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SOME RESULTS ON A TRAFFIC MODEL OF RENYI

A PREVIOUSLY-PROVED RESULT IS USED TO OBTAIN EXACT AND ASYMPTOTIC DISTRIBUTIONS OF SEVERAL RANDOM VARIABLES ARISING IN A TRAFFIC MODEL DUE TO RENYI. THE MODEL ASSUMES THAT VEHICLES ENTER A HIGHWAY AT TIMES ... WHICH FORM A HOMOGENEOUS POISSON PROCESS OF INTENSITY. THE VEHICLE ENTERING AT TIME CHOOSES VELOCITY AND TRAVELS AT THAT CONSTANT VELOCITY. THE RANDOM VARIABLES ARE INDEPENDENTLY AND IDENTICALLY DISTRIBUTED WITH CUMULATIVE DISTRIBUTION FUNCTION F AND THE VELOCITY SEQUENCE IS INDEPENDENT OF THE TIME SEQUENCE. ALL VEHICLES TRAVEL IN THE SAME DIRECTION. THE DISTRIBUTIONS STUDIED IN THIS REPORT ARE: (1) THE SPATIAL DISTRIBUTION OF VEHICLES AT TIME T, (2) THE VELOCITY DISTRIBUTION OF THOSE VEHICLES IN THE SECTION OF HIGHWAY (X,Y) AT TIME T, (3) THE DISTRIBUTION OF TIMES AT WHICH VEHICLES PASS A GIVEN POINT X ON THE HIGHWAY, (4) THE VELOCITY DISTRIBUTION OF THOSE VEHICLES PASSING THE POINT X IN THE TIME INTERVALS (S,T), (5) THE DISTRIBUTION OF THE TIMES AT WHICH IT IS PASSED BY OTHERS FOR A VEHICLE ENTERING THE HIGHWAY AT POINT X AT TIME T, AND (6) THE VELOCITY DISTRIBITION OF THOSE VEHICLES PASSING (BEING PASSED) IN (5). BATCH ARRIVALS OF VEHICLES TO THE HIGHWAY AND THE CASE OF NONCONSTANT VELOCITIES ARE DISCUSSED BRIEFLY. /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:
    • Brown, M
  • Publication Date: 1968-6-1

Subject/Index Terms

Filing Info

  • Accession Number: 00227244
  • Record Type: Publication
  • Source Agency: Traffic Systems Reviews & Abstracts
  • Report/Paper Numbers: Tech Rept No 3
  • Files: TRIS
  • Created Date: Jul 21 1970 12:00AM