Traffic signal design-III

Lecture notes in Transportation Systems Engineering

4 August 2009

Overview

Topic that will be covered in this chapter are:

1. Effect of right turning vehicles
2. Adjustments on saturatin flow
3. Clearence and change interval
4. Various delay models at signalized intersection
5. HCM procedure on signalized intersection capacity and level of service analysis

Effect of right-turning vehicles

1. A right-turnings vehicle will consume more effective green time traversing the intersection than a corresponding through vehicle.
2. Applicable especially at permitted right movements
3. right turn has great difficulty in manneouring and find a safe gap
4. right turn vehicle may block a through vehicle behind it
5. right turn vehciles may take 2, 4, or even 10 times the time to that of a through movement
6. The equivalency concept will answer how many through vehicles could pass the intersection during the time utilized by a through movement.
7. If 3 through and 2 right turn movement takes place at some time duration in a given lane. Assume at the same time duration in another identical lane if 9 through vehicles moved, then vehicles, then

   $$9=3+2\times e_{RT}, \Rightarrow e_{RT} = \frac{9-3}{2} = 3.0$$ (1)

   
   
   Therefore, the right-turn adjustment factor under the current prevailing condition is 3.0.
8. This factor is normally applied in the saturation flow by adjusting its value.

   $$h_{adj} = h_{ideal} {\mathrm sec} \times ( p_{RT} \times e_{RT} + (1-p_{RT}) \times 1 )$$ (2)

   
   
   For example, if there is 15 percent right-turn movement, $e_{RT}$ is 3, and saturation headway is 2 sec, then the adjusted staturatin headway is computed as follows:

   $$h_{adj} = 2 {\mathrm sec} \times ( 0.15 \times 3 + 0.85 \times 1 ) = 2.6 {\mathrm sec/veh}$$ (3)

   
   

9. The saturation head way is increased thereby reducing the saturatin flow $s_{adj}=\frac{3600}{h_{adj}}=\frac{3600}{2.6}=1385$ veh/hr.
10. The adjested saturation flow $s_{adj}$ can be written as

    $$s_{adj}=s_{ideal}\times f_{RT}$$ (4)

    
    

11. From the Equation 2 and 4, following relation can be easily derived:

    $$f_{RT}=\frac{1}{1+p_{RT}(e_{RT}-1)}$$ (5)

    
    
    where $f_{RT}$ is the multiplicative right turn adjustment factor to the ideal stauration flow.
12. In the above example,

    $$f_{RT}=\frac{1}{1+0.15\times (3-1)}=0.77=1386 {\mathrm veh/hr}.$$ (6)

    
    
    Therefore the adjusted saturatin flow is $s_{adj}=1800*0.77$ veh/sec.

Change interval

Change interval or yellow or amber time is given after GREEN and before RED which allows the vehicles within a 'stopping sight distance' from the stop line to leagally cross the intersectin. The amber time $Y$ is calculated as

$$Y=t+\frac{v}{2(gn+a))}$$ (7)

where $t$ is the reaction time (about 1.0 sec), $v$ is the velocity of the approaching vehicles, $g$ is the acceleration due to gravity (9.8 m/sec2), $n$ is the grade of the approach in decimels and $a$ is the deceleration of the vehicle (around 3 m/sec2).

Clearence interval

The clearence interval or all-red will facilitate a vehicle just crossed the stop line at the turn of red to clear the intersection with out being collided by a vehicle from the next phase. ITE recomends the following policy for the design of all read time, given as

$$R_{AR}== \left\{ \begin{array}{lll} \frac{w+L}{v} & \mbox{if no p... ...edestrain corossing} \\ \frac{P+L}{v} & \mbox{if protected} \end{array}\right.$$ (8)

where $w$ is the width of the intersection from stop line to the farthest conflicting trafic, $L$ is the length of the vehicle (about 6 m), $v$ is the speed of the vehicle, and $P$ is the width of the intersection from STOP line to the farthest confliting pedestrain cross-walk.

Bibliography

1 William R McShane, Roger P Roesss, and Elena S Prassas. Traffic Engineering. Prentice-Hall, Inc, Upper Saddle River, New Jesery, 1998.