Nonhomogeneous Poisson Fields of Random Lines with Applications to Traffic Flow
NAVAL POSTGRADUATE SCHOOL MONTEREY United States
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This study was prompted by investigations of models of traffic flow on a highway through analyses of the structure and properties of Poisson fields of random lines in a plane. It is possible to view the trajectory of a car produced by its time and space coordinates on the highway as a straight line in that plane if the car travels at a constant speed once it enters the highway and then never leaves the highway. These traffic considerations plus the property of time invariance for traffic flow distributions lead to one model for traffic flow on a divided highway developed by Renyi 10. This idealized model is simpler to study than the more realistic situation that provided Renyis motivation and which he also subjects to analysis, namely, cars do lose time because of an overtaking of one car by another even on a divided highway with two lanes for traffic moving in one direction.
- Statistics and Probability