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Unformatted text preview: The Pennsylvania State University
Department of Civil and Environmental Engineering
Lecture 19: Signalized Intersection Analysis CE 321: Highway Engineering Fall 2007 Purposes:
1. Orderly assigned Right-of-Way 2. Safety 3. "Not" a panacea ! Advantages
1. 2. 3. 4. 5. 6. Orderly movement Reduce right angle accidents Increased capacity Allow pedestrian crossing Coordination Driver confidence Disadvantages
1. Increased delay 2. Increase rear-end crashes 3. Promote disrespect when unwarranted or misapplied 4. Driver irritation - improperly timed 5. Cause drivers to seek less adequate routes 6. Expensive to install signals (> $100K) Manual on Uniform Traffic Control Devices (MUTCD) Eight (8) traffic signal warrants: Eight-hour volume Four-hour volume Peak-hour Pedestrian volume School Crossing Coordinated Signal Crash Experience Road Network Typical Signalized Intersection Traffic Signal Terminology Green Time (G) - time within cycle in which an approach has green indication (sec). Red Time (R) - time within cycle in which an approach has red indication (sec). Yellow Time (Y) - time within cycle in which an approach has yellow indication (sec). All-Red Time (AR) - time within cycle in which all approaches have red indication (sec). Also known as clearance interval. Traffic Signal Terminology Cycle - complete signal sequence. Cycle Length (C) - time (sec) to complete a cycle. Phase ( ) - part of a cycle allocated to specific movement(s). Sum of phase lengths (sec) is cycle length. Change Interval = Yellow + All Red (sec) Traffic Signal Controller - controls sequence, duration and logic. Traffic Signal Terminology Lost Time (tL) - Time during which intersection not effectively used by any approach (sec). tL = tsl + tcl tsl = start-up lost time (sec) Occurs when signal changes from red to green tcl = clearance lost time (sec) Last second of yellow and all-red interval Saturation Headway and Lost Time Start-up lost time (tsl) is typically ~ 2 seconds Saturation headway after 4 vehicles Traffic Signal Terminology Effective Green (g) - Time (sec) effectively used by an approach for traffic movement (g = G + Y + AR - tL)
Effective Red (r) - Time (sec) not effectively used by an approach for traffic movement (r = R + tL) Alternatively, r = C g (sec) Traffic Signal Terminology Saturation Flow (s) - Maximum hourly volume that can pass through an intersection, from a given lane or lane group, assuming that lane were allocated constant green over one hour (vph). s = 3600/h (1,900 pc/h/ln is possible) h = saturation headway (sec) Approach Capacity (c) - Maximum hourly volume (vph) that can pass through an intersection under prevailing roadway, control, and traffic conditions (c = s * g/C). Traffic Signal Terminology
Master Controller - unit which controls several intersection controllers. Signal Head - assembly containing the face(s) Signal Face - portion of head pointing toward controlled movement. Signal Indication R Y R Y G G Movement Terminology Protected Does not yield to conflicting movements. Through movements are always protected. Left- or right-turn movements are protected by green arrow indication. Permitted Must yield to opposing traffic or conflicting pedestrians. Left- and right-turns are permitted by green circle indication. Left-turns must wait for gap in opposing traffic and right-turning traffic. Right-turns must yield to pedestrians in adjacent crosswalk. Types of Control
Pretimed Semi-Actuated Fully-Actuated Pre-timed
Fixed cycle lengths over specified time Need traffic history Several timing options possible Good at predictable locations or downtown CBD Pre-timed - Advantages
Simple Can be coordinated Easy to field adjust Can handle peak and off peak conditions Pre-timed - Disadvantages
Cannot react to short-term demand changes (no detection devices). Can cause excessive delay. Sometimes disrespected. Semi-Actuated Timing affected by vehicle detection. Major Road = high volumes Minor Road = low volumes Detectors on minor approaches Minor phase ( ) = min. green interval Major phase ( ) = can extend indefinitely Minor Road gets served upon actuation Detectors: ("Presence" or "Passage") Pressure Magnetic Photocell Radar Sonic Infrared Inductive Loop Magnetometer Coaxial Self-Powered Passive Bus Microloop Fully-Actuated Signal timing is influenced by traffic volumes. Detectors on all approaches. Phases have an initial interval which provides time for starting / standing vehicles. Green interval extended by preset unit extension.... up to maximum limit of allocated time. Yellow and red intervals preset for phases. Signalized Intersection Analysis Performance measure: control delay Deceleration time Queue move-up time Stop time Acceleration time d = d1 x PF + d2 + d3 d = average control delay per vehicle (sec) d1 = average delay per vehicle due to uniform arrivals (sec) PF = progression adjustment factor d2 = average delay per vehicle due to random arrivals (sec) d3 = average delay per vehicle due to initial queue at start of analysis period (sec) Average control delay (sec) Delay for Uniform Arrivals (d1)
g 0.5C 1 - C d1 = g 1 - min(1, X ) C d1 = average delay per vehicle due to uniform arrivals (sec) C = cycle length (sec) g = effective green time for lane group (sec) X = v/c ratio for lane group
2 Progression Factor (PF) Accounts for signal progression quality. Influenced by cycle length, vehicle speeds, distance between intersections. "Good" progression = high proportion of vehicles arriving during green phase. "Poor" progression = high proportion of arrivals during red phase. Assume PF = 1.0 for neutral progression. Delay for Random Arrivals (d2) 8kIX 2 d 2 = 900T ( X - 1) + ( X - 1) + cT d2 = average delay per vehicle due to random arrivals (sec) T = duration of analysis period (hr) X = v/c ratio for lane group k = delay adjustment factor dependent on controller mode I = upstream filtering/metering adjustment factor c = lane group capacity (veh/hr) Delay for Random Arrivals (d2)
Analysis flow-rate is typically based on 15-minute period, T = 0.25 hr. Traffic signal adjustment factor, k Accounts for pretimed or actuated control Assume k = 0.5 for pretimed Delay for Random Arrivals (d2) Upstream filtering/metering factor, I Adjust for effect that upstream signal has on randomness of arrival pattern at downstream signal. Assume I = 1.0 for isolated signals. var(# arrivals / cycle ) I= mean ( arrivals / cycle ) Delay for Initial Queue (d3) Accounts for delay caused by initial queue of vehicles at beginning of analysis time. Set d3 = 0 for no initial queue. Example Problem 1 An approach at a pretimed signalized intersection has a saturation flow rate of 2,400 veh/hr and is allocated 24seconds of effective green in an 80second signal cycle. If the flow at the approach is 500 veh/hr, what is the average approach delay per cycle? Assume a 15-minute analysis period. Example 1 Solution
g 0.5C 1 - C d1 = g 1 - min(1, X ) C 24 0.5(80)1 - 80 = 24.75 sec d1 = 24 1 - 0.694 80 2 2 X= v v 500 = = = 0.694 c s g / C 2400 24 / 80 Example 1 Solution 8kIX 2 d 2 = 900T ( X - 1) + ( X - 1) + cT 8(0.5)(1.0)(0.694) 2 d 2 = 900(0.25) (0.694 - 1) + (0.694 - 1) + = 5.45 sec ( 2400 24 / 80)(0.25) Example 1 Solution
d = d1 PF + d 2 + d 3 = 24.75 1.0 + 5.45 + 0 = 30.20 sec ...
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This note was uploaded on 04/11/2008 for the course C E 321 taught by Professor Pietrucha,martinkeller,michaelwi during the Spring '07 term at Pennsylvania State University, University Park.
- Spring '07