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APPENDIX E
Pages 123-168

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From page 123... ... Worksheet 5 determines the green extension times based on the unit extension time settings. It is important to note that the analytical mode} developed in this study uses an iterative procedure to predict the tra~c-actuated signal timing plan. Read the entire page →
From page 124... ... ., ~ B ~ SYMBOLS Main Information Flow _ Worksheets Iterative Loops ~J '4,,,,,,,ei Figure E-1. Iterative loops in the phase time and cycle length computation procedure The computational worksheets are conceptually simple, but must be applied iteratively to arrive at usefill results. Read the entire page →
From page 125... ... i . Max Initial Interval, MxI Added ~itial per AcWation, AI Minimum Allowable Gap ~A , Gap Reduction Rate, GR Pedestri ~ 1 1 1 1 Maximum Green, MxG IntergreenTime,l Recall Mode (M~ Max, Ped, None) Read the entire page →
From page 126... ... Sneakers: This describes the number of left turns per cycle that are dismissed at the end of a permitted phase. An implicit default of two sneakers per cycle is built into the supplemental permitted left-turn worksheets for purposes of determining the mirumum saturation flow rate. Read the entire page →
From page 127... ... It determines the passage time between the detector and the stop line as well as the portion of inter-vehicle headways during which a presence detector is occupied. When modeling the operation of vehicles at traffic signals, it is common to assume a single value for speed throughout the cycle. Read the entire page →
From page 128... ... The detector length influences the choice of other parameters, such as the allowable gap in traffic that will terminate the phase. Detector Setback, DS: This is the space between the downstream edge of the detector and the stopline. Read the entire page →
From page 129... ... Gap Reduction Rate, GR: This determines the rate at which the allowable gap is reduced in volume-density controllers as the green display continues. There are subtle differences in the definition of the gap reduction rate among controllers. Read the entire page →
From page 130... ... It does not appear in the HCM Chapter 9 data at this time because HCM Chapter 9 does not offer the ability to compute timing plans. On the other hand, it is not possible to deal realistically with traffic-actuated control without recognizing the existence of a minimum phase time. Read the entire page →
From page 131... ... The procedure, as described later, constructs an initial timing plan based on the minimum acceptable phase times. Using the data already entered on this worksheet, the minimum acceptable phase times would be either the minimum phase time for vehicles, MnV, or the minimum phase time for pedestnans, (WDW + I) Read the entire page →
From page 132... ... ARRIVAL RATE, q2 (vps) Platoon Ratio R GREEN ARR RATE, q,2 (vps) Read the entire page →
From page 133... ... from the HCM Chapter 9 Input Data Worksheet is repeated here. Arrival type 3 is commonly used at ~ly-actuated isolated intersections, where progression is not a factor and the green arrival rate is assumed to be equal to the red arrival rate. Read the entire page →
From page 134... ... It wait be assumed that ad vehicles using the phase will activate a single detector input terminal for the phase. The last two rows on the worksheet deal with pedestrian volumes, repeated Tom the HCM Chapter 9 Input Data Worksheet, and the computed arrival rate (peds/second) Read the entire page →
From page 135... ... Movements Phase Times DIFFERENCE: ABS(Ringl-Ring2) CYCLE TIME COMPONENTS: Independent Termination Simultaneous Termination No ~ Yes l WBL ~ EBT EBL I WET North-South Movements Total No I Yes llllllllll No I Yes No IYes EBT I WBL llllllllll NBL I SBT SBT I NBL WBT I EBL IIIIIIIRI SBL I NBT NBT I SBL 11111111111 11111111111 11111111111 11111111111 Illllllllil Il! Read the entire page →
From page 136... ... Worksheet 3b: Timing plan sensitive capacity parameter estimation Appendix E: Page 14 8 NRT = = _ = = 1 = = _ = _ _ _ = _ l Read the entire page →
From page 137... ... Worksheet 3b: Timing plan sensitive capacity parameter estimation (continued) Appendix E: Page 15 Read the entire page →
From page 138... ... Interim Effective Green Time, g: IPT minus the lost time per phase. Interim Red Time, IRT: The cycle length minus the interim phase time. Read the entire page →
From page 139... ... It is important for the minimum time adjustments. Vehicle Arrival Rate, VAR: From Worksheet 2. Read the entire page →
From page 140... ... From HCM Chapter 9 Equation 9-22. Free Green (gr3 The portion of effective green until the arrival of the first leR-tLlrT ing vehicle. Read the entire page →
From page 141... ... The Service Rate, s, and Left Turn Equivalence, EII are copied Dom Worksheet 2 for each lane group. The Movements, Green Arrival Rate, qg, Red Arrival Rate, it, and QatBOS, ~ are copied from Worksheet 3b for each lane group. Read the entire page →
From page 142... ... , MxT) : Refer to Worltsheet S to determine phase extension times if the base phase time < the ma~nmum phase time. Read the entire page →
From page 143... ... Movements (LTR) Green Arrival Rate, q~N: Wksht 3b Red A'Tiva1 Ra$e, q,N: Wksht 3b LT Equivalents, E~ ~: Wksht 2 PROPORTION OF LT IN THE SHARED LANE, PLN Service Rate, sN: Wksht 2 EQUIVALENT SERVICE RATE, esN: esN = sN / (0.9S * Read the entire page →
From page 144... ... For permitted left turns from an exclusive lane, gw is equal to gq. For permitted left turns Tom a shared lane, the value of gw may be determined by the relationship among g q, gf, arrival rate and departure rates. Read the entire page →
From page 145... ... win be used to compute phase extension time. Arrival Rate, q (vps) Read the entire page →
From page 146... ... Worksheet 5: Phase extension time worksheet Appendix E: Page 24 Read the entire page →
From page 147... ... Under fudy-actuated control, without gap reduction feature, the new headway wait be equal to the magnum headway. For volume-density control, with gap reduction feature, the vehicle headway needs to be computed by an iterative procedure until it converges to a stable value. Read the entire page →
From page 148... ... Each term in this summary worksheet is described as follows: Final Cycle Length, C: This is the final cycle time in the iterative computation procedure which can be obtained from the new cycle length of the final Worksheet 3b. Final Phase Time: This is the final phase time in the iterative computation procedure which can be obtained from the interim phase time (IPT) Read the entire page →
From page 149... ... r I I T I T T I 1[ OVERFLOW DELAY, d21 (sec/veh) l l l l l l l l 1[ TOTAL DELAY, dl LeR Tum Volume, v~ LEFT TURN CAPACITY, CL I I I I I I I 1 LEFT TURN VOLUME / CAPACITY RATIO, VL / CL I I I I 1[ LEFT TURN UNIFORM DELAY, due LEFT TURN CRITICAL DEGREE OF SATURATION, XOL 1 1: I LEFT TURN OVERFLOW TERM PARAMETER, ~L LEFT TURN NON-OVERFLOW DELAY, dlL l I T I T I 1' LEFT TURN OVERFLOW DELAY, d2L I ~1 T I T I I 1 LEFT TURN TOTAL DELAY, dL l T I T I T I I 1 LANE GROUP 2 v/c RATIO Wksht 6b \| T I I I l I I 1 LANE GROUP 3 v/c RATIO Wksht 6b l l l l l l I 1: CRITICAL v/cRADO Max (v/cl, v/c2, v/c3) Read the entire page →
From page 150... ... l l l l I _ Traffic Volume(vph) ,v2 LEFT TURN FACTOR, f,'2 FINAL SATURATION FLOW RATE, Sat2 (vphg) Read the entire page →
From page 151... ... For example, the effective green for a permitted left turn movement with protected plus permitted phasing is equal to its filll phase time, as explained in HCM Chapter 9. Final Green Ratio, g/C: (g / C) Read the entire page →
From page 152... ... I: vI / cat. Left Turn Uniform Delay, due: This is computed as the area under the queue accumulation polygon for the left turn movement including both protected and permitted left turn movements. Read the entire page →
From page 153... ... IMPLEMENTATION OF COMPUTATIONAL WORKS MEETS The implementation of computational worksheets to predict average phase times, cycle length, capacity and delay is best illustrated with examples. In this working paper, two examples are designed to cover a basic two-phase operation with simple permitted left turns and a more complicated multi-phase operation with compound leR turn protection. Read the entire page →
From page 154... ... If the cycle length converges to a stable value, the iterative procedure terminates and the summary worksheet of capacity and delay is produced. Otherwise, Worksheet 3b will continue to perform the timing plan sensitive parameter computations by constructing the queue accumulation polygons. Read the entire page →
From page 155... ... LTR 3 ~ Lanes Mov'ts Vo(ume Arr Rate Rp Grn Arr Sat Flow Svc Rate - ~ 2 LTR 400 0.11 1.00 0.11 3420 0.95 275 0.08 1.00 0.08 1710 0.48 LTR 300 0.08 1.00 0.08 1579 0.44 150 0.04 1.00 0.04 1710 0.48 _ _ _ - - - - - -T ~ Lanes Mov'ts Volume Arr Rate Rp Grn Arr Sat Flow Svc Rate o o 0.00 0.00 0.00 o 0.00 TR 400 0.11 1.00 0.11 1732 0.48 o o 0.0Q 0.00 0.00 o 0.00 600 0.17 1.00 0.17 3465 0.96 T -- - - - - - - - - - _T- - - - - - _T- - - - - - _T- - - - - - _T -- - -- - _T- - - - - - _T- - - - - - _T ~T- -~ VEH ARR RATE 0.11 0.19 0.08 0.21 Ped Volume 0 0 0 0 PED ARR RATE 0.00 0.00 0.00 0.00 Figure E-IO. Worksheets ~ and 2 for the permitted left turn example Appendix E: Page 33 Read the entire page →
From page 156... ... The remainder of the input data is shown In reproductions of Worksheets 1 and 2, presented in Figure E- 16. Each phase has been assigned the following constant parameters: Detector length: Detector setback: Intergreen: Lost time per phase: Allowable gap: Minimum phase time: Maximum green time: Pedestrian recall: Walk plus Flashing Don't Walk: Pedestrian hourly volume: No volume-density features .4ppendixE: Page 34 30 feet 0 feet (placed at the stop line) Read the entire page →
From page 157... ... Movtsw~, -- -- -- -- nv~ ~ PH Time38.87 38.87 36.91 36.91 RING 1-2 DIFF-14.57 -14.57 21.65 21.65 CYCLE COMPONENTS38.87 0.00 58.56 0.00 Worksheet 3b: Timing Plan sensitivity Capacity Parameter Estimation Worksheet 3a: Traffic-Actuated Timing Computations B Total No EBT 24.30 No UBT 38.87 -14.57 38.87 No SBT -- -- -- 58.56 58.56 No NBT 36.91 21.65 58 56 Old Cyc 96.9 New Cyc 97.4 Unadj PH Time Adjustment New Ph Time Eff Green 9 Int Red Time Eff Red r Red Time Startup Time Recall Mode Veh Arr Rate Av Vehs on Red P rob (No Vehs) Read the entire page →
From page 158... ... Worksheet 5: Green Extension Times: Max Min Comp Adj New Hdwy Hdwy Ext Ext Hdwy 4.09 9.82 9.82 4.09 4.09 13.48 13.48 4.09 4.09 9.55 9.55 4.09 4.09 11.81 11.81 4.09 . 0.16 0.50 0.33 0.50 0.13 1.50 0.28 0.50 Base Ph Time Ph Ext Time REQ PH TIME MIN PH TIME COMP PH TIME 0.96 0.92 0.89 0.90 4.09 4.09 4.09 4.09 Computed Phase Times Including Extension Intervals , Phase ~12345 MovementsUBLEBTNBLSBTEBL , 44.86 13.48 58.33 15.00 58.33 14.57 9.82 24.39 15.00 24.39 29.63 9.55 39.18 15.00 39.18 78 SOLNBT 24.99 11.81 36.80 15.00 36.80 Figure E-12. Read the entire page →
From page 159... ... Movts PH Time RING 1-2 DIFF CYCLE COMPONENTS _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ No -- -- -- -- Ho EBT -- -- -- -- SBT 24.3924.39 58.33 No -- -- -- -- No UBT -- -- -- -- NBT 39.1839.18 36.80 36.80 -14.79-14.79 21.54 21.54 _ 39.180.00 58.33 0.00 Uorksheet 3b: Timing PLan sensitivity Capacity Parameter Estimation , Old Cyc 97.5 1 234 56 78 New Cyc 97.5 UBL EBT NBL SBT EBL ~JBT SBL NBT 58.33 39.18 36.80 0.00 0.00 21.S4 58.33 39.18 58.33 55.33 36.18 55.33 39.18 58.33 39.18 42.18 61.33 42.18 38.87 58.56 38.87 39.18 0.00 39.18 Unadj PH Time Adjustment New Ph Time Eff Green 9 Int Red Time Eff Red r Red Time Startup Time 24.39 24.39 14.79 39.18 36.18 58.33 61.33 58.56 0.00 , 58.33 Cycle convergence has been achieved at 97.5 Figure E-13. Worksheet 3a of the last iteration for the permitted left turn example Appendix E: Page 37 Read the entire page →
From page 160... ... Summary worksheet for the pe~mitted left turn example Appendix E: Page 38 Read the entire page →
From page 161... ... ~ N Nor t h-Bout h Or SB 19 Forth-south Or FIB Figure E-IS. Intersection layout for the example of compound! Read the entire page →
From page 162... ... LG2 ~ Lanes Mov'ts Vol~ne Arr Rate Rp Grn Arr Sat Flow Svc Rate VEH ARR RATE Ped Volume PED ARR RATE +. Read the entire page →
From page 163... ... Note that in the computation of green extension time in Worksheet 5, the arrival rate is an equivalent through flow rate for the whole lane group. However, the extension time computation for the through phases does not include the equivalent through flow rate of the permitted left turns with compound left turn protection because the permitted left turns clo not actuate the detector to extend the permitted phase. Read the entire page →
From page 164... ... NoNo MovtsEBLUBT PH Time20.0029.09 RING 1-2 DIFF0.0020.91 CYCLE COMPONENTS20.0050.00 . B TotalA B Total No No -- -- -- NBL SBT -- -- -- 70.0012.71 47.40 60.11 -- -- -- Yes Yes -- -- -- -- -- -- -NBT SBL -- -- -- 49.0930.26 13.44 43.69 20.91-t7.55 33.96 16.42 0.000.00 0.00 60.11 Uorksheet 3b: Timing Plan sensitiv~ty Capac~ty Parameter Est~mation Old Cyc 129.212 345 6 7 New Cyc 130.1UBLEBT NBL SBTEBL UBT SBL Unadj PH Time20.0050.00 12.71 47.4020.00 29.09 13.44 30.26 Adjustment0.000.00 0.00 0.000.00 20.91 16.42 0.00 New Ph Time20.0050.00 12.71 47.4020.00 50.00 29.85 30.26 Eff Green 916.0046.00 8.71 43.4016.00 46.00 29.85 26.26 Int Red Time110.1180.11 117.40 82.71110.11 80.11 100.26 99.85 Eff Red r114.1184.11 121.40 86.71114.11 84.11 100.26 103.85 Red Time60.1180.11 99.85 82.7160.11 80.11 82.71 99.85 Startup Time0.0020.00 70.00 82.710.00 20.00 100.26 70.00 Recall ModeNP N PN P N P Veh Arr Rate0.060.25 0.01 0.170.08 0.14 0.03 0.08 Av Vehs on Red6.1220.03 1.63 13.799.18 11.13 2.78 8.32 Prob (No Vehs) Read the entire page →
From page 165... ... 5(EBL) 80.11 117.40 82.71 110.11 4.00 4.00 4.00 4.00 3.00 3.00 3.00 3.00 L L L L 0.06 0.08 0.06 0.08 0.00 2.55 0.00 1.00 0.48 0.48 0.48 0.20 0.42 0.11 4.10 1.74 15.00 45.00 0.98 0.98 1.00 1.00 12.58 18.08 0.00 20.82 12.58 38.91 0.00 0.00 0.00 0.00 LG 2 Mov'ts Grn Arr Red Arr ELI PL Svc Rate Eqiv Svc Net Svc QatBOS Qs Green G fq Land Utl Svc Time blait Time Tot Time ResQ Qp ResQ Qp' 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max Ph Time 20.00 BASE PH TIME 12.58 l 0.01 0.01 5.75 1.00 0.48 0.09 0.07 0.24 25 .26 1.05 1.00 6.50 17.55 24.04 0.24 0.00 Phase # Movements Base Ph Time Ph Ext Time REQ PH TIME MIN PH TIME COMP PH TIME NBL 12.58 46.12 6.27 37.74 7.42 3.88 6.50 9.70 20.00 50.00 12.76 47.44 14.49 25.00 11.23 25.00 20.00 50.00 12.76 47.44 678 EBLUBTSBLNBT 16.3720.090.0021.31 3 639.197.919.08 20 0029.287.9130.38 14.9225.0013.5125.00 20.0029.2813.5130.38 Figure E-~. Read the entire page →
From page 166... ... No No - - - - - - - - Yes Yes Movts EBL ~JBT -- -- -- -- NBT SBL PH Time 20.00 29.28 49.28 30.38 13.51 RING 1-2 DIFF 0.00 20.72 20.72 -17.62 33.93 CYCLE COMPONENTS 20.00 50.00 0.00 0.00 0.00 Worksheet 3b: Timing PLan sensitivity Capac, OLd Cyc 130.2 1 23 New Cyc 130.2 UBL EBT NBL Unadj PH Time Adjustment New Ph Time Eff Green 9 Int Red Time Eff Red r Red Time Startup Time 20.00 50.00 0.00 0.00 20.00 50.00 16.00 46.00 1 10.20 80.20 1 14.20 84.20 60.11 80.11 0.00 20.00 43.90 16.31 60.20 ity Parameter Estimation 5 6 EBL UBT 4567 SBTEBLUBTSBL 12.7647.4420.0029.2813.51 0.000.000.0020.7216.31 12.7647.4420.0050.0029.82 8.7643.4416.0046.0029.82 117.4482.76110.2080.20100.38 121.4486.76114.2084.20100.38 99.8582.7160. Read the entire page →
From page 167... ... 00 0.001747.000.001737.00 0.0046.000.0026.38 0.000.350.000.20 0.00617.200.00351.97 0.000.490.000.71 0.0032.870.0048.35 0.000.790.000.79 0.001.110.001.14 0.000.590.000.32 0.0036.590.0054.89 0.000.000.000.00 0.0036.590.0054.89 +++ 0.881.390.06 ++++ 0.0050.00 0.00170.64 0.000.29 0.0043.83 0.000.64 0.000.07 0.0051.25 0.000.00 0.0051.25 Figure E-20. Summary worksheet for the example of compound left turn protection Appendix E: Page 45 Read the entire page →
From page 168... ... and R Ak~elik, "A Computational Framework for Modeling TrafficActuated Controller Operations," Working Paper NCHRP 3-48-1, Transportation Research Center, University of Florida, Gainesville, May 1994. Read the entire page →

From page 123...

... Worksheet 5 determines the green extension times based on the unit extension time settings. It is important to note that the analytical mode} developed in this study uses an iterative procedure to predict the tra~c-actuated signal timing plan.

APPENDIX E Pages 123-168

APPENDIX E
Pages 123-168