POINT PROCESSES ARISING IN VEHICULAR TRAFFIC FLOW

IF THERE IS A DICHOTOMY OF SLOW AND FAST POINTS (CARS) ON A ROAD WITH LIMITED OVERTAKING, IT IS ASSUMED THAT FAST POINTS ARE DELAYED BEHIND (OR ARE CLUSTERED AT) A SLOW POINT IN ACCORDANCE WITH THE PRINCIPLES OF A GI/G/S QUEUE, THE ORDER OF SERVICE BEING IRRELEVANT. THUS, EACH SLOW POINT REPRESENTS A SERVICE STATION, WITH THE INPUT INTO EACH STATION CONSISTING OF A FIXED (BUT RANDOM) DISPLACEMENT OF THE OUTPUT OF THE PREVIOUS QUEUEING STATION. IT IS FOUND THAT TRACTABLE RESULTS FOR STATIONARY POINT PROCESSES OCCUR FOR THE CASES M/M/S (S=1,2,...) AND M/G/INFINITY. FOR THESE CASES THE STEADY STATE POINT PROCESSES ARE COMPOUND POISSON AND FOR THE M/M/1 CASE THE SUCCESIVE HEADWAYS FORM A TWO STATE MARKOV RENEWAL PROCESS. THE INPUT, OUTPUT, AND QUEUE SIZE PROCESSES IN A STEADY STATE M/G/INFINITY QUEUE ARE INDEPENDENT AT ANY FIXED TIME. /AUTHOR/

• Supplemental Notes:
  • Vol 8, No 4, PP 809-814
• Authors:
  • Brill, E A
• Publication Date: 0

Media Info

• Serial:
  • Journal Applied Probability /UK/
  • Issue Number: 0

Subject/Index Terms

• TRT Terms: Mathematical models; Traffic flow
• Uncontrolled Terms: Models
• Old TRIS Terms: Point processes
• Subject Areas: Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00227340
• Record Type: Publication
• Files: TRIS
• Created Date: Mar 20 1972 12:00AM