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# Fluid-Based Analysis for Understanding TCP Performance on Scale-Free Structure
**Authors:** Yusuke Sakumoto 1,a) Hiroyuki Ohsaki 2,b)
**Year:** 2016
## **Summary**
A fluid-based analisis of TCP flows, using ODEs to describe TCP window size and queue leghts. Specifically tailored to Scale-free structure networks (where the degree distribution of nodes in the network fol-lows the power law), no TCP timeouts, sender continuosly sends at window size. Experiments with different degree of scale-free topologies concluding: "The scale-free structure has the effect of making link betweenness smaller, and it can be said that packet loss probability gets smaller when α is set to a small value as the result. The star topology is optimal for the TCP performance because it has the smallest average of path length and the smallest link betweenness". There is no comparison agaist a discrete or real model. The Window equation is a delay equation. The queue equation is rather similar to Towley's queue equation for complete fluid networks.
## Some** other papers to follow:**
where original equations are presented:
**[30]** Liu, Y., Presti, F.L., Misra, V., Towsley, D.F. and Gu, Y.: Scalable fluid models and simulations for large-scale IP networks, ACM Trans. Modeling and Computer Simulation (TOMACS), Vol.14, No.3, pp.305–324 (2004).
**[28]** Ohsaki, H., Ujiie, J. and Imase, M.: On scalable modeling of TCP congestion control mechanism for large-scale IP networks, Proc. 5th IEEE / IPSJ International Symposium on Applications and the Internet ( SAINT 2005 ), pp.361–369 (2005) .
## Fluid Equations used
### TCP Window equation
This equation is presented fully in [28], and it is simplified in this paper.
"we use Eq. (1), which is the equation in the casewhere the TCP timeout occurrence probability is 0"
### Link Queue Equation
-- MatiasAlejandroBonaventura - 2016-07-25 |