A QUEUING MODEL FOR CAR PASSING

A MODEL IS DEVELOPED FOR AUTOMOBILE FLOW IN ONE DIRECTION ALONG A TWO-LANE COUNTRY ROAD. THE MODEL TAKES INTO ACCOUNT THAT CARS DIFFER IN SPEED, SLOWER CARS ACCUMULATE QUEUES BEHIND THEM, AND THE RATE OF ESCAPE FROM SUCH A QUEUE BY PASSING THE LEAD CAR DEPENDS ON THE SPEED OF THE LEAD CAR, THE NATURE OF THE ROAD, AND THE DENSITY OF TRAFFIC GOING IN THE OPPOSITE DIRECTION. EQUATIONS FOR THE STOCHASTIC STEADY STATE OF THE SYSTEM REDUCE TO AN INTEGRAL EQUATION FOR THE MEAN QUEUE LENGTH, AS A FUNCTION OF LEAD-CAR SPEED AND OF A QUEUE-DELAY PARAMETER. SOLUTIONS ARE OBTAINED, FOR TWO DIFFERENT ASSUMPTIONS REGARDING THE DEPENDENCE OF PASSING DELAY ON LEAD-CAR SPEED. IN BOTH CASES, THE MODEL EXHIBITS A SUDDEN CHANGE FROM SPARSE-TRAFFIC CONDITIONS (WHERE QUEUING IS RARE AND DELAY OF THE FASTER CARS IS MINIMAL) TO THE DENSE-TRAFFIC CONDITIONS (WHERE NEARLY ALL CARS FIND THEMSELVES TRAPPED IN A SLOW QUEUE AS THE PASSING-DELAY PARAMETER IS INCREASED BEYOND ITS TRANSITIONAL VALUE). SUCH A SUDDEN "PHASE CHANGE" IN TRAFFIC CHARACTER IS TYPICAL OF ACTUAL TRAFFIC UNDER THE SPECIFIED CONDITIONS. MEASURED DEPENDENCE OF QUEUE LENGTH ON LEAD-CAR SPEED CHECKS NICELY WITH THE MODEL, FOR SPARSE-TRAFFIC CONDITIONS. /AUTHOR/

• Corporate Authors:

  Massachusetts Institute of Technology

  Sloan School of Management, Operations Research Center
  Cambridge, MA  United States  02139
• Authors:
  • Morse, P M
  • Yaffe, H J
• Publication Date: 1970-4

Subject/Index Terms

• TRT Terms: Integral equations; Length; Mathematical models; Passing; Queuing; Queuing theory; Traffic delays; Two lane highways
• Uncontrolled Terms: Models
• Old TRIS Terms: Queueing theory
• Subject Areas: Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00227323
• Record Type: Publication
• Source Agency: Traffic Systems Reviews & Abstracts
• Report/Paper Numbers: Tech Rept No 51
• Files: TRIS
• Created Date: Jul 2 1971 12:00AM