POISSON AND TRAFFIC: THE PROBABILITY THEORY APPLIED TO DISTRIBUTION OF VEHICLES ON TWO-LANE HIGHWAYS

A THEORETICAL STUDY OF CONDITIONS AFFECTING THE TRAFFIC OF VEHICLES ON A HIGHWAY REQUIRES THE CONSTANT USE OF PROBABILITY THEORY. POISSON'S LAW, APPLYING TO RARE EVENTS, HAS BEEN THE CHIEF THEORETICAL INSTRUMENT FOR DEALING WITH PROBLEMS OF VEHICULAR TRAFFIC ON TWO OR THREE LANE HIGHWAYS, ESPECIALLY IN THE PROBLEM OF DETERMINING THE DISTRIBUTION OF SUCH TRAFFIC BOTH IN TIME AND IN SPACE. THE PROBABILITY LAWS ARE APPLIED TO SPACINGS BETWEEN VEHICLES TO SHOW HOW THE GAP BETWEEN THEORY AND ACTUALITY CAN BE NARROWED. THE FOLLOWING QUESTIONS ARE STUDIED IN DETAIL: (1) PROBABILITY OF A SPACING LONGER THAN X, (2) PROBABILITIES THAT AN INTERVAL, TAKEN AT RANDOM, CONTAINS NO VEHICLES, THAT IS BOUNDED BY A VEHICLE ON ONE SIDE, (3) PROBABILITY THAT AN INTERVAL, TAKEN AT RANDOM, CONTAINS EXACTLY N VEHICLES, (4) PROBABLE DELAY IN WAITING FOR AN EMPTY INTERVAL, AND (5) MEAN NUMBER OF VEHICLES CONTAINED IN A GROUP AND THE PROBABILITY OF FINDING A GROUP WITH A GIVEN NUMBER OF VEHICLES. THE VALUES GIVEN TO THESE FIVE FUNDAMENTAL QUESTIONS ARE COMPARATIVELY SIMPLE USING THE SOMEWHAT COMPLICATED FORM OF THE LAW FOR THE PROBABILITY OF SPACINGS BETWEEN SUCCESSIVE VEHICLES. THE DERIVATION SHOWS THAT THESE QUESTIONS COULD BE ANSWERED WITHOUT ANY ASSUMED LAW OF PROBABILITY. CHI SQUARE TEST DATA ARE PRESENTED WHICH SHOW THE GOODNESS OF FIT OF THE TIME- SPACING DISTRIBUTION REPRESENTED BY THE FORMULA DEVELOPED.

• Supplemental Notes:
  • pp 59-75, 4 FIG, 1 APP
• Corporate Authors:

  Eno Foundation for Highway Traffic Control

  1250 I Street, NW
  Washington, DC  United States  20005
• Authors:
  • Schuhl, A
• Publication Date: 0

Subject/Index Terms

• TRT Terms: Chi square test; Highway traffic; Poisson ratio; Probability theory; Spacing; Theory; Traffic delays; Traffic flow
• Old TRIS Terms: Poissons ratio; Vehicular traffic
• Subject Areas: Data and Information Technology; Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00227144
• Record Type: Publication
• Files: TRIS
• Created Date: Aug 13 2004 6:47PM