SENSITIVITY OF DELAY AT A FIXED TIME TRAFFIC SIGNAL TO SMALL ERRORS IN THE OBSERVATIONS USED FOR CALCULATING THE SIGNAL SETTINGS

THE CYCLE TIME AND GREEN TIMES AT A ROAD JUNCTION CONTROLLED BY FIXED TIME TRAFFIC SIGNALS CAN BE CALCULATED SO AS TO MINIMIZE, SUBJECT TO CERTAIN CONSTRAINTS, WEBSTER'S SIMPLIFIED ESTIMATE OF THE DELAY PER UNIT TIME TO ALL TRAFFIC PASSING THROUGH THE JUNCTION. THE SIGNAL SETTINGS ARE DETERMINED BY A VECTOR WHOSE COMPONENTS ARE THE PROPORTION OF THE CYCLE FOR WHICH EACH GROUP OF APPROACHING TRAFFIC STREAMS HAS RIGHT OF WAY AND THE PROPORTION OF THE CYCLE TAKEN UP BY LOST TIME. THE OBSERVED DATA REQUIRED FOR THE CALCULATION OF THIS VECTOR ARE THE AVERAGE ARRIVAL RATE AND THE SATURATION FLOW OF TRAFFIC ON EACH APPROACH TO THE JUNCTION. THIS PAPER SHOWS HOW THE VECTOR DETERMINING THE SIGNAL SETTINGS IS AFFECTED BY SMALL ERRORS IN THE OBSERVED ARRIVAL RATES AND SATURATION FLOWS. IT GOES ON TO OBTAIN AN ESTIMATE OF THE DIFFERENCE BETWEEN THE DELAY PER UNIT TIME THAT WOULD OCCUR IF THE SIGNAL SETTINGS WERE CALCULATED FROM THE TRUE ARRIVAL RATES AND SATURATION FLOWS. THIS ESTIMATE IS A QUADRATIC FORM IN THE OBSERVATIONAL ERRORS, AND AN EXPRESSION IS GIVEN FOR THE MATRIX OF COEFFICIENTS IN TERMS OF KNOWN QUANTITIES. THIS MATRIX IS SHOWN TO BE SYMMETRIC. SEVERAL NUMERICAL EXAMPLES FOR A SIMPLE CROSSROADS ARE GIVEN AND THE RESULTS ARE DISCUSSED. THE DELAY PER UNIT TIME AT THE EXAMPLE JUNCTION IS FOUND NOT TO BE VERY SENSITIVE TO ERRORS IN JUST ONE ARRIVAL RATE OR SATURATION FLOW, EXCEPT WHEN THE JUNCTION IS HEAVILY LOADED WITH TRAFFIC, BUT IT IS SHOWN THAT THE COMBINED EFFECT OF SEVERAL ERRORS CAN BE QUITE LARGE. THE METHOD DEVELOPED IN THIS PAPER SHOULD ENABLE ENGINEERS TO IDENTIGY SITUATIONS IN WHICH PARTICLARLY ACCURATE MEASUREMENTS OF ARRIVAL RATES AND SATURATION FLOWS ARE NECESSARY, AND TO ESTIMATE THE RANGE OF CONDITIONS FOR WHICH PARTICULAR SIGNAL SETTINGS ARE LIKELY TO BE SUITABLE.

• Corporate Authors:

  Traffic Flow and Transportation

  ,    
• Authors:
  • ALLSOP, R E
• Publication Date: 0

Media Info

• Features: Figures; References; Tables;
• Pagination: p. 253-67

Subject/Index Terms

• TRT Terms: Errors; Green interval (Traffic signal cycle); Matrices (Mathematics); Pretimed traffic signal controllers; Traffic delays; Traffic signal timing
• Subject Areas: Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00226790
• Record Type: Publication
• Files: TRIS
• Created Date: Apr 11 1974 12:00AM