Module 7 : Traffic Signal Design

Lecture 34 : Design Principles of Traffic Signal

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	Cycle time Cycle time is the time taken by a signal to complete one full cycle of iterations. i.e. one complete rotation through all signal indications. It is denoted by $C$. The way in which the vehicles depart from an intersection when the green signal is initiated will be discussed now. Figure 1 illustrates a group of N vehicles at a signalized intersection, waiting for the green signal. Figure 1: Group of vehicles at a signalized intersection waiting for green signal As the signal is initiated, the time interval between two vehicles, referred as headway, crossing the curb line is noted. The first headway is the time interval between the initiation of the green signal and the instant vehicle crossing the curb line. The second headway is the time interval between the first and the second vehicle crossing the curb line. Successive headways are then plotted as in figure 2. Figure 2: Headways departing signal The first headway will be relatively longer since it includes the reaction time of the driver and the time necessary to accelerate. The second headway will be comparatively lower because the second driver can overlap his/her reaction time with that of the first driver's. After few vehicles, the headway will become constant. This constant headway which characterizes all headways beginning with the fourth or fifth vehicle, is defined as the saturation headway, and is denoted as $h$. This is the headway that can be achieved by a stable moving platoon of vehicles passing through a green indication. If every vehicles require $h$ seconds of green time, and if the signal were always green, then $s$ vehicles per hour would pass the intersection. Therefore, $$s=\frac{3600}{h}$$ (1) where $s$ is the saturation flow rate in vehicles per hour of green time per lane, $h$ is the saturation headway in seconds. As noted earlier, the headway will be more than h particularly for the first few vehicles. The difference between the actual headway and h for the $i^{th}$ vehicle and is denoted as $e_i$ shown in figure 2. These differences for the first few vehicles can be added to get start up lost time, $l_1$ which is given by, $$l_1 = \sum_{i=1}^n{e_i}$$ (2) The green time required to clear N vehicles can be found out as, $$T = l_1 + h.N$$ (3) where $T$ is the time required to clear N vehicles through signal, $l_1$ is the start-up lost time, and $h$ is the saturation headway in seconds. Effective green time Effective green time is the actual time available for the vehicles to cross the intersection. It is the sum of actual green time ($G_i$) plus the yellow minus the applicable lost times. This lost time is the sum of start-up lost time ($l_1$) and clearance lost time ($l_2$) denoted as $t_L$. Thus effective green time can be written as, $$g_i = G_i + Y_i - t_L$$ (4) Lane capacity The ratio of effective green time to the cycle length ( $\frac{g_i}{C}$)is defined as green ratio. We know that saturation flow rate is the number of vehicles that can be moved in one lane in one hour assuming the signal to be green always. Then the capacity of a lane can be computed as, $$c_i = s_i \frac{g_i}{C}$$ (5) where $c_i$ is the capacity of lane in vehicle per hour, $s_i$ is the saturation flow rate in vehicle per hour per lane, $C$ is the cycle time in seconds. Numerical example Let the cycle time of an intersection is 60 seconds, the green time for a phase is 27 seconds, and the corresponding yellow time is 4 seconds. If the saturation headway is 2.4 seconds per vehicle, the start-up lost time is 2 seconds per phase, and the clearance lost time is 1 second per phase, find the capacity of the movement per lane? Solution Total lost time, $t_L$ = 2+1 = 3 seconds. From equation 4 effective green time, $g_i$ = 27+4-3 = 28 seconds. From equation 1 saturation flow rate, $s_i = \frac{3600}{h} = \frac{3600}{2.4}$ = 1500 veh per hr. Capacity of the given phase can be found out from equation 5 as $C_i = 1500\times \frac{28}{60}$ = 700 veh per hr per lane. Critical lane During any green signal phase, several lanes on one or more approaches are permitted to move. One of these will have the most intense traffic. Thus it requires more time than any other lane moving at the same time. If sufficient time is allocated for this lane, then all other lanes will also be well accommodated. There will be one and only one critical lane in each signal phase. The volume of this critical lane is called critical lane volume.