Complex dynamics in communication networks by Ljupco Kocarev, Gabor Vattay

By Ljupco Kocarev, Gabor Vattay

Machine and verbal exchange networks are between society's most crucial infrastructures. the web, specifically, is a big worldwide community of networks with critical keep watch over or management. it's a paradigm of a posh approach, the place complexity could come up from assorted resources: topological constitution, community evolution, connection and node variety, and /or dynamical evolution. this is often the 1st ebook totally dedicated to the hot and rising box of nonlinear dynamics of TCP/IP networks. It addresses either scientists and engineers operating within the common box of communique networks.

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1: Investigated network model: There are three TCP flows sharing a common buffer that can store B packets and a common line with delay D0 and speed C0 . Then the common link splits into three different lines with different delays and speeds. In the actual simulations B = 100, T0 = 400 ms, T1 = 100 ms, T2 = 150 ms, T3 = 200 ms, C0 = 106 bps and C1 = C2 = C3 = 107 bps has been chosen. controlled by strict deterministic rules, that is by the TCP Reno algorithm [9]. Numerical simulations were carried out by Network Simulator (ns) version 2b5 [10].

There is a trade-off in the size of the decrease of the aggregate rate; sources with larger RTTs effect a smaller decrease in the aggregate rate but their effect takes longer to manifest. Therefore, we can treat the variability caused by the “late” reactions as a perturbation, and the system’s reaction to congestion is largely dominated by the connections with small RTT’s, which occurs quickly1 . One might think that with drops occuring one after another and not all at the same time during a congestion epoch, we can make the sources react at different times, but we find that packet drops occur in bursts of short duration, followed by longer periods in which no drops occur.

In particular, TCP uses “additive increase and multiplicative decrease” to increase the rate linearly during times of no packet loss, and to decrease the rate geometrically when loss occurs. As a consequence, the rate at which a TCP source transmits tends to be periodic over time. For example, Figure 1 shows the periodic behavior of a single TCP source in an otherwise idle network. When many TCP sources compete for the buffers in a congested router, packet loss will cause each flow to exhibit periodic behavior.

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