CE351 Transportation Systems: Planning and Design

Transcription

1 CE351 Transportation Systems: Planning and Design TOPIC: Level of Service (LOS) at Traffic Signals 1

2 Course Outline Introduction to Transportation Highway Users and their Performance Geometric Design Pavement Design Speed Studies - Project Traffic Queuing Signalized Intersections Level e of Service in Highways and Intersections s Speed Zoning - Traffic Impact Studies 2

3 Signal Design The process of designing the different components of traffic signals 3

4 REVIEW 4

5 Summary (1) Start-up Lost Time (l 1) Time used by the first few vehicles in a queue while reacting to the initiation of the green phase and accelerating. 2 seconds is typical. Clearance Lost Time (l 2 ) Time between signal phases during which an intersection is not used by traffic. 2 seconds is typical. Lost Time (t L ) Time when an intersection is not effectively used by any approach. 4 seconds is typical. t L = l 1 + l 2 Total Lost Time (L) Total lost time per cycle during which the intersection is not used by any movement. 5

6 Summary (2) Effective Green Time (g) Time actually available for movement g = G + Y + AR t L Extension of Effective Green Time (e) The amount of the change and clearance interval at the end of a phase that is usable for movement of vehicles Effective Red Time (r) Time during which a movement is effectively not permitted to move. r = R + t L r = C g 6

7 Summary (3) Saturation Flow Rate (s) Maximum flow that could pass through an intersection if 100% green time was allocated to that movement. s = 3600/h Approach Capacity (c) Saturation flow times the proportion of effective green c = s g/c Peak Hour Factor (PHF) The hourly volume during the maximum-volume hour of the day divided by the peak 15-minute flow rate within the peak hour; a measure of traffic demand fluctuation within the peak hour. 7

8 General Approach for Signal Timing 1. Select phasing plan How many possible phasing plans? Phase The sum of the displayed green, yellow, and red times for a movement or combination of movements that receive the right of way simultaneously during the cycle. The sum of the phase lengths (in seconds) is the cycle length. 8

9 General Approach for Signal Timingi 2. Find the critical movements or lanes and calculate the critical flow ratios 9

10 Critical lane groups and Total Cycle Lost Time Y c = sum of flow ratios for critical lane groups Y c n v = i= 1 s ci L= total lost time per cycle ( ) L L n = i= 1 t ci 10

11 Summary (4) Flow Ratio The ratio of actual flow rate (v) to saturation flow rate (s) for a lane group at an intersection Lane Group A set of lanes established at an intersection approach for separate analysis Critical Lane Group The lane group that has the highest flow ratio (v/s) for a given signal phase Citi Critical lvolume-to-capacity Ratio (X c ) The proportion of available intersection capacity used by vehicles in critical lane groups In terms of v/c and NOT v/s 11

12 General Approach for Signal Timing 3. Calculate the optimum cycle length 12

13 Minimum Cycle Length C min L = n X c i= 1 X c C min = estimated minimum cycle length (seconds) L = total lost time per cycle (seconds), 4 seconds per phase is typical (v/s) ci = flow ratio for critical lane group, i (seconds) X c = critical v/c ratio for the intersection v s ci How to set X c? Usually less than 1 to account for randomness 13

14 Optimum Cycle Length Estimation (Webster) C opt 1.5 = n 1 ( L) i= v s ci C opt = estimated optimum cycle length (seconds) to minimize vehicle delay L = total lost time per cycle (seconds), 4 seconds per phase is typical (v/s) ci = flow ratio for critical lane group, i (seconds) 14

15 Green Time Estimation g i = v s i C X i g = effective green time for phase, i (seconds) (v/s) i = flow ratio for lane group, i (seconds) C = cycle length (seconds) X i = v/c ratio for lane group i 15

16 Clearance Interval τ Y + AR min Y AR Y = t + r V w + l AR = 2a+ 2gG V τ min = minimum clearance interval t r = perception/reaction time (lower than 2.5, usually 1 second) w = width of intersection l = length of vehicle (feet) V = speed of vehicle a = constant rate of deceleration (ft/sec 2 ) G = percent grade divided by 100 g = acceleration due to gravity (32.2 ft/sec2) 16

17 Check for Constraints Pedestrians Bicycles Level of Service 17

18 Pedestrian Crossing Time G G p p L N ped = for WE > 10 ft. S p WE L + ( 0.27N ) for W 10 ft. = E ped S p G p = minimum green time required for pedestrians (seconds) L = crosswalk length (ft) S p W E p = average pedestrian speed (ft/s) often assumed 4 ft/s = effective crosswalk width (ft) 3.2 = pedestrian startup time (seconds) N ped = number of pedestrians crossing during an interval 18

19 Effective Width (W E ) from Highway Capacity 19 Manual 2000

20 Minimum Green Interval g = P -I min t where: g min = minimum green time (sec) P t = pedestrian crossing time (sec) I = clearance interval (sec) 20

21 Example Given: Intersection width = 60 feet 12 peds/interval S p = 4 feet/sec 9 ft crosswalk WALK interval = 10 sec Clearance time is 6 sec. G t = _L_ (N ped ) for W E <= 10 ft S p W E G t = _60 ft (12) 4 ft/sec 9 = 18.6 sec g min = P t - I = 18.6 sec - 6sec= 12.6 sec 21

22 LEVEL OF SERVICE AT SIGNALIZE INTERSECTIONS 22

23 Level of Service for car drivers: quantifying delays 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) 23

24 Design using D/D/1 System It provides a strong intuitive appeal that helps understand the analytic fundamentals underlying traffic analysis at signalized intersections. Consider the case where the approach capacity exceeds the approach arrivals. 24

25 Design using D/D/1 System λ= arrival rate, typically in veh/s, μ= departure rate, typically y in veh/s, g = effective green time in seconds, r = effective red time in seconds, and t c = time from the start of the effective green until queue clearance, in seconds. 25

26 D/D/1 Signal Analysis (Graphical) Departure Rate Arrival Rate Vehicles Queue dissipation i Total vehicle delay per cycle Maximum queue Maximum delay Time Red Green Red Green Red Green 26

27 Note Note that the per-cycle approach arrivals will be λ C corresponding approach capacity (maximum departures) per cycle will be λg. assumption that t μg > λc for all cycles (no queues exist at the beginning or end of a cycle). 27

28 D/D/1 System For the time to queue clearance after the start of the effective green The proportion of the cycle with a queue The proportion of vehicles stopped t c P P s q = = = ρr 1 ρ ( ) λ λ r + t C c ( r + tc ) ( r + g) = r + t C c = P q also, P s = λ λ ( r + tc ) μtc tc = = ( r + g) λc ρc 28

29 D/D/1 System The maximum number of vehicles in the queue, 2 The total vehicle delay λr D t = per cycle 2 ( 1 ρ ) The average delay per vehicle The maximum delay of any vehicle assuming a FIFO queuing discipline d avg Q max = λr = = 2 λr 2 1 ρ ( ) r 2C d max = 2 ( ) 1 ρ r 1 λc 29

30 Quantifying delays Analytical-Empirical Analysis 30

31 Signal Analysis Random Arrivals Webster s Formula (1958) - empirical d' = d + x 2 ( 1 ) 0.65 c 2 2 λ x λ 1/3 x 2+ 5( g / c) d = avg. veh. delay assuming random arrivals d = avg. veh. delay assuming uniform arrivals (D/D/1) x = ratio of arrivals to departures (λc/μg) g = effective green time (sec) c = cycle length (sec) 31

32 Signal Analysis Random Arrivals Allsop s Formula (1972) - empirical d' = 9 x d λ 2 ( 1 x ) d = avg. veh delay assuming random arrivals d = avg. veh delay assuming uniform arrivals (D/D/1) x = ratio of arrivals to departures (λc/μg) 32

33 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) 33

34 Signalized Intersection LOS Based on control delay per vehicle How long you wait, on average, at the stop light from Highway Capacity Manual

35 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 iti queue at start t of analysis time period (d 3 ). Often assumed zero but it depends on progression, arterial timing!!!. ( PF ) + d2 3 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 35

36 Uniform Delay (d 1 ) d 1 = g 0.5C 1 C 1 min 1, X g 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 36

37 Incremental Delay (d 2 ) d 2 = 900 T X 1 d 2 = delay due to random arrivals (s/veh) + X kix ct ( ) ( ) 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 adjustment 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 37 +

38 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 38

39 General Approach for Signal Timing Allocate available green based on critical flow ratios Calculate the capacity Check capacity/design flow rates and green intervals/minimum green intervals Adjust cycle timing if necessary 39

40 Adjustments Once done need to see if results work Make sure green meets requirements or adjust until it does pedestrian crossing Check capacity If significantly below capacity, reduce green time If close increase Compute LOS and delay and check Check for any other constraint 40