A QUEUING MODEL FOR CAR PASSING
A MODEL IS DEVELOPED FOR THE FLOW OF AUTOMOBILES IN ONE DIRECTION ALONG A TWO-LANE, COUNTRY ROAD. THE MODEL TAKES INTO ACCOUNT THE FACT THAT CARS DIFFER IN SPEED, THAT SLOWER CARS ACCUMULATE QUEUES BEHIND THEM, AND THAT THE RATE OF ESCAPE FROM SUCH A QUEUE, BY PASSING THE LEAD CAR, DEPENDS ON THE SPEED OF THE LEAD CAR, ON THE NATURE OF THE ROAD, AND ON ON 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, WITH TABLES AND GRAPHS, 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 SPARE-TRAFFIC CONDITIONS. /AUTHOR/
-
Availability:
- Find a library where document is available. Order URL: http://worldcat.org/oclc/1767714
-
Supplemental Notes:
- Vol 5, No 1, PP 48-63, 6 FIG, 2 TAB, 4 REF
-
Corporate Authors:
Operations Research Society of America
428 East Preston Street
Baltimore, MD United States 21202 -
Authors:
- Morse, P M
- Yaffe, H J
- Publication Date: 0
Media Info
-
Serial:
- Transportation Science
- Volume: 5
- Issue Number: 2
- Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
- ISSN: 0041-1655
- Serial URL: http://transci.journal.informs.org/
Subject/Index Terms
- TRT Terms: Mathematical models; Passing; Queuing; Queuing theory; Rural highways; Traffic delays; Two lane highways
- Old TRIS Terms: Queueing theory
- Subject Areas: Highways; Operations and Traffic Management;
Filing Info
- Accession Number: 00227310
- Record Type: Publication
- Files: TRIS
- Created Date: Apr 25 1971 12:00AM