Your first assignment as a transportation engineer is to design a small signalized intersection. One step in this design process requires that you find the saturation flow rate for the eastern approach. You decide to try and calculate the saturation flow rate from field observations of an approach that is part of an intersection very similar to yours. After recording the departure headways of the first few discharging vehicles for several different cycles, you calculate the average headway and get a value of 2.1 seconds.
Calculate the saturation flow rate. If the eastern approach to your intersection has an estimated green time of 20 seconds and the total cycle length will be around 45 seconds, what is the approximate capacity for the eastern approach?
[Solution Shown Below]
Since we know, from queuing theory, that the vehicles in a queue will discharge at the saturation flow rate, we can take the average headway of those vehicles and convert it into the saturation flow rate. Since one vehicle entered the intersection every 2.1 seconds when the queue was discharging, 3600/2.1 vehicles would enter the intersection in an hour if the queue were long enough and the approach was given a green signal for an entire hour. Therefore, our saturation flow rate is 1714 veh/hr. Since we weren't given any information to the contrary, we will assume that these vehicles were all passenger cars and call our saturation flow rate 1714 pcu/hr.
To find the capacity, we first need to calculate the green ratio (g/C). If the length of the green interval (g) is 20 seconds and the cycle length (C) is about 45 seconds, the green ratio will be about 0.44. Capacity is the product of the green ratio and the saturation flow rate. In this case, the capacity of the eastern approach would be about 760 pcu/hr.