Chapter 7 Traffic Control and Analysis at Signalized Intersections

1. Chapter 7Traffic Control and Analysis at Signalized Intersections Principles of Highway Engineering and Traffic Analysis, 2005 Third Edition Fred Mannering, Walter Kilareski Scott Washburn

2. Basic Concepts

3. Signal Timing Terminology Indication: illumination of signal lenses which informs the driver as to which movements are permitted or prohibited Cycle: one complete rotation through all of the indications provided Cycle length: time required to complete one rotation, given in seconds, C Yellow time: the change interval, warns drivers that the signal is changing from green to red Clearance interval: the all red indication Green time: the �go� indication for a particular movement or set of movements Red time: the �stop� indication for a particular movement or set of movements Phase: a green interval plus the change interval and clearance intervals that follow it (typically related to a particular movement or approach)

4. Modes of Operation Pretimed Operation: preset cycle lengths and intervals. 3-dial signal controllers allow for three different cycles throughout the day. Semi-Actuated: detectors at minor approaches. Green for major street unless vehicle detected on minor street Fully Actuated: every approach has detectors. Green time allocated based on vehicle detection. Each cycle different, limits placed on min/max green times and min gaps between vehicles to maintain green indication. Computer Controlled: System wide control. Optimal progression patterns determined for system wide operation. In order to optimize, however, cycle lengths must be the same or multiples of a base to achieve optima performance.

8. Left Turn Timing Permitted Left Turns: drivers permitted to cross opposing traffic but must select their own gap (green ball on signal head) Protected Left Turns: left turns made without opposing through vehicular traffic (green arrow on signal head) Protected/Permitted or Permitted/Protected: left turns protected at the beginning of a phase, then permitted during through movement green time

9. Dual-Ring Configuration Allows for maximum flexibility to control phase duration and sequencing of intervals Best hardware to have when implementing fully-actuated signals See Figure 7.3 Movements 1-4 can occur simultaneously with movements 5-8 (as long as the occur on the same side of the barrier) The dual ring ability allows for skipping of phases where there isn�t a need for them due to low flow Allows the unused green to be allocated to more congested phases

11. Discharge Headway Discharge headway: time passage between successive vehicles as they cross the curb line during a green phase. Measured at rear wheels of vehicles. First headway longer than others. Includes driver reaction time, and acceleration time. Second headway shorter, reaction and acceleration times overlap. Eventually headways level out, typically around 4-5 vehicle. Once this occurs, saturation headway can be measured.

12. Saturation Flow Rate Saturation headway: h=headway achieved by stable moving platoon of vehicles passing through a green indication Saturation Flow Rate: every vehicle assumed to occupy h seconds of green time, and if signal always green, then s vehicles/hour could enter intersection s = 3600/h If signal always green, could simply multiply by the number of lanes to estimate the capacity of the approach. *units of measure: vehicles per hour of green time per lane, (vphgpl)

13. Lost Time Time that is not effectively serving any movement or traffic Total lost time includes start-up and clearance lost times Start-up lost time = signal indication turns from red to green and vehicles do not instantly move at the saturation flow rate Clearance lost time= later portion of the yellow phase + all red phase

14. Start-up Lost Time Need to account for the time lost when first few vehicles crossing intersection Start-up lost time (l): actual headway-saturation headway multiplied by number of vehicles (n) traveling at headways greater than saturation headway (h) Lost time also occurs when a movement is stopped (at the beginning of the clearance interval)

15. Total Lost Time

17. Effective Green Time Amount of time available to be used at a rate of one vehicle every h seconds gi=Gi + Yi +AR� tL gi=effective green time Gi=actual green time for movement i,sec Yi=sum of yellow plus all red time for movement i,sec tL=total lost time per phase, sec Total lost time includes start up time and clearance lost time (tL=tsl + tcl)

18. Green Ratio Ratio of effective green time to cycle length for a particular movement Simple capacity can be determined using: ci=si(gi/C) ci=capacity of lanes serving movement i, vph C=Signal cycle length, sec si=saturation flow rate for movement i, sec gi=effective green time for movement i,sec

19. Effective Red Time Effective red time is the time in which the intersection is not being utilized by traffic

20. Simple Capacity Estimation Approach or movement capacity can be estimated through a simple relationship

21. Using Simple Queuing Models to Estimate Signal Performance Ex 7.1 in text Pretimed signal with sat flow rate of 2400 vph 24 sec of effective green time in 80 s cycle Flow at approach is 500 vph Estimate operational performance using D/D/1 queuing.

22. Example Continued Put arrival and departure rates in similar units

23. Example Continued A variety of measures can be determined using equations 7.7-7.13

24. Estimating Delay at Real-World Signals The D/D/1 models are limited by their assumption of uniform arrivals For signals, non-uniform arrivals are much more likely than uniform arrivals To determine LOS, control delay is estimated for traffic signals and unsignalized intersections Control delay = deceleration time, queue move-up time, stop time, and acceleration time through the intersection

25. HCM Delay Model Total Average Individual Stopped Delay for Random Arrivals (sec/veh)

26. HCM Delay Model d=average signal delay per vehicle in sec d1=avg delay per vehicle due to uniform arrivals in sec PF=progression adjustment factor d2=avg delay per vehicle due to random arrivals in sec d3=avg delay per vehicle due to initial queue at start of analysis period in sec

27. HCM Delay Model C=cycle length, sec g=effective green time for lane group in sec X=v/c ratio for lane group T=duration of analysis period in hours k=delay adjustment factor that is dependent on signal controller mode I=upstream filtering adjustment factors c=lane group capacity in veh/hr

28. Example An approach to a pretimed signalized intersection has: s= 2400 veh/hr 24 sec effective green C = 80 sec Given flow = 500 veh/hr; no initial queue and flow accounts for 15-min period, determine average approach delay per cycle.

29. Example Continued Calculate uniform delay first:

30. Example Continued Calculate Random Delay