Random Walk Experiment

In a dynamic network, at least one network parameter changes over time. In the random walk experiment, a network parameter is changed according to a random walk model (random process). The random walk is an abstract model that mimics the dynamics present in real networks.

Scenario

In the random walk experiment, a single flow operates in a dynamic dumbbell network. The flow generates greedy source traffic and uses a CCA. The bandwidth, two-way propagation delay, and the random loss probability can follow a random walk. In one experiment, all three network parameters may be changed simultaneously. For each network parameter, a lower bound \(x_{\min}\), an upper bound \(x_{\max}\), a correlation parameter \(\rho\), and a noise level \(\sigma\) can be specified as experiment parameters to configure the random walk models.

Each random walk is bounded between \(x_{\min}\) and \(x_{\max}\) to retain realistic values throughout an experiment. Furthermore, each random walk is correlated because network parameters often exhibit such correlations over time, e.g., the capacity deteriorates due to slow fading effects in a wireless channel. The unbounded random walk model is given by \(X_t = X_{t-1} + \Delta X_t\) with the step size \(\Delta X_t = \rho \Delta X_{t-1} + \epsilon_t\), where the correlation parameter \(\rho \in [0, 1]\) and \(\epsilon_t\) is drawn from a normal distribution \(\mathcal{N}(0, \sigma^2)\). The bounded random walk is then obtained by enforcing the boundary constraint with \(X_t = \min\left[ \max\left(X_t, x_{\min}\right),\ x_{\max} \right]\).

The experiment parameters configure the three random walks (x can be rate, delay, or loss):

• x_corr_coeff, x_noise_std, x_min, x_max: The correlation coefficient \(\rho\), standard deviation \(\sigma\) of the Gaussian noise, lower bound, and upper bound of the random walk x

To summarize the experiment setup:

• Topology: Dumbbell topology (\(K=1\)) with at least one dynamic network parameter

• Flows: A single flow (\(K=1\)) that uses a CCA

• Traffic Generation Model: Greedy source traffic