Question

An intersection has a three-timing-stage signal with the movements allowed in each timing stage and corresponding analysis and saturation flow rates shown in Table 7.1 and Table 7.2 Table 7.1 Flow Rates for Three-Timing-Stage Design at Intersection Timing stage 1 Timing stage 2 Timing stage 3 NB L: 345 veh/hr NB T/R: 1150 veh/hr EB L: 115 veh/hr WB L: 80 veh/hr SB L: 370 veh/hr SB T/R: 1080 veh/hr EB T/R: 280 veh/hr WB T/R: 265 veh/hr . Table 7.2 Saturation Flow Rates for Three-Timing-Stage Design at Intersection Timing stage 1 Timing stage 2 Timing stage 3 NB L: 1800 veh/hr NB T/R: 3400 veh/hr EB L: 650 veh/hr WB L: 600 veh/hr SB L: 1850 veh/hr SB T/R: 3300 veh/hr EB T/R: 1700 veh/hr WB T/R: 1800 veh/hr Find: a) Calculate the sum of the flow ratios for the critical lane groups. b) Calculate the minimum cycle length Assume the lost time is 4 seconds per timing stage and a critical intersection v/c of 0.90 is desired. c) Calculate the effective green time for each timing stage. d) Calculate the northbound average approach delay and level of service. e) Calculate the southbound average approach delay and level of service. f) Calculate the eastbound average approach delay and level of service. g) Calculate the westbound average approach delay and level of service. h) Calculate the intersection average approach delay and level of service.

Answer 1

a) For timing stage 1, the sum of the flow rates is 345 + 1150 + 115 + 80 + 370 + 1080 = 3140 veh/hr.

For timing stage 2, the sum of the flow rates is 345 + 1150 + 115 + 80 + 370 + 1080 + 280 + 265 = 3665 veh/hr.

For timing stage 3, the sum of the flow rates is 345 + 1150 + 115 + 80 + 370 + 1080 + 280 + 265 = 3665 veh/hr.

b) The minimum cycle length is 5.22 + 2.96 + 5.65 + 4 = 18.83 sec.

c) For timing stage 1, the effective green time is (3140/3665) * 18.83 - 4 = 12.82 sec.

For timing stage 2, the effective green time is (3665/3665) * 18.83 - 4 = 14.83 sec.

For timing stage 3, the effective green time is (3665/3665) * 18.83 - 4 = 14.83 sec.

d) the average approach delay for the northbound direction is (0.8 + 0.65)/2 = 0.725 sec.

e) the average approach delay for the southbound direction is (0.8 + 0.67)/2 = 0.735 sec.

f) the average approach delay for the eastbound direction is (0.822 + 0.647)/2 = 0.734 sec.

g) the average approach delay for the westbound direction is (0.867 + 0.683)/2 = 0.775 sec.

h) the intersection average approach delay is (0.725 + 0.735 + 0.734 + 0.775)/4 = 0.742 sec.

Step-by-step explanation:

a) To calculate the sum of the flow ratios for the critical lane groups, we need to sum the flow rates for each timing stage.

The critical lane groups are NB L, NB T/R, EB L, WB L, SB L, and SB T/R.

For timing stage 1, the sum of the flow rates is 345 + 1150 + 115 + 80 + 370 + 1080 = 3140 veh/hr.

For timing stage 2, the sum of the flow rates is 345 + 1150 + 115 + 80 + 370 + 1080 + 280 + 265 = 3665 veh/hr.

For timing stage 3, the sum of the flow rates is 345 + 1150 + 115 + 80 + 370 + 1080 + 280 + 265 = 3665 veh/hr.

b) To calculate the minimum cycle length, we need to consider the flow rates and saturation flow rates for each timing stage.

The minimum cycle length is calculated as the sum of the effective green times for each timing stage, plus the lost time.

The effective green time is the saturation flow rate divided by the flow ratio. For timing stage 1, the effective green time is 1800/345 = 5.22 sec.

For timing stage 2, the effective green time is 3400/1150 = 2.96 sec.

For timing stage 3, the effective green time is 650/115 = 5.65 sec.

Adding the 4 seconds of lost time, the minimum cycle length is 5.22 + 2.96 + 5.65 + 4 = 18.83 sec.

c) To calculate the effective green time for each timing stage, we need to multiply the flow ratio by the minimum cycle length and subtract the lost time.

For timing stage 1, the effective green time is (3140/3665) * 18.83 - 4 = 12.82 sec.

For timing stage 2, the effective green time is (3665/3665) * 18.83 - 4 = 14.83 sec.

For timing stage 3, the effective green time is (3665/3665) * 18.83 - 4 = 14.83 sec.

d) To calculate the northbound average approach delay, we need to calculate the delay for each movement and sum them up.

The delay is calculated using the formula (1/1-v/c) - 1, where v is the volume and c is the saturation flow rate.

For NB L in timing stage 1, the delay is (345/1800) - 1 = 0.8.

For NB T/R in timing stage 2, the delay is (1150/3400) - 1 = 0.65.

Summing up the delays, the average approach delay for the northbound direction is (0.8 + 0.65)/2 = 0.725 sec.

The level of service can be determined using delay thresholds specific to the intersection.

e) To calculate the southbound average approach delay, we follow the same process as in (d), but for the southbound movements.

For SB L in timing stage 1, the delay is (370/1850) - 1 = 0.8.

For SB T/R in timing stage 2, the delay is (1080/3300) - 1 = 0.67.

Summing up the delays, the average approach delay for the southbound direction is (0.8 + 0.67)/2 = 0.735 sec.

f) To calculate the eastbound average approach delay, we follow the same process as in (d), but for the eastbound movements.

For EB L in timing stage 1, the delay is (115/650) - 1 = 0.822.

For EB T/R in timing stage 2, the delay is (280/1700) - 1 = 0.647.

Summing up the delays, the average approach delay for the eastbound direction is (0.822 + 0.647)/2 = 0.734 sec.

g) To calculate the westbound average approach delay, we follow the same process as in (d), but for the westbound movements.

For WB L in timing stage 1, the delay is (80/600) - 1 = 0.867.

For WB T/R in timing stage 2, the delay is (265/1800) - 1 = 0.683.

Summing up the delays, the average approach delay for the westbound direction is (0.867 + 0.683)/2 = 0.775 sec.

h) To calculate the intersection average approach delay, we calculate the average of the average approach delays for all directions.

The intersection average approach delay is (0.725 + 0.735 + 0.734 + 0.775)/4 = 0.742 sec.