Existing macroscopic models for the flow of traffic treat traffic as a continuum or employ techniques similar to those used in the kinetic theory of gases. Spurious two- way propagation of disturbances that are physically unacceptable are predicted by continuum models for the flow of traffic. The number of vehicles in a typical section of a freeway does not justify traffic being treated as a continuum. It is also important to recognize that the basic premises of kinetic theory are not appropriate for the flow of traffic. A model for the flow of traffic that does not treat traffic as a continuum or use notions from kinetic theory is developed in this dissertation and corroborated with traffic data collected from the sensors deployed on US 183 freeway in Austin, Texas, USA. The flow of traffic exhibits distinct characteristics under different conditions and reflects the congestion during peak hours and relatively free motion during off-peak hours. This requires one to use different governing equations to describe the diverse traffic characteristics, namely the different traffic flow regimes of response. Such an approach has been followed in this dissertation. An observer based on extended Kalman filtering technique has been utilized for the purpose of estimating the traffic state. Historical traffic data has been used for model calibration. The estimated model parameters have consistent values for different traffic conditions. These esti- mated model parameters are then subsequently used for estimation of the state of traffic in real-time. A short-term traffic state forecasting approach, based on the non-continuum traffic model, which incorporates weighted historical and real-time traffic information has been developed. A methodology for predicting trip travel time based on this approach has also been developed. Ten and fifteen minute predictions for traffic state and trip travel time seem to agree well with the traffic data collected on US 183.