Research On Dynamic Model And Parameter Relationships Of Mixed Traffic Flow

Traffic flow theory is a frontier subject that describes the characteristic and the formation mechanism of traffic in mathematical, physical and mechanical way. It makes the plan, design and operational management of the road and highway effective. In China, it is not practical to apply the same theory and method on car flow using in the developed countries because of our mixed traffic flow and the special road system. So, it is important to indicate the formation mechanism of the traffic flow in which vehicles mixed with each other, build mixing traffic flow model by dynamics, seek the relationships between the traffic parameters, analyze the factors that influence the capacity, control the traffic system, and improve the traffic status according to the nature of the mixed traffic flow in China.The paper sets up the traffic flow model by means of dynamics. The relationships between the traffic parameters in the mixed traffic flow are obtained by introducing the overtaking flow into the model. The relationships between the parameters in the ramp junctions are obtained by introducing the ramp flow. The field data and the empirical formula in Highway Capacity Manual 2000(USA) are adopted to testify the relationships. Details are as follow.(l)The formation mechanism of the mixed traffic flow in China is analyzed from three essential elements, such as human, vehicle and road. It is considered that the mixed traffic flow will exist a long time.(2) The principle of choosing standard car is put forward. The micro passenger car equivalent, class passenger car equivalent and macro passenger car equivalent are defined and calculated.(3) This paper analyzes the traditional car following models, indicates that there is a blemish in the reasoning of the linear car following model. By means of time-space plane, three car following models are set up: the vehicle following the lead vehicle at the same speed, the low speed vehicle following the high speed lead vehicle, and the high speed vehicle following the low speed lead vehicle. Based onthese models, three speed-spacing relations and three rear-end collision models are obtained.(4) The traffic flow dynamic model is constructed. Considering the overtaking flow and ramp flow, this paper builds the continuum equation of the traffic flow, and sets up the kinematics differential equation by means of differential calculus. The paper proposes viscosity resistance and viscosity factor. Traffic viscosity is defined as the interference of traffic wave from down stream. Wave velocity minus the maximum wave velocity is defined as the section viscosity factor. Wave velocity minus speed is the cross viscosity factor. Section viscosity resistance is in proportion to the length of the section, flow grads along stream direction and section viscosity factor. Cross viscosity resistance is in proportion to the negative overtaking flow or ramp flow and cross viscosity factor.(5) Solving the model by characteristic curve method, two groups of characteristic curves and corresponding related equation are gained in high speed(low density ) states and low speed (high density ) states. The ratio of overtaking flow to mainline flow is defined as the overtaking rate. The ratio of the in-ramp flow to the total flow entering the junction is defined as the merging rate. The ratio of the off-ramp flow to the total flow entering the junction is defined as the diverging rate. Integrating the related equations, the relationships between traffic parameters, such as the overtaking flow or ramp flow, speed, density and mainline flow, are established.(6) The relationships between the traffic parameters in the mixed traffic flow are testified with the field data. The relationships between the traffic parameters in the ramp junction flow are compared with the example problem and the empirical formula. The result indicates that the model coincide with the field data and the formula.