TY - JOUR ID - TI - Traffic Flow Problem with Differential Equation( Mathematical Model) AU - عبد السلام الخزرجي PY - 2008 VL - 4 IS - 35 SP - 129 EP - 138 JO - Al-Fatih journal مجلة الفتح SN - 87521996 AB - Car following theory is a model for the motion of a number of individual vehicles as they proceed down along straight road with no passing allowed. Many mechanical physiological aspects of the deriver-vehicle-road systems make modeling difficult. However we can assume that we have a line of n perfect derivers, in the sense that each driver can follow eaxactly the low of motion which pertinent.
Now assume the position of vehicle j at time t is given by , see figure(1) below

Fig(1) Position of the Vehicles
A good rule of thumb for following another vehicle at a safe distance is allowing you the length of a car for ten meter per hour (14.67) m/s.
When we are travelling in terms of function , we have
1.A
Where =length of the car (normaly of 15 feet) and =speed of jth vehicle.
Length of a vehicle, must be added to the separation between vehicles to give the spacing

We assume that each driver is able to follow (1.A) at each time t.
This means that the driver must accelerate (or decelerate) his vehicle according to

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