| Various traffic control measures have been developed to relieve traffic congestion on a freeway system. For these measures to be effective and reliable, it is required to understand the attributes of congested traffic flow and model it. However, current traffic flow theories fall short in describing the prominent attributes of congested traffic such as capacity drop, traffic hysteresis, and random propagation of traffic waves. In this thesis, we identify the ‘time gap’ as an important parameter in congested traffic. We propose that the time gap is a function of both vehicle spacing and traffic phase and develop a multi-phase car-following model. By specifying various functional forms for the time gap, one obtains specific cases of the general car-following theory, some of which can model capacity drop and/or traffic hysteresis while others are shown to be equivalent to the well-known existing theories. By taking the time gap as a stochastic parameter and distinguishing time gap from driver reaction time, we can explain the random propagation of traffic waves. The amplification and decay of disturbances are also explained in accordance with the random transition of observation points in the fundamental diagram. An equation for stochastic wave propagation is developed and it is shown that the developed equation is a general form of the shock speed equation in the continuum traffic flow theory. The stochastic wave propagation model is also applied to model the probability of breakdown. Both the multi-phase car-following model and stochastic wave propagation model developed in this thesis, by taking the time gap as a primary parameter, are closely related to each other. This thesis explains and models the complex features of congested traffic in a unified and consistent way and contributes to the development of more reliable and accurate traffic flow models for congested traffic. |
