figure-4.13-congctrl_tcpsim.py

# tcpsim.m - congestion control simulation
# RMM, 9 Sep 2006 (from MATLAB)

import matplotlib.pyplot as plt
import numpy as np
import random
import control as ct
import congctrl
import fbs                      # FBS plotting customizations

# Create an I/O system for simulation
M = 6                           # simulate 6 aggregated sources
N = 60                          # modeling 60 independent sources
congctrl_sys = congctrl.create_iosystem(M, N=N)

# Find the equilibrium point
xeq, ueq = ct.find_eqpt(congctrl_sys, np.ones(M+1), 0)
weq, beq = xeq[0], xeq[-1]              # first N states are identical

# Compute a perturbation for the initial condition
random.seed(6)                          # for repeatability
w0 = np.array([
    weq + 2 * (random.random() - 0.5) * weq for i in range(M)])
b0 = beq/2

# Run a simulation
tvec = np.linspace(0, 500, 100)
resp = ct.input_output_response(
    congctrl_sys, tvec, U=0, X0=[w0, b0])

# Plot the results
# Set up a figure for plotting the results
fbs.figure('mlh')

for i in range(M):
    plt.plot(resp.time, resp.states[i], 'k')
plt.plot(resp.time, resp.states[-1] / 20, 'b')

# Now change the number of sources and rerun from the old initial condition
M = 4                           # simulate 4 aggregated sources
N = 40                          # modeling 40 independent sources
congctrl_pert = congctrl.create_iosystem(M, N=N)

# Run a simulation starting from where we left off
tvec = np.linspace(500, 1000, 100)
pert = ct.input_output_response(
    congctrl_pert, tvec, U=0, X0=[resp.states[0:4, -1], resp.states[-1, -1]])

# Plot the results
for i in range(M):
    plt.plot(pert.time, pert.states[i], 'k')
plt.plot(pert.time, pert.states[-1] / 20, 'b')

# Label the plots and make them pretty
plt.axis([0, 1000, 0, 20])
plt.xlabel("Time $t$ [ms]")
plt.ylabel("States $w_i$ [pkts/ms], $b$ [pkts]")
plt.title("Time response")
plt.text(250, 3, "$w_1$ - $w_{60}$")
plt.text(700, 4, "$w_1$ - $w_{40}$")
plt.text(700, 10, "$b$")

# Save the figure
fbs.savefig('figure-4.13-congctrl_tcpsim.png')          # PNG for web