Macroscopic traffic model with variable optimal density of traffic flow

The traditional traffic flow equations of road derive the optimal density only with the blockage density(kj), but not with the maximum road speed limit or free flow speed(vf), the calculation results vary greatly; some other models will be the optimal density(km) as input conditions, need to be given by empirical formulas or a priori parameters; With the improvement of vehicle performance and the promotion of road speed limits, there are some unavoidable difficulties in the traditional models to explain the traffic flow problem. The paper starts from the safety of following driving, and uses the calculus equivalence relationship between the microscopic following criterion and macroscopic traffic flow three-parameter model to construct a fundamental diagram traffic model for determining the optimal density by the free flow velocity; according to the different characteristics of the non-congested section and congested section of the traffic flow, three fitting expressions of free flow with different traffic velocity decaying according to density are proposed for high-speed limit and medium, low-speed limit roads. The results show that the proposed equations reveal that the traffic waves generated in congested areas are constant velocity backward traffic waves, which is supported by the empirical results of the relevant authoritative literature.