WEB 81 Newell's Car Following Model: A Comprehensive Overview
Introduction
Background
WEB 81 Newell's car following model is a mathematical model that describes the behavior of vehicles following each other in a traffic stream. It is one of the simplest and most widely used car-following models, and it has been used to study a variety of traffic phenomena, including traffic flow, congestion, and safety.
Assumptions of the Model
Newell's model is based on the following assumptions:
- Vehicles are point masses that move in a single lane.
- Vehicles have a constant desired speed.
- Vehicles adjust their speed to maintain a constant headway (or following distance) from the vehicle in front of them.
Mathematical Formulation
Basic Equation
The basic equation of Newell's model is as follows:
v(k+1) = v(k) + a[v*(k) - v(k)] - b[h(k) - h*(k)]
where:
- v(k) is the speed of vehicle k at time step k
- v*(k) is the desired speed of vehicle k
- a is a positive constant that represents the acceleration of the vehicle
- b is a positive constant that represents the braking of the vehicle
- h(k) is the headway of vehicle k
- h*(k) is the desired headway of vehicle k
Parameters
The parameters of Newell's model are as follows:
- a: The acceleration of the vehicle.
- b: The braking of the vehicle.
- v*: The desired speed of the vehicle.
- h*: The desired headway of the vehicle.
Applications
Traffic Flow
Newell's model has been used to study a variety of traffic flow phenomena, including:
- Congestion
- Speed-density relationships
- Capacity
Safety
Newell's model has also been used to study traffic safety, including:
- Collision avoidance
- Rear-end collisions
- Traffic calming
Conclusion
WEB 81 Newell's car following model is a versatile and widely used model that can be used to study a variety of traffic phenomena. It is a powerful tool for understanding how vehicles interact with each other and can be used to improve the safety and efficiency of traffic flow.
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