At a signal-controlled intersection, a two-way road meets three one-way roads (s
ID: 470411 • Letter: A
Question
At a signal-controlled intersection, a two-way road meets three one-way roads (see figure below). Permitted turning movements a, b, c, d and e can be paired off for greens by the phasing of traffic lights. The average flow of vehicles for each turn is given in the following table
a
b
c
d
e
7
24
10
30
5
and the possible phasing (i.e., pairs of lights that turn green at the same time) are:
Find out what proportion of green time should be given to the various phasing such that the smallest average number of vehicles allowed through a, b, c, d, or e on a green phase is as large as possible.
Is the solution unique? If it is not unique find another solution. (Hint: Use sensitivity analysis)
a
b
c
d
e
7
24
10
30
5
O nExplanation / Answer
This problem can be solved in Excel solver as a Optimization Problem.
The objective is to have maximum traffic flow. In the solver we have defined the function as minimizing the number of traffic remaining.
We have multiplied the traffic from each direction by a factor to get a sufficient but no to calculate. (Table 1).
The final flow after multiplying the factor with traffic flow factor is defined as Vehicle Flow. (Table 1).
We have defined the following constraints in the solver - all the traffic should go and there should not be any traffic remaining.
No traffic should be remaining in any of the direction (Flow).
In Table no 2, the Formulas are built.
Based on the objective, the conclusion is shown in table 2. (% of Time each signal should be green)
TABLE 1 TARGET CELL 0 Turning Flow Factor Multiply Factor Total Flow Green Signal Nos Vehicle Fow Vehicle Remaining a 7 1000 7000 1000 7000 0 b 24 1000 24000 1000 24000 0 c 10 1000 10000 1000 10000 0 d 30 1000 30000 1000 30000 0 e 5 1000 5000 1000 5000 0Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.