ABSTRACT: Traffic flow on a unidirectional roadway in
the presence of raffic lights is modeled. Individual car responses
to green, yellow, and red lights are postulated and these results in
rules governing the acceleration and deceleration of individual cars.
The essence of the model is that only specific cars are directly
affected by the lights. The other cars behave according to simple
follow-the-leader rules which limit their speed by the spacing
between it and the car directly ahead. The model has a number of
desirable properties; namely cars do not run red lights, cars do not
smash into one another, and cars exhibit no velocity reversals. In a
situation with multiple lights operating in phase we get, after an
initial startup period, a constant number of cars through each light
during any green-yellow period. Moreover, this flux is less by one
or two cars per period than the flux obtained in discretized versions
of the idealized Lighthill, Whitham, Richards model which allows for
infinite accelerations.
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