SOME MATHEMATICAL ASPECTS OF THE PROBLEM OF MERGING
AS ROADS AND HIGHWAYS BECOME CAPABLE OF CARRYING HIGHER TRAFFIC VOLUMES, THE PERTURBATIONS INTRODUCED BY VEHICLES TRAVELING AT SPEEDS OR IN PATHS THAT DIFFER FROM THE NORM BECOME INCREASINGLY HARMFUL TO SAFE AND EFFICIENT OPERATION OF THE ROAD NETWORK. SOME OF THIS INDIVIDUAL VARIATION CAN BE REMOVED, OR DIMINISHED, BY SENSIBLE EFFORTS TO EDUCATE AND CONTROL DRIVERS. THE NECESSITY REMAINS FOR ACCELERATING, DECELERATING, WEAVING, AND MERGING. PERHAPS THE MOST IMPORTANT EXAMPLE OF SUCH A SITUATION IS THE FREEWAY ON-RAMP AND ACCELERATION LANE. AT THESE POINTS, WHICH MUST BE PROVIDED FAIRLY FREQUENTLY IN URBAN AREAS, THE SMOOTH FLOW OF TRAFFIC IS PERPETUALLY HARASSED BY NEW ARRIVALS. LOCATION AND DESIGN OF ON-RAMPS AND ACCELERATION LANES ARE CLOSELY CONNECTED WITH THE INFLUENCE THEY EXERT ON TRAFFIC STABILITY. A COMPLETE MATHEMATICAL MODEL FOR MERGING CANNOT BE CLAIMED, BUT IT IS HOPED INSTEAD TO POINT OUT THE PROBLEMS IN FORMULATION OF SUCH A MODEL, AND SOLVE A FEW OF THEM. THE MERGING PROBLEM HAS SOME INTEREST BEYOND THE SIMPLE QUESTION OF WAITING FOR A SUITABLE GAP IN TRAFFIC. FOR EXAMPLE, A CAR TRAVELING ALONG AN ACCELERATION LANE WHILE WAITING FOR THE OPPORTUNITY TO MERGE IS MATHEMATICALLY EQUIVALENT TO A CAR WAITING AT A STOP SIGN, OR THE DIFFERENCE RESIDES ONLY IN THE MOVING COORDINATE SYSTEM. HOWEVER, THE DRIVER ON THE ACCELERATION LANE IS ABLE TO CONTROL THE TRAFFIC STREAM WITH WHICH HE WISHES TO MERGE BY CHANGING HIS OWN SPEED, THEREBY INCREASING OR DECREASING HIS HEADWAY AND SPACING RELATIVE TO THE MAIN STREAM. THE STOP SIGN PROBLEM DOES NOT CONTAIN THIS IMPORTANT INGREDIENT, AND THEREFORE QUESTIONS OF DRIVING POLICY DO NOT ARISE. THERE IS ONLY ONE POSSIBLE POLICY AT A STOP SIGN: WAIT FOR A SUITABLE GAP. THEREFORE, A MATHEMATICAL MODEL FOR A STOP SIGN IS PURELY DESCRIPTIVE AND ITS PRINCIPAL RESULT CONSISTS OF A PROBABILITY DISTRIBUTION FOR DELAY. THERE IS A MUCH MORE VARIED AND INTERESTING COLLECTION OF PROBLEMS AVAILABLE WHEN THE DRIVER IS ALLOWED TO ALTER (WITHIN LIMITS) HIS ATTITUDE WITH RESPECT TO THE MAIN STREAM. /AUTHOR/
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Supplemental Notes:
- Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the Transportation Research Board of the National Academy of Sciences. Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved.
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Authors:
- Haight, Frank A
- Bisbee, E Farnsworth
- Wojcik, Charles
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Conference:
- 41st Annual Meeting of the Highway Research Board
- Location: Washington DC, United States
- Date: 1962-1-8 to 1962-1-12
- Publication Date: 1962
Language
- English
Media Info
- Media Type: Digital/other
- Features: Figures; References;
- Pagination: pp 1-14
- Monograph Title: Theory of traffic flow
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Serial:
- Highway Research Board Bulletin
- Issue Number: 356
- Publisher: Highway Research Board
Subject/Index Terms
- TRT Terms: Acceleration lanes; Deceleration; Driver training; Gap acceptance; Headways; Interchange ramps; Location; Mathematical models; Merging traffic; On ramps; Spacing; Speed; Stop signs; Traffic control; Traffic flow; Urban highways; Weaving traffic
- Uncontrolled Terms: Speed differential
- Old TRIS Terms: Freeway ramps; Ramp location & spacing; Traffic control systems
- Subject Areas: Highways; Operations and Traffic Management;
Filing Info
- Accession Number: 00227068
- Record Type: Publication
- Files: TRIS, TRB
- Created Date: Aug 13 2004 6:56PM