Car-Following Theory Glossary Car-following theories Ca-following theory applications Traffic stability

Glossary Distance headway 车头间距 Density 密度 Car-following theory 跟车理论 Reaction time 反应时间 Stimuli 刺激 Sensitivity 敏感度 Traffic stability 交通稳定性 Local stability 局部稳定性 Asymptotic stability 渐进稳定性

Car-following theories Notations and definitions Acceleration Speeds Following vehicle Lead vehicle Positions Continue……

Pipes’ theory A good rule for following another vehicle at a safe distance is to allow yourself at least the length of a car between your vehicle and the vehicle ahead for every ten miles per hour of speed at which you are traveling. Let (feet) Or Continue……

Forbes’ theory The minimum time headway is equal to the reaction time and the time required for the lead vehicle to traverse a distance equivalent to its length. Or Continue……

What is the sensitivity term? General Motors’ theories A law of psychology: response = func(sensitivity, stimuli) Response acceleration Stimuli relative velocity What is the sensitivity term? Continue……

If sensitivity = constant, then It is called the linear car-following model. If sensitivity Then Continue……

If sensitivity Then Generalized model l, m = parameters

Car-following theory applications An example Lead vehicle: accelerate at a constant rate of 3.3 ft/sec2 until a speed of 44 ft/sec is reached; maintain the constant speed 44 ft/sec for 10 sec; decelerate at a constant rate of 4.6 ft/sec2 until it is stopped. Following vehicle: follow the lead vehicle with a safe minimum distance headway. Initial distance headway: 25 ft Reaction time: 1.0 sec Sensitivity parameter: 0.5 How about the trajectory of the following vehicle? 11/21/05 Continue……

T = time slice Equations Speed Distance Lead vehicle Following vehicle Acceleration

Traffic stability “Unstable” behavior “Stable” behavior When a driver of a following vehicle responds slowly, he might finally responds, over responds by exerting significantly large acceleration or deceleration rates. It is characterized by higher reaction times and higher sensitivity responses. “Stable” behavior A driver of a following vehicle is very attentive to the car-following process and does not resort to sudden accelerations or decelerations except in extreme emergencies. It is characterized by lower reaction times and lower sensitivity responses. Continue……

C = a(Dt) is used to classify stable and unstable behaviors Local stability The stability of a single following car. Lead vehicle: decelerates for 2 seconds then accelerates for 2 seconds, return back to original speed. Following vehicle: react…decelerate…accelerate…decelerate… Distance headway: lager…smaller…larger…smaller Local stability: nonoscillatory, damped oscillatory, increased oscillatory Asymptotic stability The stability of a line of following vehicles. Asymptotic stability: damped oscillatory and increased oscillatory. In case of increased oscillatory, the variance of distance between successive two vehicles becomes larger and larger, collision would occur.