Transportation Engineering Lecture 8: Traffic Signal

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

Example The cycle length is 40 sec, 2 phase cycle and saturation headway 2.3sec. What should be the lane numbers for each approach?

Solution

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

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,

Adding consideration of v/c ratio and PHF Critical Lane & Time Budget Adding consideration of v/c ratio and PHF

Effects of right-turning vehicles Effect of Turning Vehicles Effects of right-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

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 The right turn adjustment factor is related to the fraction of RT vehicles and the TH equivalency

Effect of Turning Vehicles

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)

Performance measures Delay Delay Queuing Stops Delay most directly affects driver experience.

Performance measures Delay Stopped Time Delay: time a vehicle stopped waiting to pass the intersection. Approach Delay: stopped time + acceleration + deceleration Travel Time Delay: (actual travel time-desired travel time) Time-in-queue Delay: Total time from joining a queue to passing the stop line

Delay Delay

Delay Webster’s Delay Model Webster’s uniform delay (UD) formula

Webster’s Delay Model Delay Webster’s uniform delay (UD) formula Red time, Height of the triangle, Area of the triangle, (UD) Average delay per vehicle,

Webster’s optimum cycle length Delay Webster’s optimum cycle length developed based on minimization of overall delay at intersection

Webster’s optimum cycle length Delay Webster’s optimum cycle length

Notes on cycle length Delay Optimum cycle length is min. delay point of the suitable curve Unnecessarily long cycle lengths cause substantial delays; short cycle lengths may cause congestion or violate the pedestrian crossing times. Cycle lengths between 45 and 180 s are used in the field. All cycle lengths typically end in 0 or 5; thus, if the cycle length estimate is 52s, a cycle equal to 50 or 55s should be selected.

Notes on cycle length Delay Optimum cycle length is min. delay point of the suitable curve Unnecessarily long cycle lengths cause substantial delays; short cycle lengths may cause congestion or violate the pedestrian crossing times. Cycle lengths between 45 and 180 s are used in the field. All cycle lengths typically end in 0 or 5; thus, if the cycle length estimate is 52s, a cycle equal to 50 or 55s should be selected.

Delay Example Consider an approach volume of 1000 vph, saturation flow rate of 800vphg, cycle length 90 s and g/C ratio 0.55. What average approach delay per vehicle is expected?