To calculate the minimum cycle length and timing for the given four-timing-stage traffic signal, we can use the following steps:
1. Calculate the total critical volume (Vc) for the intersection:
Vc = (flow ratio 1 + flow ratio 2 + flow ratio 3 + flow ratio 4) × 3600 seconds/hour
Substituting the given values, we get:
Vc = (0.225 + 0.175 + 0.200 + 0.150) × 3600 = 2520 vehicles/hour
2. Calculate the effective green time (Tg) for each critical lane group:
Tg = (flow ratio / Vc) × (cycle length - lost time)
Substituting the given values, we get:
Tg1 = (0.225 / 2520) × (cycle length - 5)
Tg2 = (0.175 / 2520) × (cycle length - 5)
Tg3 = (0.200 / 2520) × (cycle length - 5)
Tg4 = (0.150 / 2520) × (cycle length - 5)
3. Calculate the total effective green time (Tg_total) for all critical lane groups:
Tg_total = Tg1 + Tg2 + Tg3 + Tg4
4. Calculate the v/c ratio for the intersection:
v/c = (V / (Tg_total + lost time)) × (3600 seconds/hour)
We want the v/c ratio to be 0.85, so we can rearrange this equation to solve for the minimum cycle length:
cycle length = ((V / (v/c × 3600)) - lost time) / (Tg_total / Tg_total)
Substituting the given values and solving for cycle length, we get:
cycle length = ((2520 / (0.85 × 3600)) - 5) / ((0.225 / 2520) + (0.175 / 2520) + (0.200 / 2520) + (0.150 / 2520))
cycle length ≈ 117 seconds
Now that we know the cycle length, we can calculate the effective green time for each critical lane group:
Tg1 = (0.225 / 2520) × (117 - 5) ≈ 10.4 seconds
Tg2 = (0.175 / 2520) × (117 - 5) ≈ 8.1 seconds
Tg3 = (0.200 / 2520) × (117 - 5) ≈ 9.2 seconds
Tg4 = (0.150 / 2520) × (117 - 5) ≈ 6.9 seconds
Therefore, the minimum cycle length for the given traffic signal is approximately 117 seconds, and the effective green times for each critical lane group are 10.4 seconds for group 1, 8.1 seconds for group 2, 9.2 seconds for group 3, and 6.9 seconds for group 4.