6. signalized Intersections

Transcription

1 6. signalized Intersections 1 References 1. HCM 2000, chapter safety.fhwa.dot.gov/intersection/signalized/sig_int_pps /short/sigint_short.ppt 3. mason.gmu.edu/~aflaner/ceie_360/signalized%20intersectio n_ch7_part_1_student.ppt 4. Sarraj, Y. and Almasri, E. 2007, Advanced traffic engineering, lecture notes. Note: - some slides are quoted from given references. - text is from HCM. 2 1

2 4-way Intersection Conflicts 32 conflict points 3 Objectives of Signal Timing Minimize delay Minimize conflicts Maximize capacity Reduce crashes Each objective leads to a different solution We must find an appropriate compromise 4 2

3 Warrants for the use of traffic signals A decision on the installation of traffic signals may be made on the basis of: Traffic flow Pedestrian safety Accident experience And the elimination of traffic conflict. 5 Warrants for the use of traffic signals Quick guide: For traffic flow: Traffic signals are justified if the following traffic flow exists for eight hours on an average day Flow on the major road (1+2) Flow on the minor road (3) or (4) 900 vehicles/hour and 100 vehicles/hour. 6 3

4 Warrants for the use of traffic signals For Pedestrian safety: Signal control offers considerable assistance to pedestrian movements. The Department of Transport in the UK advises that a pedestrian stage is required: 1. if pedestrians across any arm of the junction is 300 ped./hour 2. or if turning traffic flow into any arm has an average headway of < 5 seconds and conflicting with a pedestrian flow of 50 pedestrian/hour 7 Signal aspects The indication given by a signal is known as the signal aspect. The usual sequence of signal aspects or indications in the UK and USA is: In UK Red Red/Amber Green and Amber In USA Red Green and Amber 8 4

5 Meaning of traffic signal indications Color Red Red-Amber Green Amber Signal indication Meaning Stop & keep stopping Prepare to go but do not move Go Clear the intersection but do not cross the stop line Duration (s) Terms Cycle: a complete rotation through all the indications provided. Every legal movement receives a green Cycle Length (C): time (seconds) for the signal to complete one full cycle. Interval: an interval of time during which none of the lights at a signalized intersection changes Change interval: yellow indication for a given movement 10 5

6 Terms Clearance interval: all red, after yellow Green interval: green indication for a particular movement Red interval: red indication for a particular movement All-Red: red indication for all approaches Phase: the aspect of a cycle allocated to one or more streams of traffic 11 Example: T intersection of two one-way streets Cycle: a complete rotation through all the indications provided. Every legal movement receives a green Cycle length: sec = 53 sec 12 6

7 Terms Permitted Left Turns: a permitted left turn receives a green ball but must yield right of way to opposing movements, used when left turn movements are reasonable and gaps in opposing traffic flow are adequate 13 Terms Protected Left Turns: provided separate phase, left turn movements are protected by arrow, left turns on one-way or T-intersection are considered protected within that phase

8 Terms Protected/Permitted : left turns are given permitted for part of the cycle and then protected for another part of the cycle or protected and then permitted Image source: 15 Types of Signal Timing Isolated Signals: Fixed / Pretimed Signals which have a designated cycle which does not change regardless of flow or time of day Semi-actuated Signals in which a major flow sees green unless: a detector on a minor approach is triggered AND a preset, minimum green time is exceeded on the major approach Fully actuated t Signals in which current flow sees green unless: a detector is triggered AND the preset, minimum green time is exceeded on the current approach OR the preset, maximum green time is exceeded 16 8

9 Design Process (Webster s Method) Collect Traffic Variables: Hourly volume Peak hour volumes for all movements Peak 15-min volumes for all movements Design 17 Isolated Intersections Basic Timing Elements: Green: Green time Yellow: Yellow time Effective Green: Green + Yellow time vehicles are discharging All-Red: All movements have red Intergreen time: Yellow + All-Red Pedestrian WALK: 4-7 seconds when sign says WALK Pedestrian crossing time (PCT): time required for a pedestrian to cross the intersection 18 9

10 General Approach for Signal Timing (step1) Select phasing plan Calculate design flow rate using peak hour volume and PHF 19 Peak Hour Factor (PHF) Design Hourly Volume (DHV): DHV = (Peak-Hour Volume / PHF) Design Hour Volume is the one hour traffic volume used as the basis of design (usually as a prediction of a future condition) 20 10

11 Design Hour Volume PHF Adjusts volume to match peak 15 minutes PHF = 0.85 Calculated Volume = 1200 v/hr DHV=1,200 vph = 1,411 vph General Approach for Signal Timing (Step2) Find the critical movements or lanes and calculate the critical flow ratios 22 11

12 Lane Group Separates traffic into consecutive movements Lane group set of movements that has same green phase and move together Can be one or more lanes Guidelines for deciding lane groups: use separate lane groups for exclusive left-turn lane(s) unless a shared left-through also exists for the approach use separate lane groups for exclusive right-turn lane(s) unless a shared right-through also exists for the approach 23 Lane Group 24 12

13 Saturation Flow Rate service rate: maximum vehicles that can be served in 1 hour assuming continuous green and a continuous queue of vehicles Represents capacity for the lane group when signal turns green reaction and delay time as vehicles start up, then flow becomes uniform headway becomes uniform 25 Saturation Flow Rate sat. flow can be determined directly in the field or calculated ideal s o = 1,900 pcphgpl (passenger cars per hour of green per lane) adjust s o to reflect non-ideal conditions 26 13

14 Saturation Flow Rate Number of vehicles that could enter the intersection after initial startup if constant queue existed and constant green s = _3600_(sec/hour) h where: s = saturation flow rate in vehicles per hour of green per lane(vphgpl) h = saturation headway (seconds)

15 prevailing saturation flow for a specific lane group: s = s o * N * f w * f HV * f g * f p * f bb * fa * f LU * f LT * f RT * f Lbp * f Rbp N = number of lanes in lane group f w = lane width adjustment factor f HV = heavy vehicle adjustment factor Ideal saturation flow rate f g = grade adjustment factor is adjusted to represent f p = parking adjustment all the factors for the lane group which decrease f bb = bus blockage factor capacity (non-ideal ffa = area type conditions) LU = lane utilization factor f LT = left turn adjustment factor f RT = right turn adjustment factor f Lbp = pedestrian and bike adjustment factor for left turn movement f Rbp = pedestrian and bike adjustment factor for right turn movement

16 31 See Appendix D in Chapter 16 of HCM of more details for pedestrian and bicycle blockage 32 16

17 Example of pedestrian blockage 33 Critical Lane Group For a given phase: several lanes of traffic on one or more approaches move simultaneously One of those movements has the most intense traffic One lane (movement) requires the most time, all others require less Becomes the design lane If sufficient time is given to the critical lane, all other lanes moving within the phase will be accommodated Only one critical lane (movement) per phase 34 17

18 Critical Movement or Lane Movement that requires the most time to execute If phase is long enough for the most critical movement, other movements in phase will be serviced as well Can be determined using flow ratios Movement with highest flow ratio is critical movement (ratio of flow to saturation flow) 35 Flow Ratio Flow ratio = actual flow saturation flow rate Flow = 1,200 vph Saturation flow = 1500 vph Flow ratio = 1,200 vph = ,500 vph Same as volume/capacity 36 18

19 Critical Lane Example Find critical lanes for each phase Phase 1 (v/s) north = 250/1700 = 0.15 Phase 2 (v/s) west = 750/1700 = 0.44 (v/s) east = 600/1700 = 0.35 (v/s) south = 300/1700 = Critical Lane Example v/s for critical lane group (v/s) west = 0.44 (v/s) south =

20 Example For a NB/SB phase the following flows and saturation flow rates are available Movement Design Flow Rate (pcu/hr) Sat Flow Rate (pcu/hr) NB L,T NB R,T SB L,T SB R,T Which is the critical lane movement? What is the critical flow ratio? Solution: for NB L,T flow ratio = 600/1200 = 0.5 Movement Flow Ratio NB L,T 0.50 NB R,T 0.29 SB L,T 0.34 SB R,T General Approach for Signal Timing (step 3) Calculate intergreen time 40 20

21 Intergreen Time The intergreen period of a phase consists of both the yellow (amber) indication and the all-red indication Determined based on: Stopping Sight Distance Intersection clearance time Pedestrian crossing time if there are no pedestrian signals (will discuss under minimum green) gee 41 Intergreen Time Examples of inter-green periods at a two-phase traffic signal 42 21

22 Intergreen Time Examples of inter-green periods at a two-phase traffic signal 43 Calculation of Intergreen Time First, we calculate the minimum safe stopping distance. The equation for this distance is given below. Minimum Safe Stopping Distance: SD = 1.47*Vo*tr + (1.47*Vo)2/(30*[f ± G]) Where: SD = Min. safe stopping dist. (ft) Vo = Initial velocity (mph) tr = Perception/Reaction time (sec) f = Coefficient of friction G = Grade, as a percentage 44 22

23 Calculation of Intergreen Time Next, we calculate the time required for a vehicle to travel the minimum safe stopping distance and to clear the intersection. This is simple kinematics as well. Intersection Clearance Time: T = (SD + L + W)/(1.47*Vo) Where: T = Intersection clearance time (sec) Vo = Initial velocity (mph) L = Length of the vehicle (ft) SD = Min. safe stopping dist. (ft) W = Width of the intersection (ft) 45 Calculation of Intergreen Time Now that you ve determined the first two elements of the intergreen period length stopping distance and intersection clearance time you need to consider the pedestrians. The intergreen time for intersections that have signalized pedestrian movements is the same as the intersection clearance time

24 Calculation of Intergreen Time If you have an intersection where the pedestrian movements are not regulated by a separate pedestrian signal, you need to protect these movements by providing enough intergreen time for a pedestrian to cross the intersection. In other words, if a pedestrian begins to cross the street just as the signal turns yellow for the vehicular traffic, he/she must be able to cross the street safely before the next phase of the cycle begins. 47 Calculation of Intergreen Time The formula for this calculation is shown below. Pedestrian Crossing Time: PCT = W/V Where: PCT = Pedestrian crossing time (sec) W = Width of the intersection (feet) V = Velocity of the pedestrian (usually 4 ft/sec) The intergreen time is equal to whichever is larger, the pedestrian crossing time or the intersection clearance time

25 General Approach for Signal Timing (step 4) Calculate the optimum cycle length 49 Cycle Length Cycle should be long enough to serve critical movements but no longer If cycle is too short -- inefficient because of time lost to too many changes high compared to usable green time If too long, delays will be lengthened as vehicles wait Several ways to calculate optimum cycle length Webster's: most common minimizes intersection delay Gives optimum cycle length as a function of lost time and critical flow ratio 50 25

26 Cycle Length C o = 1.5L Σ(Y i ) where: C o = optimum cycle length L = sum of the lost time for all phases Y i = ratio of the design flow rate to the saturation flow rate for the critical approach or lane in each phase cycle length should be increased to the nearest multiple of 5 seconds once have cycle length subtract intergreen time allocate green based on critical movements 51 Lost Time Some time is lost as vehicles start up from a stop until vehicles are progressing at the saturation flow rate through the intersection Vehicles utilize some the yellow interval so this adds to the actual time available to vehicles 52 26

27 Start up lost time Average headway is greater than h First 3 or 4 vehicles at signal require more time to react and accelerate than subsequent 53 Start up lost time h = saturation headway (seconds) Average headway for first few vehicles in queue > h Start up lost time l1 = i where l1 = start-up lost time (sec/phase) i = incremental headway (time > h) for vehicle i 54 27

28 Time to discharge Queue Green time to discharge queue of vehicles T n = l 1 + nh Where T n = GREEN time to move queue of n vehicles through signalized intersection for phase l 1 =start-up lost time n = number of vehicles in queue h = saturation headway (s/veh) 55 Clearance Lost time Lost time associated with stopping queue at end of GREEN signal (l2) Difficult to observe in field Time between last vehicle s front wheels crossing stop line and initiation of GREEN for next phase 56 28

29 Total lost time Lost time due to vehicles starting up at beginning of green and vehicles stopping at end of green t L = l1 + l2 Where: tl = total lost time (sec/phase) l1 = start-up lost time (sec/phase) l2 = clearance lost time (sec/phase) 57 Lost Time for Phase i l i =G ai + y G ei Where: l i = lost time for phase i G ai = actual green time for phase i y = yellow interval for phase I G ei = effective green time for phase i 58 29

30 Lost time includes start-up delay plus any portion of yellow not used for vehicle movement Image source: 59 Effective green time Amount of time during cycle that vehicles are moving for a particular movement g 1 = G i + Y i t Li Where: g 1 = effective green time (sec) for movement i G i = actual green time (sec) for movement i Yi = sum of yellow interval for movement i t Li = total lost time for movement i Y i = y i + a ri Where: y i = yellow interval for movement i a ri = all red interval for movement i 60 30

31 Effective Red time Amount of time vehicles for a particular movement are not moving 61 Total Lost Time Total lost time for a cycle is given by: Where L = Σl i + R L = lost time per cycle l i = lost time for phase i R = total all red during cycle 62 31

32 Example Given: 3 phases, Calculate the optimum cycle length based on the following information Phase Critical Flow Ratio Lost Time (sec) Solution: C o = 1.5L + 5 = 1.5(6+4+7) +5 = 1.5(17) Σ (V/s) 1 - ( ) C o = 80.3 sec, use 80 sec 63 General Approach for Signal Timing(step5) Allocate available green based on critical flow ratios 64 32

33 Green Split Calculations With C o, allocate available green to phases Allocated by critical flow ratios Each phase receives green consistent with it's ratio of critical flow compared to that for other phases 65 Green Split Calculations For phase I: g i = (V/s) i * G te Σ (V/s) where: g i = length of green interval for phase i (sec) (V/s) i = critical flow ratio for phase i G te = available green for the cycle (sec) 66 33

34 Total Available Green G te =C L Where: G te = total effective green time per cycle C = actual cycle length L = total lost time 67 Example Given: 2 phase cycle s = same for both phases= 900 pcu/hr available green time = 60 sec Phase 1: critical flow rate = 500 pcu/hr Phase 2: critical flow rate = 250 pcu/hr 68 34

35 Example Given: 2 phase cycle s = same for both cycles = 900 pcu/hr available green time = 60 sec Phase 1: critical flow rate = 500 pcu/hr, flow ratio = 0.56 Phase 2: critical flow rate = 250 pcu/hr, flow ratio = 0.28 Solution for phase I: g 1 = (V/s) 1 _*G TE = 0.56 * 60 = 40 sec Σ (V/s) ( ) 69 General Approach for Signal Timing (Step 6) Calculate length of minimum green time 70 35

36 Minimum Green Interval Pedestrian crossing time is the minimum green that can be given Pedestrians can only cross intersection as long as no conflicting movements are present (with the exception of permitted left and right turns) Sum of green and intergreen must provide time for ped. to cross approach 71 Minimum Green Interval With pedestrian signal Assumptions: pedestrian walk signal will be on for approx. 7 sec a pedestrian may begin crossing the street as DON'T WALK begins to flash pedestrians walk about 4 ft/sec WALK interval is contained in the green interval of the corresponding approach 72 36

37 Minimum Green Interval P t = _L_ + 2.7(N ped ) S p W E P t = _L_ + 2.7(N ped ) for W E > 10 ft for W E <= 10 ft S p where: P t = pedestrian crossing time (sec) for pedestrian signal L = width of intersection (feet) S p = velocity of the pedestrian (usually 4 ft/sec) --depends on ped. N ped = number of pedestrians crossing during an interval 3.2 = pedestrian start-up time W E = effective crosswalk width (feet) 73 Minimum Green Interval g min = P t -I where: g min = minimum green time (sec) P t = pedestrian crossing time (sec) I = clearance interval (sec) 74 37

38 Given: Intersection width = 60 feet S p = 4 feet/sec Clearance time is 6 sec. Example 12 peds/interval 9 ft crosswalk G t = _L_ (N ped ) for W E <= 10 ft S p W E G t = _60 ft (12) = 18.6 sec 4 ft/sec 9 75 Given: Intersection width = 60 feet S p = 4 feet/sec Clearance time is 6 sec. Example 12 peds/interval 9 ft crosswalk P t = 18.6 sec g min = P t - I = 18.6 sec - 6 sec = 12.6 sec 76 38

39 General Approach for Signal Timing Allocate available green based on critical flow ratios Calculate the capacity Check design flow rates /capacity and green intervals/minimum green intervals Adjust cycle timing if necessary 77 Adjustments Once done need to see if results work Make sure green meets requirements or adjust until it does (ped crossing) Check capacity If significantly below capacity, reduce green time If close increase Compute LOS and delay and check 78 39

40 Determination for Left Turn Phasing 79 Left turn phasing Additional phases increase lost time Consider protected or protected/permitted: VLT >= 200 veh/hr VLT*(v o /N o ) >= 50,000 Where VLT = left-turn flow rate Vo = opposing thru movement flow rates No = number of lanes for opposing through movement 80 40

41 Left turn phasing Usually not provided when V lt < two vehicles per cycle (sneakers) When protected left is used for opposing left, consider even if not needed 81 Protected Safest Recommended when 2 of following are met Left-turn flow rate > 320 veh/h Opposing flow rate > 1,100 veh/hr Opposing speed limit >= 45 mph Two or more left turn lanes 82 41

42 Protected Recommended when 1 of following is met Three opposing traffic lanes with >= 45 mph speed limit Left turn flow rate > 320 and % of HV > 2.5% >= 7 left turn accidents in 3 years have occurred Average stopped delay to left turning traffic is accepatble for fully protecte phasing and engineer judges that additional left-turn accidents will occur 83 anual 2000 from Highway Capacity Ma 42

43 Baseline Assumptions D/D/1 queuing (deterministic (D) arrival/ deterministic (D) departure/ 1 server. Approach arrivals < departure capacity (no queue exists at the beginning/end of a cycle) Quantifying Control Delay Two approaches Deterministic (uniform) arrivals (Use D/D/1) Probabilistic (random) arrivals (Use empirical equations) Total delay can be expressed as Total delay in an hour (vehicle-hours, person-hours) Average delay per vehicle (seconds per vehicle) 43

44 D/D/1 Signal Analysis (Graphical) Departure Rate Arrival Rate Vehicles Queue dissipation Total vehicle delay per cycle Maximum queue Maximum delay Time Red Green Red Green Red Green Signal Analysis Random Arrivals Webster s Formula (1958) 44

45 Definition Level of Service (LOS) Chief measure of quality of service Describes operational conditions within a traffic stream Does not include safety Different measures for different facilities Six levels of service (A through F) Signalized Intersection LOS Based on control delay per vehicle How long you wait, on average, at the stop light from Highway Capacity Manual

46 Typical Approach Split control delay into three parts Part 1: Delay calculated assuming uniform arrivals (d 1 ). This is essentially a D/D/1 analysis. Part 2: Delay due to random arrivals (d 2 ) Part 3: Delay due to initial queue at start of analysis time period (d 3 ). Often assumed zero. ( PF ) + d2 d3 d = d + 1 d d = Average signal delay per vehicle in s/veh PF = progression adjustment factor d 1, d 2, d 3 = as defined above Uniform Delay (d 1 ) d 1 g 0.5C 1 C = g 1 min 1, X C ( ) d 1 = delay due to uniform arrivals (s/veh) C = cycle length (seconds) g = effective green time for lane group (seconds) X = v/c ratio for lane group 46

47 Meaning of signal progression Simple Progression On A One-way Street Progression adjustment factor 47

48 Progression adjustment factor 2012/3/11 Traffic Control Design TC6 95 Incremental Delay (d 2 ) d 2 = 900T 2 8kIX ( X 1) + ( X 1) + ct d 2 = delay due to random arrivals (s/veh) T = duration of analysis period (hours). If the analysis is based on the peak 15-min. flow then T = 0.25 hrs. k = delay adjustment factor that is dependent on signal controller mode. For pretimed intersections k = 0.5. For more efficient intersections k < 0.5. I = upstream filtering/metering i t i adjustment t factor. Adjusts for the effect of an upstream signal on the randomness of the arrival pattern. I = 1.0 for completely random. I < 1.0 for reduced variance. c = lane group capacity (veh/hr) X = v/c ratio for lane group 48

49 Initial Queue Delay (d 3 ) Applied in cases where X > 1.0 for the analysis period Vehicles arriving during the analysis period will experience an additional delay because there is already an existing queue When no initial queue d 3 = 0 49