Introduc)on	

No one seems to know what level of realism should be 

required in network models that study congestion. This 

raises questions about ten years of extant studies [e.g.,1-6]. 

How do various realism elements influence congestion 

spread? Are some elements essential? Can some be ignored? 

Method	(network	simula)ons)

Acknowledgments	

Results

We simulated 34 configurations at increasing packet injection rates, p = 1 to 2500, plotted on the x axes against four responses, χ, α, π and δ, plotted on 

the y axes. We used hierarchical clustering to identify configurations with similar congestion behavior, and used those clusters to identify realism 

elements with largest influence on each response. We also compared responses for the most abstract (C0) [6] and realistic (C127) [7] configurations.

Conclusions	

Abstract (C0) and realistic (C127) network models exhibit 

very different congestion behaviors. 

Variable speeds (VS) among router tiers, engineered to 

ensure adequate throughput, are very important to model. 

And modeling VS requires node classification (NC), which 

restricts packet injection to nodes on the network edge. 

The transmission control protocol (TCP), which detects 

congestion and adapts packet injection rate accordingly, is 

very important to model. In addition, modeling TCP requires 

modeling sources and receivers (SR) and flows (FL). 

Packet dropping (PD) due to finite FIFO buffers is 

important to model for accurate measures of packet latency. 

Propagation delay (DE) is not important to model in 

networks spanning the US, but could be important in global 

networks or networks with satellite hops, and would be very 

important to model in inter-planetary networks. 

A decade of studies [e.g., 1-6 and many more] used models 

too abstract to simulate realistic congestion behavior in 

communication networks based on Internet technology. The 

validity of findings from such studies appears suspect. 

Christopher	Dabrowski	and	Kevin	Mills		

NIST	Informa,on	Technology	Laboratory	

Literature	cited	

[1] Solé and Valverde, Information transfer and phase transitions in a 

model of internet traffic. 2001. Physica A 289:595-605. 

[2] Woolf et al., Optimization and phase transitions in a chaotic model 

of data traffic. 2002. Phys Rev E 66:046106. 

[3] Mukherjee and Manna, Phase transition in a directed traffic flow 

network. 2005. Phys Rev E 71(6):066108. 

[4] Rykalova et al., Critical phenomena in discrete-time interconnection 

networks. 2010. Physica A389:5259-5278. 

[5] Sarkar et al., Statistical mechanics-inspired modeling of 

heterogeneous packet transmission in communication networks. 

2012. Systems, Man and Cybernetics 42(4):1083-1094. 

[6] Echenique et al., Dynamics of jamming transitions in complex 

networks. 2005. Europhys Lett 71(2) 

[7] Mills et al., How to model a TCP/IP network using only 20 

parameters. 2010. Winter Simulation Conference 849-860. 

Further	informa)on	

For information about related research into complex systems 

behavioral modeling and analysis with emphasis on 

communication networks and clouds, see 

http://www.nist.gov/itl/antd/emergent_behavior.cfm or 

contact kmills@nist.gov. 

Seven Network Realism Elements and Dependencies 

One Network Topology 34 Configurations 

Four Responses 

χ = |Gχ|/|GN| congestion spread 

α = |Gα|/|GN| connectivity breakdown 

π = 1 – ρ – x packets delivered 

packet latency 

Congestion Spread (χ) Connectivity Breakdown (α) Packets Delivered (π) Packet Latency (δ) 

250 Load Levels 

p = 1 to 2500 by 10 

VS & TCP Influence 

Congestion Spread (χ) 

VS & TCP Influence 

Connectivity Breakdown (α) 

TCP & VS & PD Influence 

Packets Delivered (π) 

PD & VS & TCP Influence 

Packet Latency (δ) 

Thanks to Philip Gough of 

CSIRO for creating a 

dynamic visualization that 

allowed us to investigate 

details of congestion spread 

in our topology. 

No#

PD# PD#

No#

VS# VS# TCP#

No#

VS#

Congestion Spread (χ) Connectivity Breakdown (α) 

Packets Delivered (π) Packet Latency (δ) 

C0 

C127 

C0 

C127 

C127 

C127 

C0 

C0