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A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections

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Abstract

This paper proposes a macroscopic behavioral theory of traffic dynamics for homogeneous, multi-lane freeways. The theory makes predictions for separate groups of lanes while recognizing that the traffic stream is usually composed of aggressive and timid drivers. Its principles are so simple that non-scientist drivers can understand them. The simplest version of the theory, which is described in its full complexity without calculus, is shown to be qualitatively consistent with experimental observations, including the most puzzling. Its predictions agree with the following phenomena: (i) the 'reversed lambda' pattern frequently observed in scatter-plots of flow versus occupancy and the lane-specific evolution of the data points with time, including the 'hysteresis' phenomenon, (ii) the lane-specific patterns in the time series of speed (and flow) in both queued and unqueued traffic, and (iii) the peculiar ways in which disturbances of various types propagate across detector stations. The latter effects include the evolution of both, stoppages and transitions between the queued and unqueued traffic regimes. The simple model is specified by means of eight observable parameters. The paper gives a recipe for solving any well-posed problem with this model and does so in sufficient detail to allow the development of computer models. A few approaches and possible generalizations are suggested. Part II of this paper, devoted to freeway sections near on-ramps, will attempt to explain in more detail than previously attempted how queuing begins at merges.

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