Abstract
A crude mathematical model is constructed to represent the flow of traffic in tunnels or other finite sections of highway on which passing is impossible. The main ingredients of the model are: (1) each car has a desired speed which is considered to be a random variable, (2) the actual speed of any car is the smaller of its own desired speed and the actual speed of the car ahead of it, (3) if the latter speed is the smaller, the trailing car maintains some fixed spacing Δ behind its predecessor. The consequences of the model are: (1) the capacity of a tunnel is a monotone decreasing function of its length, (2) the velocity of any car is an increasing function of its distance from the entrance and is equal to the smallest of its own desired speed and those of all other cars in the tunnel ahead of it, (3) the spacing between cars is equal to Δ for most cars but when the spacing is larger than Δ, it is usually much larger and increases with the distance from the entrance.
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