WAITING FOR A GAP IN A TRAFFIC STREAM

IN PROBLEMS CONNECTED WITH TIMING TRAFFIC-ACTUATED SIGNALS AND MANY OTHER APPLICATIONS, IT IS IMPORTANT TO KNOW NOT ONLY HOW MANY GAPS OF VARIOUS SIZES EXIST AND WHAT PROPORTION OF THE TOTAL TIME IS OCCUPIED BY EACH BUT ALSO HOW LONG A VEHICLE ARRIVING AT ANY INSTANT WILL HAVE TO WAIT FOR A SPECIFIED GAP, GIVEN THE HOURLY VOLUME WHICH IS TO BE INTERRUPTED. J.C. TANNER GAVE A FORMULA, BASED UPON A POISSON DISTRIBUTION AND UPON PREVIOUS WORK BY ADAMS AND GARWOOD, FOR COMPUTING THE PROBABILITY OF WAITING ANY LENGTH OF TIME FOR ANY GAP IN A STREAM OF ANY AVERAGE (I.E. HOURLY) RATE OF FLOW. OBSERVATIONS WERE MADE OF GAPS AND WAITING TIMES AT FIVE VOLUME LEVELS, FROM 650 VPH. TO 2400 VPH., AND THE RESULTING PROBABILITY CURVES CHECKED EXACTLY WITH TANNER'S FORMULA. THE FORMULA IS PRETTY COMPLEX TO WORK OUT FOR AN INDIVIDUAL CASE, SO A SET OF CURVES SHOWING THE RELATIONSHIP OF THESE FOUR VARIABLES HAS BEEN PLOTTED AND IS PRESENTED AS A PART OF THE PRESENT PAPER. THE CURVES COVER A RANGE OF GAPS FROM 3 TO 8 SECONDS AND OF VOLUMES UP TO 4,000 VPH. EXPERIMENTAL WORK REPORTED HERE SIMPLY CONFIRMS FINDINGS OF OTHERS THAT TRAFFIC FLOW IS A RANDOM SERIES, AND THE PURPOSE OF PUBLISHING THE REPORT IS PRIMARILY TO MAKE THESE GRAPHS AVAILABLE. /AUTHOR/