Question

6, Traffic Shockwave theory (15%) Vehicles approaching an signalized intersection are traveling at speed 40 miles per hour and the density is about 40 vehicle/miles/lane (vehicle arrival). The red light last about 40 sec. If the saturation flow is 1900 vehhr/lane with a density of 52 veh/miles/hour (queue discharging). and the jam density is 120 veh/mile lane, please determine: a. the queue length at the end of the red light: b. the maximum queue length: c. The time it takes for the queue to dissipate after the end of the red indication (Hint: You have three traffic states and two shockwaves to calculate in this question)

Answer 1

The flow at siynalized intersection q_1 = k_1 v_1 k_1 = density = 40 reh/m: /lane v_1 = flow = 40 mi/h q_1 = 40 times 40 = 1600 veh/h/m shock wave velocity w_3 = q_1/K_1 - k_j = 1600/40 - 120 w_13 = -20 m: /hr length of the queue at the end the red phase L = 5 times w_,3 w_13 = -20 m: /hr = -20 times 5280/3600 Ft/s w_13 = -29.33 Ft/s red signal light about 40 sec L = 40 times 29.333 L = 1173.33 ft \r\n Back ward recovery shock wave velocity w_34 = -q_4/k_j - k_4 = -1900/120 - 52 w_34 = -27.94 m: /hr converting shock wave velocity m: /hr to ft/s w_34 = -27.94 times 5280/3600 Ft/s w_34 = -40.98 Ft/s The maximum queue length ST^bar = r_w_13 w_34/w_34 - w_13 = 40 times (29.33)(40.98)/40.98 - 29.33 ST^bar = 48077.736/11.65 ST^bar = 4126.85 ft