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 Signal Timing Design: Example Problems

 
Cycle Length Determination

As part of a signal design team, you have been assigned to find the optimum cycle length for a three-phase cycle. Field observations and calculations by yourself and others are the basis for your work. So far, you know the critical flow ratio for each phase and the intergreen time for each phase. Calculate the optimum cycle length for your signal, given the critical flow ratios and intergreen times below. What would the optimum cycle length be if all of the critical flow ratios were near zero?  

Phase Number Critical Flow Ratio Intergreen Time
1 0.233 6 sec
2 0.13 4 sec
3 0.256 7 sec

[Solution Shown Below]

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution

Webster's optimum cycle length equation, which is shown below, has two variables on the right-hand side.  These are the total cycle lost time (L) which is usually taken as the sum of all the intergreen times, and the sum of all the critical flow ratios (S(V/s)).  

Co=        1.5L + 5    
             1 - S (V/s)

In this case, the sum of the intergreen period lengths is 17 seconds (L=17). The sum of the critical flow ratios is 0.619. When we substitute these values into the equation above we obtain an optimum cycle length of 80 seconds. If all of the critical flow ratios were very near zero, the denominator in Webster's equation would approach unity and the optimum cycle length would be 31 seconds.