Traffic Models for Wireless Communication Networks

In this paper, we introduce a deterministic fluid model and two stochastic traffic models for wireless networks. The setting is a highway with multiple entrances and exits. Vehicles are classified as calling or noncalling, depending upon whether or not they have calls in progress. The main interest is in the calling vehicles, but noncalling vehicles are important because they can become calling vehicles if they initiate (place or receive) a call. The deterministic model ignores the behavior of individual vehicles and treats them as a continuous fluid, whereas the stochastic traffic models consider the random behavior of each vehicle. However, all three models use the same two coupled partial differential equations (PDE‘s) or ordinary differential equations (ODE‘s) to describe the evolution of the system. The call density and call bandoff rate (or their expected values in the stochastic models) are readily computable by solving these equations. Since no capacity constraints are imposed in the models, these computed quantities can be regarded as offered traffic loads. The models complement each other, because the fluid model can be extended to include additional features such as capacity constraints and the interdependence between velocity and vehicular density, while the stochastic traffic model can provide probability distributions. Numerical examples are presented to illustrate how the models can be used to investigate various aspects of time and space dynamics in wireless networks. The numerical results indicate that both the time-dependence and the mobility of vehicles can play important roles in determining system performance. Even for systems in steady state with respect to time, the movement of vehicles and the calling patterns can significantly affect the number of calls in a given region of the system. The examples demonstrate that the proposed models can serve as useful tools for system engineering and planning. For instance, we calculate approximate call blocking probabilities.