AN INVARIANCE PROPERTY OF POISSON PROCESS ARISING IN TRAFFIC FLOW THEORY

THE GENERALIZED POISSON PROCESS HAS FREQUENTLY BEEN EMPLOYED IN DESCRIBING THE FLOW OF TRAFFIC. THIS PAPER DERIVES A PROPERTY OF POISSON PROCESSES OF WHICH SPECIAL CASES HAVE PREVIOUSLY ARISEN IN TRAFFIC THEORY. THE PROPERTY MAY BE STATED AS FOLLOWS: LET (GI), BE AN INDEPENDENTLY AND IDENTICALLY DISTRIBUTED SEQUENCE OF MEASURABLE RANDOM FUNCTIONS AND (TI), BE THE ARRIVAL TIMES OF GENERALIZED PIOISSON PROCESS. IF THE GI AND TI SEQUENCES ARE INDEPENDENT, THEN UNDER A MILD CONDITION THE COUNTING PROCESS GENERATED BY THE PRODUCT IS A GENERALIZED POISSON PROCESS. THE AUTHOR SHOWS BY COUNTER-EXAMPLE THAT IF GI IS AN INDEPENDENTLY AND IDENTICALLY DISTRIBUTED SEQUENCE OF RANDOM FUNCTIONS AND THE PRODUCT IS A POISSON PROCESS, THEN (TI) IS NOT NECESSARILY A POISSON PROCESS. /AUTHOR/

• Corporate Authors:

  Stanford University

  Department of Statistics
  Stanford, CA  United States 
• Authors:
  • Brown, M
• Publication Date: 1968-5-1

Subject/Index Terms

• TRT Terms: Mathematical models; Poisson ratio; Probability theory; Random functions; Traffic flow; Traffic flow theory
• Old TRIS Terms: Poissons ratio
• Subject Areas: Data and Information Technology; Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00227242
• Record Type: Publication
• Source Agency: Traffic Systems Reviews & Abstracts
• Report/Paper Numbers: Tech Rept No 1
• Files: TRIS
• Created Date: Jul 21 1970 12:00AM