Question

The saturation flow rate for an intersection approach is 3600 veh/h. At the beginning of a cycle (effective red) no vehicles are queued. The signal is timed so that when the queue (from the continuously arriving vehicles) is 13 vehicles long, the effective green begins. If the queue dissipates 8 seconds before the end of the cycle and the cycle length is 60 seconds, what is the arrival rate, assuming D/D/1 queuing? Draw D/D/1 queuing diagram and label accordingly ??

**** please provide a D/D/1 drawing its important ***

Thanks in advance :D

Answer 1

Given u = 3600 veh/hr 3600 veh/sec 3600 u=1 veh/sec Cycle length (C)=60 sec Since at the beginning of the signal number of vehicles is zero and when the time begin, 13 number of vehicles are in the queue. Thus, 0+it = 13 t== Since C= red time + green time. Therefore, 1(C-8)= u(C-8-t) Substitute the value in the equation above. A(C-8) = uc--1 2(60 – 8) = 1(60-8-13) 2= 0.5 veh/sec 2=0.5x3600 2=1800 veh/hr

Now calculate the red and green time. red time 0.5 red time = 26 sec green time =60-26 greentime = 34 sec Draw the D/D/1 queuing as follows: Service rate Arrival rate Flow rate Time Red Green