THE PROBABILITY THEORY APPLIED TO DISTRIBUTION OF VEHICLES ON TWO-LANE HIGHWAYS

SINCE THE WIDELY USED POISSON LAW DESCRIBES VEHICULAR DISTRIBUTION QUITE WELL FOR VERY LOW TRAFFIC FLOW RATES, BUT DEVIATES SIGNIFICANTLY FROM REALITY WHEN THE FLOW RATE RISES ABOVE A FEW DOZEN VEHICLES PER HOUR PER LANE, MR. SCHUHL DEVELOPS A DESCRIPTION OF THE VEHICULAR DISTRIBUTION FOR A TRAFFIC STREAM COMPOSED OF TWO DISTINCT POISSON FLOWS THROUGH THE APPLICATION OF PROBABILITY THEORY. THE ENTIRE TRAFFIC STREAM IS CONSIDERED AS HAVING A SET OF GAPS CONTAINING TWO SUB-SETS. EACH SUB-SET HAS A DISTINCT MEAN AND BOTH OBEY SOME POISSON-TYPE LAW. ASSUMING THAT VEHICLES CAN BE REPRESENTED BY POINTS ON A STRAIGHT LINE, THE PROBABILITY OF A GAP GREATER THAN SOME FIXED VALUE IS DEVELOPED IN GENERAL TERMS AND MODIFIED TO CONSIDER A LOWER BOUND ON THE SIZE OF THE GAP. THE MODIFIED MODEL IS FIT TO TWO DATA SAMPLES AND COMPARED WITH A POISSON FIT IN ONE CASE. SCHUHL'S EQUATION PROVIDES A MUCH CLOSER FIT THAN DOES THE POISSON LAW. FURTHER MATHEMATICAL RELATIONS DEVELOPED ARE: (1) THE PROBABILITY OF A FIXED TIME INTERVAL, SELECTED AT RANDOM, CONTAINING NO VEHICLES BEING BOUNDED ON ONE SIDE BY A VEHICLE, (2) THE PROBABILITY OF A FIXED TIME INTERVAL, SELECTED AT RANDOM, CONTAINING EXACTLY N VEHICLES, (3) THE PROBABLE DELAY TO A VEHICLE WAITING FOR A GREATER GAP IN THE OPPOSING LANE OF TRAFFIC, AND (4) THE PROBABILITY OF FINDING A PLATOON OF VEHICLES WITH A GIVEN NUMBER OF VEHICLES IN IT WHERE A PLATOON IS DEFINED BY THE CONSECUTIVE VEHICLES SEPARATED BY A GAP LESS THAN SOME GIVEN VALUE.

• Record URL:
  • https://rosap.ntl.bts.gov/view/dot/16299
• Supplemental Notes:
  • Poisson and TRAFFIC
• Corporate Authors:

  Eno Transportation Foundation

  P.O. Box 2055, Saugatuck Station
  Westport, CT  United States  06880-0055
• Authors:
  • Schuhl, A
• Publication Date: 1955

Media Info

• Media Type: Web
• Features: Appendices; Tables;
• Pagination: pp 59-75

Subject/Index Terms

• TRT Terms: Alternatives analysis; Equations; Gap acceptance; Headways; Mathematical models; Physical distribution; Poisson ratio; Probability theory; Statistical sampling; Traffic delays; Traffic flow; Traffic platooning; Two lane highways; Vehicles
• Uncontrolled Terms: Data sampling; Models
• Old TRIS Terms: Poissons ratio
• Subject Areas: Data and Information Technology; Freight Transportation; Highways; Operations and Traffic Management; Vehicles and Equipment;

Filing Info

• Accession Number: 00227093
• Record Type: Publication
• Files: NTL, TRIS
• Created Date: Aug 13 2004 6:47PM