research report)", University of Southern
California USC/CS Report, Los Angeles, CA, 2004
[37] K. Papagiannaki, N. Taft, Z.L. Zhang, and C. Diot, "Long-term forecasting
of Internet backbone traffic: observations and initial models" in Proc.
of INFOCOM 2003, San Francisco, CA, vol. 2, 2003, pp.1178-1188
[38] M. Barth'elemy, B. Gondran, and E. Guichard, "Large scale crosscorrelations
in internet traffic", Phys. Rev. E, vol. 66, 056110, 2002
[39] M. Mathis, "Pushing up the Internet MTU (conference report)", Joint-
Techs Workshop, Miami, FL, 2003
@article{"International Journal of Information, Control and Computer Sciences:54012", author = "Reginald D. Smith", title = "Data Traffic Dynamics and Saturation on a Single Link", abstract = "The dynamics of User Datagram Protocol (UDP) traffic
over Ethernet between two computers are analyzed using nonlinear
dynamics which shows that there are two clear regimes in the data
flow: free flow and saturated. The two most important variables
affecting this are the packet size and packet flow rate. However,
this transition is due to a transcritical bifurcation rather than phase
transition in models such as in vehicle traffic or theorized large-scale
computer network congestion. It is hoped this model will help lay
the groundwork for further research on the dynamics of networks,
especially computer networks.", keywords = "congestion, packet flow, Internet, traffic dynamics,
transcritical bifurcation", volume = "3", number = "3", pages = "624-6", }
