CAR FOLLOWING MODELS AND THE FUNDAMENTAL DIAGRAM OF ROAD TRAFFIC

THE DYNAMICS OF TRAFFIC FLOW WERE STUDIED TO DEVELOP A BETTER UNDERSTANDING OF HOW TO COPE WITH THE TREMENDOUS VOLUME OF VEHICULAR TRAFFIC. A BRIEF REVIEW IS PRESENTED OF SEVERAL TYPES OF CAR-FOLLOWING MODELS AND THE TYPES OF FUNDAMENTAL DIAGRAMS WHICH THEY IMPLY ARE DISCUSSED. ONE CAR-FOLLOWING MODEL IS BASED ON THE RATE OF CHANGE OF THE TWO-DIMENSIONAL VISUAL ANGLE OF THE IMAGE OF THE PRECEDING VEHICLE. THIS MODEL ASSUMES THAT A FOLLOWING DRIVER COULD IMPART TO HIS VEHICLE AN ACCELERATION PROPORTIONAL TO HIS PERCEPTION OF THE RATE OF CHANGE OF HIS VISUAL ANGLE ON THE PRECEDING VEHICLE. FOR THIS MODEL THE FUNDAMENTAL DIAGRAM (FLOW RATE VERSUS VEHICLE DENSITY) IS A PARABOLA WHICH IS CONCAVE DOWNWARD. FOR THIS PARABOLIC FLOW DISTRIBUTION THE MAXIMUM FLOW RATE OCCURS WHEN THE TRAFFIC DENSITY EQUALS ONE-HALF THE MAXIMUM POSSIBLE TRAFFIC DENSITY, I.E., A TRAFFIC JAM SITUATION. GREENBERG'S MODEL IS DIFFERENT IN THAT HE ASSUMES THE ACCELERATION IS PROPORTIONAL TO THE INVERSE OF THE HEADWAY INSTEAD OF THE SQUARE OF THIS INVERSE AS CONSIDERED IN THE PREVIOUS MODEL. BECAUSE OF THE LOWER POWER OF THE HEADWAY, IT APPEARS THAT GREENBERG'S MODEL IS LESS SENSITIVE TO SEPARATION DISTANCES THAN THE PREVIOUS MODEL. A GENERALIZATION OF GREENBERG'S FOLLOWING LAW IS PRESENTED BY ALLOWING THE EXPONENT OF THE HEADWAY TO BE A VARIABLE INSTEAD OF ONE OR TWO AS IN THE PREVIOUS TWO MODELS. OBVIOUSLY, THE HIGHER THE POWER OF THIS EXPONENT THE MORE SENSITIVE THE ACCELERATION OF THE FOLLOWING VEHICLE BECOMES. THE VARIOUS POSSIBLE FUNDAMENTAL DIAGRAMS ARE DISCUSSED FOR SELECTED VALUES OF THIS EXPONENT.

• Supplemental Notes:
  • Vol 1, pp 21-29
• Authors:
  • Pipes, L A
• Publication Date: 0

Media Info

• Serial:
  • Transportation Research /UK/
  • Publisher: Pergamon Press, Incorporated

Subject/Index Terms

• TRT Terms: Acceleration (Mechanics); Car following; Headways; Mathematical analysis; Mathematical models; Traffic density; Traffic flow; Traffic simulation; Traffic volume; Vehicles
• Uncontrolled Terms: Models
• Subject Areas: Highways; Operations and Traffic Management; Vehicles and Equipment;

Filing Info

• Accession Number: 00227683
• Record Type: Publication
• Source Agency: Bureau of Public Roads /US
• Files: TRIS
• Created Date: Aug 15 2004 1:44AM