Modeling TCP/RED: a Dynamical Approach

Abstract

Summary. Interaction between Transmission Control Protocol (TCP) and Random Early Detection (RED) gateways can be captured using dynamical models. The communication network is viewed as a discrete-time feedback control system where TCP adjusts its window size depending on whether or not it has detected a packet loss during the previous round trip time (RTT) interval. In this article, we describe a discrete-time nonlinear dynamical model for interaction between TCP and RED gateways. The model, constructed using an iterative map, captures a detailed dynamical behavior of TCP/RED, including slow start, fast retransmit, and timeout events common in TCP. Model performance for various RED parameters is evaluated using ns-2 network simulator.

Steady State Analysis of the TCP Network with RED Algorithm

“…In recent year, there have been many investigations of TCP/RED with numerical simulations [2], [11]. Mathematical models of these techniques are studied actively to investigate reliance with parameters [12].…”

“…Mathematical models of these techniques are studied actively to investigate reliance with parameters [12]. The S-model, proposed by Zhang et al, has good approximation of TCP/RED without random numbers, and it is used for numerical simulations [2]. It is described as a discrete-time hybrid dynamical system, and occurs global bifurcation phenomena; border-collision (BC) bifurcation phenomena are reported in Ref.…”

Dynamics of the Internet TCP–RED congestion control system

“…The basic idea of the TCP is to ascertain the congestion by identifying the increase of the loss of the data packages and the growth of the delay time, and then to ease the congestion by reducing the data flow at the sources. The basic idea of the RED is to detect the appearance of congestion by inspecting the averaged queue length at the routers in order to depress the global synchronization at the sources [4][5][6]. Before the real congestion takes place, the data packages will be dropped or marked with some probability in the caches to inform sources of the coming congestion.…”

Discontinuity-induced bifurcations in TCP/RED communication algorithms

“…Based on the concepts reported in [1]- [3], we proposed the S-model [4] that employs window size and average queue size as state variables. Variations of the window size reflect the dynamics of TCP congestion control.…”

“…We derive a secondorder discrete-time model to capture interactions of the TCP congestion control algorithm with the RED mechanism. Based on the concepts reported in [1]- [3], we construct a nonlinear dynamical model of TCP/RED that employs two state variables: the window size and the average queue size [4]. The change of window size reflects the dynamics of TCP congestion control, while the average queue size captures the queue dynamics in RED gateway.…”