|
Sub-problem 1b: Maxwell Drive PM Peak Hour - With Conditions
Cycle Length
Education
where vi is the volume for the critical movement in phase i, si 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 dual-ring controllers like the one we portrayed in
Exhibit 2-11, 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
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:
The third equation takes the two results from Equation (3) and computes a minimum cycle length:
Equations (2) through (4)
show that Equation (1) can
be obtained easily. First, realize that N equals 4.
Second, see that the sequence of critical movements is either:
1,2,3,4; 1,2,7,8; 5,6,3,4; or 5,6,7,8. Third, notice that the
sum of the vi/si ratios identified in
the denominator of Equation (1) is the same as the left and
right half based sum shown in Equation (4).
|
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
shorthand-way of expressing ideas. You might check-out the spreadsheet and
see if you can identify how equations (2), (3) and (4) have been
implemented.