Abstract
Every year countless hours are lost in traffic jams. When the density of traffic is sufficiently high small disturbances in vehicle’s accelerations can cause phantom traffic jams. We can relate the traffic flow to mathematics and physics like that of liquids and gases. This paper presents mathematical model for phantom jams and Gauss Jordan elimination for traffic flow.
Highlights
Countless hours are lost every year in traffic jams
The most frustrating are all those traffic jams without a clear cause, without accidents, without stationary vehicles, without closed lanes for construction. Such phantom jams can be formed when there are a large number of cars on the road. In this high traffic density, minor faults can quickly become a traffic jam that is selfsufficient and complete
If the vehicles are moving in a normal speed, any change in vehicle acceleration will reflect immediately and a heavy traffic jam will happen
Summary
The most frustrating are all those traffic jams without a clear cause, without accidents, without stationary vehicles, without closed lanes for construction. Such phantom jams can be formed when there are a large number of cars on the road. If the vehicles are moving in a normal speed, any change in vehicle acceleration will reflect immediately and a heavy traffic jam will happen. This type of jams follow a particular rule that we call as “jamitons”, similar to the behaviour of the wave called soliton, in the same way as a jamiton. Several researchers have tried to make more sophisticated models that contain jamitons and phantom traffic jams
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