Introduction to Transport Lecture 3: Traffic Signal

Basic Principles of Intersection Signalisation Four basic mechanisms Discharge headways at signalised intersections The critical lane and time budget concept Effects of right turning vehicles Delay

Discharge Headways Discharge headways etc. Consider N vehicles discharging from the intersection when a green indication is received. The first discharge headway is the time between the initiation of the green indication and the rear wheels of the first vehicle to cross over the stop line. The Nth discharge headway (N>1) is the time between the rear wheels of the N-1 th and N th vehicles crossing over the stop line.

Discharge Headways Discharge headways etc. The headway begins to level off with 4 or 5th vehicle. The level headway = saturation headway

Saturation flow rate Discharge headways etc. In a given lane, if every vehicle consumes an average of h seconds of green time, and if the signal continues to be uninterruptedly green, then S vph could enter the intersection where S is the saturation flow rate (vehicles per hour of green time per lane) given by

Lost time Discharge headways etc. Start-up lost time: At the beginning of each green indication as the first few cars in a standing queue experience start-up delays, e(i) = (actual headway-h) for vehicle I Calculated for all vehicles with headway>h green time necessary to clear N vehicles,

Lost time Discharge headways etc. The change interval lost time: It is estimated by the amount of the change interval not used by vehicles; this is generally a portion of the yellow plus all-red intervals The 1994 Highway Capacity Manual (HCM) adds the two lost times together to form one lost time and put it at the beginning of an interval. Default value = 3.0 seconds per phase

Effective green time Discharge headways etc. Actual green time Yellow + all red time The ratio of effective green time to cycle length is ‘green ratio’ Capacity of a lane,

Graphical representation Discharge headways etc.

Notes on saturation flow Discharge headways etc. Updated Greenshield’s Equation Ideal saturation headway and flow rate occurs under ideal conditions of 12-ft lanes, no grades, no parking zone, all passenger cars, no turning and location outside CBD Saturation flow rate in single lane approaches is less than multilane approaches Saturation flow rate and headway has a significant probabilistic component

Example Discharge headways etc. A given movement at a signalised intersection receives a 27-second green time, and 3 seconds of yellow plus all red out of a 60- second cycle. If the saturation headway is 2.14 seconds/vehicle, the start-up lost time is 2 seconds/phase and the clearance lost time is 1 second/phase, what is the capacity of the movement per lane?

Critical Lane Critical Lane & Time Budget This concept is used for the allocation of the 3600 seconds in the hour to lost time and to productive movement. The amount of time required for each signal phase is determined by the most intensely used lane which is permitted to move during the phase. All other lane movement in the phase require less time than the critical lane. The timings of any signal phase is based on the flow and lost times of the critical lane. Each signal phase has one and only one critical lane.

Capacity (using critical Lane volume) Critical Lane & Time Budget Capacity can be maximum sum of critical lane volumes that a signal can accommodate. the max. total volume that can be handled on all critical lanes for a given time budget (within an hour), tL total lost time per phase N is total number of phases in a cycle C is cycle length

Capacity (using critical Lane volume) Critical Lane & Time Budget the effect of number of phases and cycle time on Vc Lost time remains constant through out (h= 2.15s, lost time = 3s/phase)

Adding consideration of v/c ratio and PHF Critical Lane & Time Budget Adding consideration of v/c ratio and PHF (volume-to-capacity) V/C ratio: flow rate in a period expressed as an hourly equivalent over capacity (saturation flow rate) the proportion of capacity being utilized A measure of sufficiency of existing or proposed capacity V/C ratio = 1.00 is not desirable

Adding consideration of v/c ratio and PHF Critical Lane & Time Budget Adding consideration of v/c ratio and PHF Peak Hour Factor (PHF) : To account for flow variation within an hour PHF For 15 min. aggregate volume, PHF = The lower the value, the greater degree of variation in flow during an hour.

Adding consideration of v/c ratio and PHF Critical Lane & Time Budget Adding consideration of v/c ratio and PHF Min. cycle length, Considering desired v/c ratio, Considering peaking within hour, Desirable cycle length,

Effects of right-turning vehicles Effect of Turning Vehicles Right turns can be made from a Shared lane operation Exclusive lane operation Traffic signals may allow permitted or protected right turn Right-turning vehicles look for a gap in the opposing traffic on a permitted turning movement, which is made through a conflicting pedestrian or an opposing vehicle flow. Right-turning vehicles consume more effective green time than through vehicles.

Effects of right-turning vehicles Effect of Turning Vehicles

Effects of right-turning vehicles Effect of Turning Vehicles Effects of right-turning vehicles Through Car Equivalent Example: with an opposing flow of 700 vph which has no platoon structure, it is observed that the right lane of the figure processes two RT vehicles and three TH vehicles in the same time that the left lane processes 17 TH vehicles. What is the “THcar” equivalent of one right-turning vehicle (RT equivalent) in this case? 3 + 2 ERT = 17 or ERT = 7 In this situation, 1 RT vehicle is equivalent to 7 TH vehicles in terms of headway.

Effects of right-turning vehicles Effect of Turning Vehicles Effects of right-turning vehicles Through Car Equivalent depends on the opposing flows, and the number of opposing lanes

Example Effect of Turning Vehicles Example: consider an approach with 10% RT, two lanes, permitted RT phasing, a RT equivalency factor of 5, and an ideal saturation headway of 2 sec per veh. Determine the equivalent saturation headway for this case, the saturation flow rate for approach, and the adjustment factor for the sat. flow rate? (adj. flow rate / sat flow rate of TH vehicles)