Question

6- At the beginning of an effective red, vehicles are arriving at an approach at the rate of 600 veh/h and 18 vehicles are left in the queue from the previous cycle (at the end of the previous cycle’s effective green). However, due to the end of a major sporting event, the arrival rate is continuously increasing at a constant rate of 150 veh/h/min (after 1 minute the arrival rate will be 750 veh/h, after 2 minutes 900 veh/h, etc.). The saturation flow rate of the approach is 1800 veh/h, the cycle length is 60 seconds, and the effective green time is 40 seconds. Determine the total vehicle delay until complete queue clearance. (Assume D/D/1 queuing.)

can someone please help

Answer 1

Solution . Ciseen time = go seands Red time = to Beconde 100 Seconds Cycle length Amival Rate = Soo Vehler (0.138 Vehl bec) neborstine Rate - 3000 vehlho (0.833 vehl sec) Intensity Traffic p=2 p is the frost value to calculate soo Зооо = 0.167 Time to quelle clerimce after the Stent of effection goren pr to 0.167(70) I-P 1-0.167 11.69 0.833 14.03 Proportion of the cycle with a queue 70+1403 rt to こ Pa 84-03 = 0.8403

Proportion of vehicles Estopped. Ps xlot to) +18+9) 84.03 = 0.128 ( 70+ 14,01) 0.138 (70 +30) = 0.8403 Maximum number of vehicles in the queue Oman ex 0.138 (70) 99.5 = 2 Total Vehicle Delay per cycle: 0.1381 70) 211-0.157) tra to (d-106 2 676.2 1,666 → 406 5-han Average Delay per velicle = (703² 2011- 21100) (1 -0.167) 22 brap = 4900 166.6 = 29.415

Maximum Delay of my whicle dmax r = Tos They Solution combe determined; with a = 0.84 Pooperties the cycle queue mumber of vehicles in the queue =9.66 o Maximum o Total Deday 406 Veh-bec Auerage Delay = 29:41 be a Maximum delay = 7o Bec