CHAPTER 26 - SIGNAL COORDINATION - UNSATURATED CONDITIONS

CHAPTER 26 - SIGNAL COORDINATION - UNSATURATED CONDITIONS -...

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Unformatted text preview: CHAPTER 26 Coordination of Signals for Arterials and Networks – Undersaturated Conditions Objectives of Coordination 1. To allow continuous movement of vehicles through a series of signalized intersections without stopping. 2. To encourage vehicular movement at a preferred speed. 3. To minimize the number of stops and delay at signalized intersections. 4. To encourage platoon formation and cohesion. 5. To reduce air pollution in the vicinity of signalized intersections. • Coordination is most easily achieved using pre-timed signal networks where the cycle length is easily controlled. • Modern signal systems now include using coordinated actuated signal networks. Cycle lengths are fixed, but splits can be altered. “Excess” green time in any cycle is generally assigned to the major street. Platoon Formation: Platoons form as vehicles depart a signal from a standing queue. standing Platoon Dispersal Occurs Because of: 1. Driver variations over distance. 2. Vehicles turning into the traffic stream from Vehicles unsignalized driveways and streets. unsignalized 3. Vehicles turning out of the traffic stream onto 3. Vehicles unsignalized driveways and streets. unsignalized 4. Side friction factors (parked vehicles, goods Side movement, transit and taxi stops, etc.) movement, General Policies: 1. Platoon dispersal is not significant for distances Platoon up to 1,000 ft from the discharging signal. up 2. Coordinate all signals spaced more closely than Coordinate ½ mile. mile. 3. Signals spaced at more than 2 miles are Signals considered to be independent. considered A Graphic Tool: The Time-Space Diagram D istance (ft) First Vehicle Trajectory Last Possible Vehicle Trajectory Bandwidth V 1 t1 t2 Time (secs) Define: Offset = t2 – t1 Offset may be established for a desired progression Offset speed, v. speed, A Requirement for Coordination: Requirement COMMON CYCLE LENGTHS C = 75 secs BW1 C = 90 secs BW2 V1 1 1 V2 C = 60 secs 0 30 60 90 120 150 180 A Constraint of Coordination: Constraint NETWORK CLOSURE Offset t 2 Offset t 1 Offset t 3 Offset t 4 i s fully determined by Offsets 1-3. For any set of four signals that interlock as shown, For only three offsets may be arbitrarily established. Once three are established, the fourth is also set as a consequence of the first three. consequence A Consequence of Network Closure Illustrated: 1. All streets in a primary direction can be progressed. 1. 2. One cross-street can be progressed. 3. All other signals are “locked in” due to network closure. Decomposing a Network for Progression: C BD center A north-south primary system, progressed away north-south from the CBD; discontinuous at the CBD center. from The Ideal Offset for Progressive Movement The Example: Distance to downstream signal (d) = 1,000 ft Desired progression speed (v) = 30 mph = 44 fps Ideal Offset Assuming Moving Platoons: d 1000 t= = = 22.7 s v 44 Ideal Offset Assuming Start-Up From a Standing Ideal Queue: Queue: d 1000 t = 2 .0 + = 2 .0 + = 24.7 s v 44 Illustration of Ideal Offsets Illustration Distance (ft) 1,000 0 22.7 24.7 Time (secs) A Signal Progression on a One-Way Street Signal - Example 1 1200' 2 1200' 3 1200' 4 600' 5 1800' 6 C = 60 secs 50/50 splits S = 60 fps Ideal Offsets t (1→2)1200/60 = t (2→3)1200/60 = t (3→4)1200/60 = t (4→5) 600/60 = (4 t (5→6)1800/60 = Relative 20 secs 20 secs 20 secs 10 secs 30 secs From t = 0 20 secs 40 secs 60 secs 70 secs 100 secs DISTANCE (ft) THE TIMETHE SPACE SPACE DIAGRAM DIAGRAM 6000 4200 3600 2400 1200 0 0 60 120 180 240 TIME 300 (secs) DISTANCE (ft) Equal Bandwidths of 30 Seconds Provided Under Ideal Progression 6000 THE PERFECT PROGRESSION WORKING AS INTENDED INTENDED 4200 3600 2400 1200 0 0 60 120 180 240 TIME 300 (secs) DISTANCE (ft) Test Vehicle at 70 fps Arrives at Signals Too Soon, and Experiences Slight Delay. Bandwidth is Decreased as Shown. What If Drivers Try to Travel Too Fast? Too 6000 4200 3600 2400 1200 0 0 60 120 180 240 TIME 300 (secs) DISTANCE (ft) Test Vehicle at 50 fps Passes Through All Signals Without Stopping. Bandwidth is Reduced to a Very Small Value. What If Vehicles Travel Too Slowly? Slowly? 6000 4200 3600 2400 1200 0 0 60 120 180 240 TIME 300 (secs) DISTANCE (ft) At 60 fps, a reverse vehicle must stop twice in traversing the signal system. A small bandwidth exists, but would only process vehicles through signals 6,5,4, and 3. What If It is a Two-Way Street? Two-Way The Reverse The Progression Progression 6000 4200 3600 2400 1200 0 0 60 120 180 240 TIME 300 (secs) The Effect of Queued Vehicles on Progression The S “Q” vehicles waiting at STOP line. The offset must be adjusted to allow queued vehicles to The depart before the platoon arrives at the downstream signal. before Where: d t = − ( Qh + 1 ) v t = offset, secs d = distance to downstream signal, ft Q = number of vehicles queued at number downstream signal downstream h = average headway, secs, and Distance (ft) 1000 t(ideal) = 1000 ft / 50 fps = 20 secs 0 Distance (ft) 1000 20 40 60 Time (secs) t(ideal) = [1000/50 ] - [(2)(2) + 2] = 14 secs 0 20 40 60 Time (secs) Effect of Queues on a Progressive System Effect Example Consider the impact of 2 vehicles queued at each Consider intersection on the ideal one-way progression of previous illustrations: previous Link Offset (secs) Cumulative Offset (secs) 1 → 2(1200/60)-(4+2) =14 2 → 3(1200/60)-(4) = 16 3 → 4(1200/60)-(4) = 16 4 → 5( 600/60)-(4) = 6 5 → 6(1800/60)-(4) = 26 14 30 46 52 78 DISTANCE (ft) Green Wave 60 fps Effect on the System System 6000 4200 3600 2400 1200 0 0 60 120 240 TIME 300 (secs) Sources of Queued Vehicles • Vehicles turning into the link between platoons from unsignalized driveways and streets. • Vehicles leaving platoons to enter parking • Stragglers from the previous platoon; or places, and/or unsignalized driveways and streets. vehicles “chopped” off the end of the platoon by the RED signal. Some Practical Problems In Dealing with Queues • • Queue size varies on a cycle-by-cycle basis, while offset adjustment is based upon an average value. Predicting the average queue size is neither straightforward or easy. If the adjustment to offset, Qh + l , is greater than Progressions on a Two - Way Arterial Principal Characteristic of Closure on a Two-Way Facility: t dir 1 + t dir 2 = nC Example With n = 1: 1: L t (NB) t (SB) C To have n = 1: t (NB) < C Example With n = 2: 2: L C t (NB) t (SB) 2C To have n = 2: C < t (NB) < 2C A Trial-and-Error Approach to Two-Way Progression: Manipulate the Time-Space Diagram to Provide the Desired Results 1. Provide ideal progression in one direction, accept whatever results in the other direction. 2. Establish a balance based upon volumes, with primary direction getting good, but not perfect progression, and the other getting some progression of lesser quality. Example: The Perfect One- Way Progression Solution Example: Modified for Two-Way Operation: Modified DISTANCE (ft) BW = 22 secs NB BW = 11 secs SB Solution favors NB flow, but accommodates some platoon movement SB. 6000 4200 3600 2400 1200 0 0 60 120 180 240 TIME 300 (secs) Bandwidth Concepts Bandwidth Caution: Queuing affects bandwidths and can minimize their effectiveness. Bandwidth Efficiency (E) BW E (%) = C 100 Bandwidth Capacity (C ) 3600 * BW * N 3600 BW cB = * *N = h *C Ch For the Two-Way Progression Shown: For 22 E NB = * 100 = 36.6 % 60 11 E SB = * 100 = 18.3 % 60 3600 * 22 * 1 cB ,NB = = 528 veh / h / ln 2.5 * 60 3600 * 11 * 1 cB ,SB = = 264 veh / h / ln 2.5 * 60 Some Commonly Effective Two-Way Progressions 1. ALTERNATE PROGRESSION • Requires uniform block spacing. • Requires 50-50 green splits at all intersections. • Link travel time = ½ C • Requires uniform block spacing. • Requires 50-50 greens splits at all intersections. • Link travel time = 1/4 C • Uniform block spacing desirable (not required). • Green splits must be uniform (not necessarily 5050). • Progression only good for n signals. 2. DOUBLE ALTERNATE PROGRESSION 3. SIMULTANEOUS PROGRESSION THE ALTERNATING PROGRESSION THE DIST. 4L 3L 2L L 0 0 C 2C 3C TIME CL = E = 50% BW = 0.50 C 2v 1800 N 3600 0.50 C cB = * *N = C h h THE DOUBLE ALTERNATING PROGRESSION THE DIST. 4L 3L 2L L 0 0 C 2C 3C TIME CL = 4v E = 25% BW = 0.25 C 900 N 3600 0.25 C cB = * *N = C h h THE SIMULTANEOUS PROGRESSION THE DIST. 4L 3L 2L L 0 0 C 2C 3C TIME 1 (N − 1) L E E= − * 100 BW = *C 2 vC 100 36 E N 3600 (E / 100) * C cB = * *N = h h C Some Observations 1. Block length has a great deal to do with selection of a pattern: shorter block lengths tend to push towards double alternate and simultaneous progressions. 2. All of these progressive patterns involve some loss of flexibility in timing of individual intersections. 3. Simultaneous progressions offer additional benefits in terms of queue clearance and prevention of spillbacks. DIST. 4L DIST. 4L DIST. 4L 3L 3L 3L 2L 2L 2L L L L 0 0 C 2C 3C TIME 0 0 C 2C 3C TIME 0 0 C 2C 3C TIME Alternate System Double Alternate System Simultaneous System CITY LINE A TYPICAL PATTERN: TYPICAL AN ARTERIAL ENTERING A CITY AREA A Typical Problem: Typical A NEW SIGNAL IN AN ESTABLISHED PROGRESSION DIST. 4L 3L NEW 2L L 0 0 C 2C 3C TIME Introduction of new signal disrupts existing bandwidths. Introduction Must locate optimally by trial-and-error. A Typical Problem: Typical THE EFFECT OF USING MULTIPLE CYCLE LENGTHS DIST. 4L 3L 2L L 0 0 C 2C 3C TIME ...
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This note was uploaded on 01/18/2011 for the course PROJECT MA PM 587 taught by Professor Lee during the Spring '10 term at Keller Graduate School of Management.

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