A NOTE ON A MATHEMATICAL MODEL OF TRAFFIC FLOW ON A DIVIDED HIGHWAY

RENYI HAS RECENTLY CONSIDERED A MODEL OF TRAFFIC FLOW ON A DIVIDED HIGHWAY WHICH EXTENDS TO INFINITY IN ONE DIRECTION. ALL CARS ENTER THE HIGHWAY AT THE SAME PLACE IN A HOMOGENEOUS POISSON FASHION AND THERE ARE NO EXITS. RENYI SHOWS THAT THE ASYMPTOTIC SPATIAL DISTRIBUTION OF CARS ALONG THE ROAD IS A HOMOGENEOUS POISSON PROCESS. SUPPOSE AN OBSERVER CAR IS TRAVELLING ON THE HIGHWAY WITH FIXED VELOCITY. THE INSTANTS ARE DENOTED AT WHICH THE OBSERVER CAR OVERTAKES A SLOWER CAR AND IS OVERTAKEN BY A FASTER CAR, RESPECTIVELY. RENYI PROVES THAT THE SEQUENCES OF INSTANTS FORM INDEPENDENT (HOMOGENEOUS) POISSON PRRCESS AS THE TRAVEL TIME TENDS TO INFINITY. IN THIS PAPER A NEW PROOF OF RENYI'S RESULTS IS GIVEN. SIMILAR RESULTS ARE OBTAINED FOR FINITE TRAVEL TIME AND THE PROBABILITY DENSITY FUNCTION OF THE VELOCITY OF CARS IN A SEGMENT OF THE ROAD AT FINITE TIME IS COMPUTED. THE EXTENSION OF THIS MODEL TO THE CASE OF SEVERAL ENTRANCES AND EXITS IS ALSO CONSIDERED. /AUTHOR/ REFERENCES: ON TWO MATHEMATICAL MODELS OF THE TRAFFIC ON A DIVIDED HIGHWAY, A. RENYI, JOURNAL OF APPLIED PROBABILITY, VOL. 1, PP 311-320, 1964.

• Corporate Authors:

  Stanford University

  Department of Statistics
  Stanford, CA  United States 
• Authors:
  • Srivastava, R C
• Publication Date: 1968-6-5

Subject/Index Terms

• TRT Terms: Divided highways; Interchange ramps; Mathematical models; Poisson ratio; Probability theory; Spacing; Traffic density; Traffic simulation; Travel time
• Old TRIS Terms: Freeway entrances and exits; Poissons ratio
• Subject Areas: Data and Information Technology; Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00227245
• Record Type: Publication
• Source Agency: Traffic Systems Reviews & Abstracts
• Report/Paper Numbers: Tech Rept No 4
• Files: TRIS
• Created Date: Jul 21 1970 12:00AM