THE APPLICATION OF THE THEORY OF PROBABILITY TO THE OPERATION OF VEHICULAR CONTROLLED TRAFFIC SIGNALS

A MATHEMATICAL BASIS IS PROVIDED WITH EXPERIMENTAL DATA SUPPORT OF THE CONSEQUENCES OF THE SETTINGS OF VEHICLE INTERVAL EXTENSION AND MAXIMUM EXTENSION AT VEHICULAR- ACTUATED TRAFFIC SIGNALS ON DELAY CHARACTERISTICS TO SIDE- STREET VEHICLES. THE TRAFFIC AT A SIMPLE CROSS-ROAD, CONSISTING OF A MAIN STREAM AND A SUBSIDIARY STREAM CROSSING IT, IS SUPPOSED TO BE CONTROLLED BY VEHICLE-ACTUATED SIGNALS OPERATING ON THE FOLLOWING PRINCIPLE. A VEHICLE IN THE SUBSIDIARY STREAM WILL BE KEPT WAITING UNTIL A TIME INTERVAL I, KNOWN AS THE VEHICLE INTERVAL, OCCURS BETWEEN SUCCESSIVE MAIN ROAD VEHICLES, EXCEPT THAT IN ANY CASE IT WILL NOT BE KEPT WAITING LONGER THAN M, THE MAXIMUM PERIOD. TABLES AND CURVES GIVE, FOR VARIOUS VALUES OF I, M, AND THE INTENSITY OF THE MAIN-ROAD TRAFFIC, THE PROBABILITY THAT THE WAITING PERIOD RUNS TO VARIOUS TIMES UP TO AND INCLUDING THE MAXIMUM AND ALSO THE AVERAGE VALUE OF THE WAITING PERIOD. THE MAIN- ROAD TRAFFIC IS ASSUMED TO FOLLOW THE POISSON DISTRIBUTION, AND IT IS FOUND THAT OBSERVATIONAL VALUES AGREE WITH THE THEORY. THE CALCULATIONS INVOLVE THE FOLLOWING PROBLEMS OF THE RANDOM DIVISION OF AN INTERVAL. A NUMBER OF POINTS ARE PLACED AT RANDOM ON A LINE, AND THE PROBABILITY THAT NONE OF THE PARTS INTO WHICH THE LINE IS DIVIDED IS MORE THAN A GIVEN FRACTION OF THE WHOLE IS DETERMINED.

• Supplemental Notes:
  • Supplement, VOL 7, PP 65-77
• Corporate Authors:

  J Roual Statistical Society

  ,    
• Authors:
  • Garwood, F
• Publication Date: 0

Subject/Index Terms

• TRT Terms: Headways; Intersections; Poisson ratio; Probability theory; Traffic actuated controllers; Traffic delays; Waiting time
• Old TRIS Terms: Poissons ratio
• Subject Areas: Data and Information Technology; Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00225260
• Record Type: Publication
• Files: TRIS
• Created Date: Jan 31 1994 12:00AM