Subproblem 1b  Page 5 of 9 
ID# C201B05 
Subproblem 1b: Maxwell Drive PM
Peak Hour  With Conditions
Cycle Length
Education
For a pretimed signal, the standard equation for computing the minimum
cycle length is:
(1) 

where v_{i}
is the volume for the critical movement in phase i, s_{i}
is the saturation flow rate for the critical movement in phase i,
N is the number of phases per cycle, and L is the lost time per
phase.
For actuated signals
with dualring controllers like the one we portrayed in
Exhibit 211, it
helps to expand Equation (1) into three equations. The first one computes
the v/s ratio for sequential pairs of movements to the left
and right of the middle barrier in the A and B rings:
(2) 

Here
pq takes on the values 1&2, 3&4, 5&6, and
7&8 corresponding to the four quadrants of the dual ring pattern.
The second equation
computes the maximum v/s ratio for the left and right halves
of the dual ring pattern:
(3) 
(v/s)_{L}
= max((v/s)_{12},(v/s)_{56})
and (v/s)_{R}
= max((v/s)_{34},
(v/s)_{78}) 
The third equation
takes the two results from Equation (3) and computes a minimum cycle length:
(4) 

Discussion:
In
practice, we don't often use equations in the formal style they are
presented here. The equations are helpful, though, because they are a
shorthandway of expressing ideas. You might checkout the spreadsheet and
see if you can identify how equations (2), (3) and (4) have been
implemented.
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Critical Movement Techniques 