Statistical Equivalent Models for Computer Simulators with an Application to the Random Waypoint Mobility Model

Statistical Equivalent Models, or SEMs, have recently been proposed as a general approach to study computer simulators. By fitting a statistical model to the simulator’s output, SEMs provide an efficient way to quickly explore the simulator’s result. In this paper, we develop a SEM for random waypoint mobility, one of the most widely used mobility models employed by network simulators in the evaluation of communication protocols for wireless multi-hop ad hoc networks (MANETs). We chose the random waypoint mobility model as a case study of SEMs due to recent results pointing out some serious drawbacks of the model (e.g., [1]). In particular, these studies show that, under the random waypoint mobility regime, average node speed tends to zero in steady state. They also show that average node speed varies considerably from the expected average value for the time scales under consideration in most simulation analysis. In order to investigate further the behavior of the random waypoint model, we developed a SEM that captured speed decay over time under random waypoint mobility using maximum speed and terrain size as input parameters. A Bayesian approach to model fitting was employed to capture the uncertainty due to unknown parameters of the statistical model. The SEM is given by the posterior predictive distributions of the average node speed as a function of time. A direct result from our model is that, by characterizing average node speed as a function of time, our approach provides an accurate estimate of the “warm-up” period required by simulations using the random waypoint mobility model. Simulation data from the “warmup” period can then be discarded to obtain accurate protocol performance results. Given that random waypoint mobility is still, by far, the most widely used mobility model in the evaluation of MANETs, the contribution of this work is potentially significant as it allows network protocol designers to continue to use the original random waypoint mobility model and yet obtain accurate results characterizing MANET protocol performance.