FHA Signal Timing On A Shoestring

Cycle Length Issues
As noted above, having a common cycle length is fundamental to coordinated signal
operation. The cycle length must be evaluated from two different perspectives; individual
intersection and the group cycle length.
For the individual intersection, the recommended approach is to focus on the one or two
major intersections in the group – the intersections with the highest demand because these
intersections are the ones that will set the minimum cycle length limits. When evaluating
cycle lengths, it is important to verify that the pedestrian timing is sufficient to allow
pedestrians to cross the street. When the pedestrian timing is known, say 7 seconds Walk,
10 seconds Pedestrian Clearance, and 3 seconds yellow change, and the vehicle phase is to
be allocated at least 25 percent of the cycle, then the minimum cycle length that can meet
both constraints is 20 seconds divided by 25%, or 80 seconds (assuming two critical phases).
In general, the intersection in the group that requires the longest cycle length will set the
group cycle length. The cycle length and splits can be determined by using either Webster’s
equation or the Greenshields-Poisson Method. Both of these methods are explained below.
In general, for a given demand condition, there is a cycle length that will provide the
optimum two-way progression. This cycle length is a function of the speed of the traffic on
the links between intersections and the link distance between intersections. This cycle
length is called the “Resonant Cycle” and is explained further below.
Webster’s Equation
One approach to determining cycle lengths for an isolated pre-timed location is
based on Webster's equation for minimum delay cycle lengths. The equation is as
follows:
Where:
Cycle Length = (1.5 * L + 5) / (1.0 - Yi)
L = The lost time per cycle in seconds
Yi = Sum of the degree of saturation for all critical phases 5
This method was developed by F. V. Webster of England’s Road Research
Laboratory in the 1960’s. The research supporting this equation is based on
measuring delay at a large number of intersections with different geometric designs
and cycle lengths. These observations yielded the equation that is used today. It is
important to recognize that this work assumed random arrivals and fixed-time
operation – two conditions that can rarely be met in the United States. Notice that
the equation becomes unstable at high levels of saturation and should not be used at
locations where demand approaches capacity. Nevertheless, this technique provides
a starting point when developing signal timings. To use this equation,
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The critical phases are the ones that requires the most green time. The flow ratio is calculated by dividing the volume by the
saturation flow rate for that movement.
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