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APPENDIX E A COMPUTATIONAL FRAMEWORK AND ILLUSTRATED EXAMPLES FOR TRAFFIC-ACTUATED CONTROLLER MODELING INTRODUCTION The procedure for modeling traffic-actuated control developed under NIP Project 3~S contains a number of analytically complex and iterative steps that do not lend themselves to manual computa- tions. Therefore, an analysis program called ACT3-48 was developed in this study as a too! to provide for demonstration and testing of the model. A computational Damework involving five worksheets has been incorporated into the ACT3~8 program. The worksheets presented in this report propose extensions to the original worksheets proposed by Courage and Ak~elik [~] for modeling simple through and protected left turn phases. The worksheets play a very important part in overcoming the "black box" image of complex models. They provide a structure for presenting the results of intermediate computations in a common form that is compatible with the proposed techniques. Thus, the format for the intermediate outputs pro- duced by ACT348 was designed to be identical to the format of the worksheets. The computational process is illustrated with two examples. The details of the analytical mode! and procedure used to predict the trafflc-actuated signal timing plan [l, 2, 3, 4] and delay estimate [5] were described in the indicated references. These details wall not be repeated here. COMPUTATIONAL PROCESS Each worksheet has its own purpose. The purpose of Worksheet ~ is to enter the data required speci- fically for traffic-actuated control. Worksheet 2 is used to perform lane group data computation. Worksheet 3 sets up the traffic-actuated timing computation. Worksheet 4 computes the green times required to service the queues accumulated on the red phase. 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. Thus, while the worksheets themselves are quite simple, the overall procedure contains iterative loops. The complete procedure involving the work- sheets is illustrated in Figure EM In addition to the five worksheets, two iterative loops are indicated as "Loop A" and "Loop B". ~AIL - Loop A. Required Time: This is an iteration between Worksheets 3 and 4. The purpose of this iteration is to make the phase times converge to a stable cycle length. Worksheet 4 must also refer to Worksheet 5 if phase time extensions are required to compute the required phase times. Appendix E: Page 1

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Loop B. Phase Extension Time: This is an internal iteration within Worksheet 5. It is only required when gap reduction features are employed. When the allowable gap is a function of the phase time, the phase time cannot be computed without an iteration process. 4. Required Times (.,~,, r ~ -I *-a. 5. Phase Extension Times 1. Data I ~1 2. Lane Input ~ Groups .~. ~ 3. Cycle Time Adjustments ., A. ., ~ 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. The program is required because the iterative nature of the procedure makes it totally impractical for manual implementation. The program is now fully functional and able to evaluate the analytical models using a variety of data. It also provides a flexible computational tool for examining other models that may be proposed. WORKSHEET 1: lllAFFIC-ACTUATED CONTROL INPUT DATA This first worksheet, presented in Figure E-2, gathers together all data required by the proposed analytical model. As a convention that will be used in the presentation of all worksheets, the row identification headings at the left side of the worksheets will be shown in lower case text if they are input data and In UPPER CASE text if they belong to intermediate computations based on input data. Appendix E: Page 2

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l WORKSHEET 1: TRAFFIC-ACT UATED CONTROL INPUT DATA APPROACH-SPECIFIC DATA Northbound Southbound Eastbound Westbound | Left Turn: Treatment Codet 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 Position | Lead Lag N/A | Lead Lag N/A | Lead Lag N/A | Lead Lag N/A || Max Sneakers, S~, (vein) Free Queue, Qf (vein) ; Approach Speed, SP (mph) Ring 1 and 2 T~ation Simultaneous Independent N/A Simultaneous Independent N/A ~_ F_ DESIGN PARAMETERS | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 WBL EBT NBL SBT EBL WBT SBL NBT l Ph~eType(LT,G,N,X) l l l l l l I 1 l Phase Reversal? Y N Y N Y N Y N Detector Location: Length, DL Setback, DS i . 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) ! ! ! ! ! ! ! MIN VEH PHASE TIME, MnV: | STARTING GAP, SG | MIN INITIAL INTERVAL, MnI | MAXIMUM PHASE TIME,MxT: MxG+I | DETECTOR OCCUPANCY TIME, DT 1 (DL+18)/1~47SP I I I I | TRIALPHASE TIME: Max(MnV,WDW+I) Notes: 1. LT Treatment codes: (0) Prohibited, (1 ) PermiKed' (2) Protected, (3)Protected ~ Permitted, (4) Not Opposed. Figure E-2. Worksheet I: Traff~c-actuatecl contro! input data = _ T I 1 T Appendix E: Page 3

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Approach-Specific Data The top portion of Worksheet 1 summarizes the approach-specific information. A separate column is used for each of the four approaches. The following items are required: Left Turn (:LT) Treatment Codes: The logic of the proposed mode} requires that the LT treatment be identified explicitly. The codes used here are consistent with the HCM Chapter 9 planning method worksheets. These codes are defined in Section ~ of HCM Chapter 9. 0 = LT does not exist ~ = Permitted 2= Protected 3 = Protected plus permitted or permitted plus protected 4 = Not Opposed The term "simple leR-turn protection"will refer to treatment number 2, in which the left turn moves only on the protected phase. The terser "compound leflc-turn protection" will be used to denote either protected plus permitted or permitted plus protected treatments. This is not an attempt to replace any HCM terminology, but to augment the terminology with more concise and easily understood references. Position Codes: These are required to distinguish between leading and lagging led turn protection. The terms "leading" and "lagging" apply equally to the cases of simple and compound le~c-turn protection. These codes do not apply if the leg turn is not protected. The worksheet offers a simple choice of "Lead," "Lag" or "N/A". The definition is very simple: leading left turns precede the movement of the opposing through traffic and lagging left turns follow it. 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. Since any vehicle that rests in the detection zone wait extend its respec- tive phase, a more detailed treatment of sneakers will be required for traffic-actuated control. Free Queue: The current pretimed mode! assumes that the first perrn~tted leg turn at the stop line will block a shared lane. This is not always the case, as the through vehicles in the shared lane are often able to "squeeze" around one or more led turns. This is a definite defi- ciency of the pretimed model, but it is especially critical with traffic-actuated control, because vehicles In the free queue do not occupy the detector and therefore do not extend the green phase. A permitted left turn stopped on the detector must be treated entirely differently in the modeling process than one that is stopped beyond the detector. Appendix E: Page 4

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Approach Speed, SP: The speed of vehicles on a signalized intersection approach is not important to the current HCM Chapter 9 methodology. It is, however, required in the analysis of tra~c-actuated operation. 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. Termination of Rings ~ and 2: The nature of dual-ring control requires that the second phases of rings ~ and 2 terminate simultaneously because they yield control to approaches with convicting traffic. However, control may pass Tom the first phase to the second phase of either ring without causing any conflict. Independent termination of the first phases improves efficiency in the allocation of time among competing movements and is generally exploited for this reason. The type of operation created by independent termination is sometimes referred to as "phase overlap." It is, however, not essential that the phases terminate independently. Older single-ring con- troller operation may be approximated by requiring that the first phases of each ring (i.e., phases ~ and 5 or 3 and 7) terminate simultaneously. In some situations involving coordi- nated arsenal routes, it is common to force both rings out of their first phase simultaneously. The model developed considered simultaneous or independent termination as legitimate alter- natives. It is possible that one or more of the first phases will not be used, because its associated left turn is not protected. In this case, the question of simultaneous or independent termination will not apply. This is another multiple-choice entry on the worksheet. The alternatives are "Simultaneous," "Independent" and "N/A". Phasing and Detector Design Parameters The bottom portion of the worksheet includes all the data items specific to each of the eight phases represented on Figure E-~. A separate column is provided on the worksheet for each phase. The first group includes the design parameters relating to phasing and detector placement. The following data items are included: --I- r Phase Type: This is the first of several phase-specific inputs that are required. A phase that is not active will not be recognized in any of the subsequent computations. Inactive phases are indicated by an "X" in the appropriate column of the worksheet. A leflc-turn phase will be considered active only if it accommodates a protected left turn. A through phase will be considered active whenever it accommodates through, left or right traffic. Active phases will be designated by: Appendix E: Page 5

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"it" If the phase accommodates a protected ieDc turn on a green arrow. t'Tt' ttGt' t'N't If the phase accommodates through and right-turning traffic only. In this case, all leD turns are accommodated entireIv on another chase (i.e.. leflc-turn protection). , ~simple If any left turns are accommodated on this phase, opposed by oncoming traffic. This will occur on phases with permitted led turns and those with compound leflc-turn protection. If the phase accommodates, in addition to other movements, led turns that are not opposed at any time in the phase sequence. This will happen at "T" intersections, on one-way streets and in cases in which the phasing completely separates all movements on opposing approaches. Note that right turns are not referenced specifically in these designations. Right turns are assumed to proceed concurrently with the through traffic. Phase Reversal: Normally the first phase in each ring on each side of the battier (odd numbered phase) handles protected left turns and the second phase (even numbered) handles the remaining traffic. This creates a condition of leading left-turn protection. When lagging lefc-tu~n protection is desired, the movements In the first and second phases are interchanged. Most controllers provide an internal function to specify phase reversal. For purposes ofthis discussion, two phases may only be swapped if both phases are active. Detector Length, DL: Defined as the effective distance, measured parallel to the direction of travel, through which a vehicle will occupy the detector. A user-specified design parameter influenced by local practice. 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. Controller Settings The controller itself has several operating parameters that must be specified for each phase. Collectively, these will be referred to as the "controller settings," because they must be physically set In the controller with switches, alpha-numer~c keypads or some other electrical means. The following settings will exert a significant influence on the operation of the intersection and must therefore be recognized by the analysis methodology: Appendix E: Page 6

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Maximum Initial Interval, M0: Used only when the initial interval is extended under volume-density control. Must be long enough to ensure that a queue of vehicles released at the beginning of green will be in motion at the detector before it terminates. Added Initial Per Actuation, Al: Used only when the initial interval is extended under volume density control. This value wall depend on the number of approach lanes. It should be long enough to ensure that each vehicle crossing the approach detector on the red will add an appropriate increment of time to the initial interval. Minimum Allowable Gap, MnA: This is a user-specified controller parameter, the effect of which wid be discussed later as the proposed models are exercised. It is typically set in the range of 2-3 seconds. It establishes the threshold for the length of the gap in traffic that wait cause the phase to terminate. The value of MnA is usually influenced to some extent by local practice. It is important to distinguish between the time gap and the time headway between vehicles. The time headway indicates the elapsed time between the successive arrival of two consecutive vehicles at a detector. The time gap indicates the elapsed time between the departure of the first vehicle from the detector and the arrival of the second. The time gap is what is led of the headway after the detector occupancy time has been subtracted. A tra~c-actuated controller using presence detectors views the passage of traffic in terms of gaps and not headways. 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. For purposes of this project, a linear reduction rate (seconds reduction of gap per second of elapsed green time) will be assumed. Pedestrian Walk plus Don't Walk, WDW: This is m~n~rnum time given to each phase when pedestrian demand is registered or the pedestrian recall is active. It inclucles both the pedestrian walk and flashing don't walk intervals. These are actually entered into the controller as two separate parameters, but wall be combined for purposes of this analysis. If the pedestrian timing function is not implemented in a particular phase, the WDW value should be entered as zero. Maximum Green, MxG: This is a user-specified parameter, the effect of which will be discussed later. Local practice open plays an important part in the determination of maximum green times. Appendix E: Page

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Intergreen Interval, I: Another user-specified controller parameter determined in accor- dance with local practice. The intergreen interval consists of a yellow change interval fol- iowed by an all-red clearance interval. These two intervals are entered separately into the controller, but will be combined here to simplify the analysis. Recall Mode: This detenn~nes how a phase will be treated in the absence of demand on the previous red phase. The options are: None: The phase will not be displayed. Max: The phase will be displayed to its specified maximum length. Min: The phase will always be displayed to its specified minimum length, but may be extended up to its specified maximum length by vehicle actuations. Ped: The phase will be given the filet Walk plus Flashing Don't Walk and may be extended farther, up to its specified maximum by vehicle actuations. This function will have a significant effect on the operation of the controller. For example, the maximum recall option wall have the effect of creating a pretuned phase. Preliminary Computations Several items computed Tom the above data will remain fixed, and are not subject to modification as a result of iterative computations. These values are included at the bottom ofthe worksheet for use in subsequent computations. They appear on the worksheet in upper case letters because they are computed values. In some cases, they are actually controller settings, but their values may be computed in terms of data that have already been established. Minimum Phase Time for Vehicles, MnV: This is actually a traffic engineering input, but it is included here as a computed value because it is subject to modification by other control parameters. It is an important input to any process for computing an implementable timing plan. 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. For compatibility with other signal timing programs, the phase times include all intervals, including green, yellow and all-red. For purposes of the worksheet, the minimum phase time must be replaced by the maximum phase time MUG + ~ if the "Recall to Maximum" mode is In effect, and therefore, it is treated on the worksheet as a computed value. Appendix E: Page 8

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Starting Gap, SG: If the gap is reduced during the green phase under volume-density control, a starting gap must be specified. It is common to choose a value for the starting gap equal to the passage time Tom the detector to the stop line. The SG may be computed as: SG= DS / 1.47SP If this value is equal to or less than the minimum allowable gap, MnA, then gap reduction would not normally be employed. In this case, SG = ~A. Min Titian Literal, MnI: This determines the minimum green time to be displayed. Given a specified value of the minimum phase time for vehicles, MnV, the minimum initial interval may be calculated as: HI = MT1V - ~ - SG Maximum Phase Time: The maximum time that may be assigned to the phase. This may be computed as (MUG + T). Throughout the iterative process, the computed green times must be checked to ensure that they do not exceed this value. Detector Occupancy Time, DT: This is the time during which a vehicle passing over the detector at the approach speed will occupy the detector. It may be computed as (DL+~) / I.47SP. This assumes an average vehicle length of IS feet. In computing the estimated length of a phase extension, DT must be added to the controller's current allowable gap threshold to determine the vehicle headway value that win cause a phase to terminate. Trial Phase Time: This will provide the starting point for the iterative procedure that will determine the estimated phase times. 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), whichever is greater. WORKSHEET 2: LANE GROUP ASSIGNMENTS Figure E-3 shows the Lane Group Assignment Worksheet. The purposes ofthis worksheet are: I) To associate each of the lane groups with a signal phase; 2) To identify the movements that occur in each lane group; and 3) To convert the volumes and saturation flow rates entered on previous HCM Chapter 9 worksheets into units of vehicles per second. The timing computations on subsequent worksheets wait require these units. Appendix E: Page 9

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; -- WBL EBT NBL SBT EBL WBT SBL NBT Thase Movement~ (T TR) . Opposing Through Phase LT EQUIVALENT S. E~ LG 1: No of!~nes LG Movements (LTR) ~7 ~T Volume(vph) l I T I I 1 1 1 ARRIVAL RATE, ql (vps) ~T I I I I T Platoon Ratio Rp GREEN ARR RATE, q.1 (vps) Sat Flow Rate (vphg) l l l l l l l l SERVICE RATE, sl (vps) l l l l l l l | LG2: No.ofLanes l l l l l l l | Movements (LTR) l l l l l | Volume (vph) ARRIVAL RATE, q2 (vps) Platoon Ratio R GREEN ARR RATE, q,2 (vps) Sat Flow Rate (vphg) SERVICE RATE, s2 (vpsg) l l l l l l LG3: No. of Lanes l l l l l l I Movements (LTR) l l l l l l l Volume(vph) l l l l l I 1. GREEN ARR RATE, q,3 (vps) ARRIVALRATE, q3 (vps) l l l l l | ~ Platoon Ratio Rp l l l l l l l Sat Flow Rate (vphg) l l l l l l 1: SERVICE RATE, s3 (vpsg) T I T T T I VEHICLE RIVAL RATE, VAR PedVolume(pph) l I ~ ~= PED ARRIVAL RATE. PAR: (pps) Figure E-3. Worksheet 2: Lane group data Appendix E: Page 10

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The lane group breakdown should come directly from the HCM Chapter 9 Volume Adjustment Worksheet. Typically, the lefc-turn phases will have only one lane group and the through-traffic phases may have up to three lane groups. The first line ofthis worksheet indicates ad the movements ~,T,R) accommodated by the phase. The next line deals with progression quality. Basically, the arrival type (AT) 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. In coordinated operation, the AT input value will determine the green and red arrival rates ofthe through movements ofthe arterial. The next line is the phase number of the opposing through phase which opposes the permitted left turns of the subject phase. For example, NEMA phase 6 is the opposing through phase of NEMA phase 2 because the movements for NEMA phase 6 will oppose the permitted leD turns for NEMA phase 2. The last line for this top portion is left turn equivalence, Eat, which is the through-car equivalent for each permitted le~c-turning vehicle during the unsaturated opposing flow. The values of Eel can be obtained from Figure 9-7 of HCM Chapter 9. Six subsequent lines are associated with each lane group: Number of Lanes: From the HCM Chapter 9 Input Data Worksheet Volume (vph): From the HCM Chapter 9 Volume adjustment worksheet. The adjust ment for PHE should be applied if a peak IS-m~nute analysis is desired. The lane utilization adjustment should not be applied since this adjustment adds fictitious vehicles. Arrival Rate: Convert hourly volumes to vehicles per second. Platoon Ratio: tne platoon ratio, Rp, is obtained from HCM Table 9-3. This value is based on the arrival type. Rp will be used to determine amval rates on the red and green phases. In HCM Table 9-3, the default values for amval types I, 2, 3, 4, 5 and 6 are of 0.333, 0.667, 1.000, 1.333, 1.667 and 2.000, respectively. Green Arrival Rate: The arrival rate during the green phase (veh/sec) which is equal to the product of arrival rate and platoon ratio. Sat Flow Rate: From the HCM Chapter 9 Saturation Flow Adjustment Worksheet (vphg). Service Rate: Convert the hourly rate to vehicles per seconds of green. Appendix E: Page 11

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Worksheet 4: Required Phase Times Based on 1 PHASE DATA Int Red Time Lost Time tl Lost Time tsl LG 1 Mov'ts Grn Arr Red Arr ELI PL Svc Rate Eqiv Svc Net Svc QatBOS Qs Green G fq Land Utl Svc Time Wait Time Tot Time ResQ Qp ResQ Qp' 2 Mov'ts Grn Arr Red Arr ELI PL Svc Rate Eqiv Svc Net Svc QatBOS Qs Green G fq Land Utl Svc Time Wait Time Tot Time ResQ Qp ResQ Qp' Max Ph Time BASE PH TIME Ph No. 4 6 Q --------____l________________________________ v/c Ratio RING 1 RING 2 1(WBL) 2(EBT) 3(NBL) 4(S8T) 5(EBL) 6(WBT) 7(SBL) 8(NBT) 58.56 38.87 58.56 38.87 3.00 3.00 3.00 3.00 2.00 2.00 2.00 2.00 LT L LTR 0.04 0.08 0.08 0.04 0.08 0.08 2.65 2.90 2.60 0.68 1.00 0.33 0.48 0.48 0.44 0.22 0.17 0.29 0.18 0.10 0.20 0.10 3.61 4.44 34.87 54.56 34.87 1.05 1.00 1.05 1.00 1.00 1.00 2.59 39.48 24.94 11.98 5.37 4.69 14.57 44.86 29.63 0.00 0.00 0.00 0.00 0.00 0.00 TR 0.07 0.07 2.65 0.00 0.43 0.43 0.36 4.33 34.87 1.05 1.00 14.51 0.00 14.51 0.00 0.00 . 64.00 14.57 . 0.08 0.08 2.90 1.00 0.48 0.17 0.10 3.61 54.56 1.00 1.00 39.48 5.37 44.86 0.00 0.00 TR 0.11 0.11 2.90 0.00 0.48 0.48 0.37 4.65 54.56 1.00 1.00 14.54 0.00 14.54 0.00 0.00 64.00 44.86 Arr Delta Rate Value 0.04 0.04 2.60 1.00 0.48 0.19 0.15 2.12 54.56 1.00 1.00 16.02 8.96 24.99 0.00 0.00 TR 0.17 0.17 2.60 0.00 0.96 0.96 0.80 6.98 54.56 1.00 1.05 11.18 0.00 11.18 0.00 0.00 64.00 24.99 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 64-00 29.63 . 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. Worksheets 4 of iteration 14 for the permitted left turn example Appendix E: Page 36

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blorksheet 3a Traffic-Actuated Timing Computations Iteration 15 A B Total A B Total Ring 1 PH Swap? Movts PH Time Ring 2 PH Swap? 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

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EXAMPLE 1 Cycle: 97.5 1,JBL EBT 39.18 14.57 Phase T i me Sat Green + + + + + + + + + + ~56 SBTE3L~JBT SBL 58.33 39.18 44.86 29.63 + 7 8 NBT 58.33 24.99 LG 1 Mov' tsLTLLTRL Volune147.37275.00300.00150.00 f lt0.480.310.640.32 Finat Sat828.26560 651003.10580.62 Eff g36.1855 3336.1855.33 Final g/C0.370 570.370.57 Capacity307.30318 14372.17329.48 v/c Rat'o0.480.860.810.46 QAP du22.8720.8227.8417.12 xo0.830.830.830.83 fdl1.161.181.161.16 kd0.290.920.600.47 Delay d126.5424.4732.2319.90 Delay d20.002.710.000.00 Tot Delay26.5427.1832.2319.90 + + + + + + + + + + LT Vol0.00 275.00 0.00 150.00 LT Cap0.00 318.14 0.00 329.48 LT v/c0 . 00 0 .86 0 .00 0 .46 LT QAPdu 0.00 20.82 0.00 17.12 LT xo0.00 0.00 0.00 0.00 LT kd0.00 0.00 0.00 0.00 LT d10.00 24.47 0.00 19.90 LT d20.00 2.71 0.00 0.00 LT Delay0.00 27.18 0.00 19.90 + + + + + + + + + + LG 2 Mov'ts TR TR TR Volune 252.63 400.00 0.00 600.00 f lt 1.00 1.00 0.00 1.00 Final Sat 1556.00 1732.00 0.00 3465.00 Eff g 36.18 55.33 0.00 55.33 Final g/C 0.37 0.57 0.00 0.57 Capaci ty 577.30 982.83 0.00 1966.23 v/c Rat, o 0.44 0.41 0.00 0.31 QAP du 23.03 1 1 86 0.00 1 1 .03 xo 0.83 0 83 0.00 0.83 fd1 1.13 1.11 0.00 1.08 kd 0.43 0.94 0.00 1.15 Delay d1 25.97 13.16 0.00 11.95 Delav d2 0.00 0.00 0.00 0.00 Tot belay 25.97 13.16 0.00 11.95 _ _ _ v/c Ratio 0.48 0.86 0.81 0.46 + + + + + + + + + + Figure E-14. Summary worksheet for the pe~mitted left turn example Appendix E: Page 38

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~ N Nor t h-Bout h Or SB 19 Forth-south Or FIB Figure E-IS. Intersection layout for the example of compound! left turn protection 4ppendixE: Page 39

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NCHRP PROdECT 3-48: CAPACITY ANALYSIS OF TRAFFIC ACTUATED SIGNALS Worksheet 1: Traffic-Actuated Controt Input Data Filename: EXAMPLE2 (Conpound LT Prot) Museum Rd at North-south Dr + + APPROACH NORTHBOUND SOUTHBOUND DATA EASTBOUND ~JESTBOUND LT Treatment3333 LT PositionLeadLanLeadLead Sneakers2.002.002.002.00 Free Queue0.000.000.000.00 Speed30303030 Termination ---- Independent - ~- Simultaneous PHASE RING 1 RING 2 DATA 1(WBL) 2(EBT) 3(NBL) 4(SBT) 5(EBL) 6(WBT) 7(SBL) 8(NBT) Phase Type PH Reverse? Det Length SetBack L G L G L GLG No No No No No NoYesYes 30 30 30 30 30 303030 O O O O O OOO ~+ + + + + + + + + Max Initial 8 18 8 18 8 18 8 18 Add Initial 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Min Gap 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 Reduce Gp By 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ilalk + FDW 0 20 0 20 0 20 0 20 Max Green 15 45 15 45 15 45 15 45 Change + Clr 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 Recall Mode N P N P N P N P . . . . . . . . . . VEH MINIMUM 15 25 15 25 15 25 15 25 STARTING GAP 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 MIN INITIAL 7.50 17.50 7.50 17.50 7.50 17.50 7.50 17.50 MAX PH TIME 20 50 20 50 20 50 20 50 DT OCC TIME 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 TRIAL TIME 15.00 25.00 15.00 25.00 15.00 25.00 15.00 25.00 + + + + + + + + + + tJorksheet 2: Lane Group Data + + PHASE RING 1 RING 2 DATA 1(~BL) 2(EBT) 3(NBL) 4(SBT) 5(EBL) 6(\JBT) 7(SBL) 8(NBT) PH Movements L LTR Arr Type 3 3 Oop PH 0 6 Lt Equiv 0.00 2.55 + + + + LG1 # Lanes 1 1 Mov'ts L L Vol~ne 200 300 Arr Rate 0.06 0.08 Rp 1.00 1.00 Grn Arr 0.06 0.08 Sat Flow 1710 1710 Svc Rate 0.48 0.48 + ~. LG2 ~ Lanes Mov'ts Vol~ne Arr Rate Rp Grn Arr Sat Flow Svc Rate VEH ARR RATE Ped Volume PED ARR RATE +. o ; 3 o 0.00 L LTR L LTR L LTR 3 3 3 3 3 3 0 8 0 2 0 4 0.00 2.18 0.00 8.20 0.00 5.75 + + + + + + 1 1 1 1 1 1 L L L L L L 50 100 300 200 100 50 0.01 0.03 0.08 0.06 0.03 0.01 1.00 1.00 1.00 1.00 1.00 1.00 0.01 0.03 0.08 0.06 0.03 0.01 1710 1710 1710 1710 1710 1710 0.48 0.48 0.48 0.48 0.48 0.48 , + + + + + 10 1 0 1 0 1 TR TR TR TR 0 6000 500 0 300 0 250 0.00 0.170.00 0.14 0.00 0.08 0.00 0.07 0.00 1.000.00 1.00 0.00 1.00 0.00 1.00 0.00 0.170.00 0.14 0.00 0.08 0.00 0.07 0 17470 1737 0 1747 0 1737 0.00 0.490.00 0.48 0.00 0.49 0.00 0.48 + + + + + + + + 0.06 0.25 0.01 0.17 0.08 0.14 0.03 0.08 0 50 0 50 0 50 0 50 0.00 0.01 0.00 0.01 0.00 0.01 0.00 0.01 L LTR 3 3 0 2 0.00 8.20 0.17 0.08 50 0 0.01 0.00 + + . Figure E-16. Worksheets ~ and 2 for the example of compound left turn protection Appendix E: Page 40

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The signal timing computations for the last two iterations of the compound led turn protection example are illustrated on Figures E-17, ENS and E-19. Figure E-20 shows the summary worksheet for capacity and delay. 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. The final cycle length for this example is 130.2 seconds. Both eastbound phases, through and protected left turn, are at their maximum times. Movements with overflow delays include the eastbound through and left turn movement, the southbound through and the westbound left turn movement. Appendix E: Page 41

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Worksheet 3a: Traffic-Actuated Timing Computations A Ring 1 PH Swap?NoNo MovtsUBLEBT PH Time20.0050.00 Ring 2 PH Swap?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)0.030.00 0.25 0.000.01 0.00 0.10 0.00 Veh Min Time15.0025.00 15.00 25.0015.00 25.00 15.00 25.00 Adj Veh Min14.4925.00 11.23 25.0014.92 24.97 13.51 24.98 Ped Arr Rate0.000.01 0.00 0.010.00 0.01 0.00 0.01 Av Peds on Red0.000.00 0.00 0.000.00 0.00 0.00 0.00 Prob (No Peds)1.000.00 1.00 0.001.00 0.00 1.00 0.00 Ped Min Time5.0025 .00 5 .00 25 .005 .00 25 .00 5 .00 25 .00 Adj Ped Min0.0025 .00 0.00 25 .000 .00 25 .00 0.00 25 .00 + _ + + + + + + + + + LG 1 Mov'ts L L L L L L L L Grn Arr 0.06 0.08 0.01 0.03 0.08 0.06 0.03 0.01 Red Arr 0.06 0.08 0.01 0.03 0.08 0.06 0.03 0.01 EL2 0.00 0.00 0.00 0.00 0.00 0.00 0 .00 0.00 Free G gf 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 QSTOoD gq 0 .00 20.82 0.00 0 .04 0.00 46. 06 0.00 17.55 QatEb~ Qr 4.10 0.00 1.44 2.41 5.34 0.00 0.00 0.00 QatEOF Qf 4.10 0.00 1.44 2.41 5.34 0.00 0.00 0.00 QatEOQ Qq 3.56 1.74 1.44 2.41 5.34 2.56 2.78 0.24 QatBOS Qs 4.10 1.74 1.44 2.41 5.34 2.56 0.00 0.24 + + + + + + + + + + LG 2 Mov'ts TR TR TR TR Grn Arr 0.00 0.17 0.00 0.14 0-.00 0.08 0.00 0.07 Red Arr 0.00 0.17 0.00 0.14 0.00 0.08 0.00 0.07 EL2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Free G gf 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 QSTOpP gq 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 QatEOk Qr 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21 QatEOF Qf 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21 DatEOQ Qq 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21 QatBOS Qs 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21 8 NBT Cycte convergence has not been achieved. Difference = .8 Figure E-17. Worksheet 3 of iteration 5 for the example of compound left turn protection Appe~zdix E: Page 42

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Worksheet 4: ~red Phase Times Based on 1 Target Ratio PHASE DATA1(1JBL) Int Red Time110.1t Lost Time tl4.00 Lost Time tsl3.00 LG 1 Mov'ts Grn Arr Red Arr ELI PL Svc Rate Eqiv Svc Net Svc QatBOS Qs Green G fq Land Utl Svc Time Wait Time Tot Time ResQ Qp ResQ Qp' RING 2 6(WBT) 7(SBL) 8(NBT) 80.11 100.26 99.85 4.00 4.00 4.00 3.00 3.00 3.00 0.01 0.03 0.08 0.06 0.03 0.01 0.03 0.08 0.06 0.03 0.00 2.18 0.00 8.20 0.00 0.00 1.00 0.00 1.00 0.00 0.48 0.48 0.48 0.48 0.48 0.48 0.23 0.48 0.06 0.48 0.46 0.20 0.39 0.01 0.45 1.44 2.41 5.34 2.56 0.00 8.97 42.40 15.00 45.00 15.00 1.04 0.99 0.98 0.98 0.98 1.00 1.00 1.00 1.00 1.00 6.27 14.82 16.37 465.63 0.00 0.00 0.04 0.00 46.06 0.00 6.27 14.86 16.37 511.69 0.00 0.00 0.00 0.00 2.54 0.00 0.00 0.00 0.00 0.54 0.00 TR TR TR TR 0.17 0.00 0.14 0.00 0.08 0.00 0.07 0.17 0.00 0.14 0.00 0.08 0.00 0.07 2.55 0.00 2.18 0.00 8.20 0.00 5.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.49 0.00 0.48 0.00 0.49 0.00 0.48 0.49 0.00 0.48 0.00 0.49 0.00 0.48 0.32 0.00 0.34 0.00 0.40 0.00 0.41 14.02 0.00 12.04 0.00 7.01 0.00 7.21 45.00 0.00 42.40 0.00 45.00 0.00 25.26 0.98 0.00 0.99 0.00 0.98 0.00 1.05 1.00 0.00 1.00 0.00 1.00 0.00 1.00 46.12 0.00 37.74 0.00 20.09 0.00 21.31 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46.12 0.00 37.74 0.00 20.09 0.00 21.31 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 50.00 20.00 50.00 20.00 50.00 20.00 50.00 46.12 6.27 37.74 16.37 20.09 0.00 21.31 ilorksheet 5: Green Extens i on T i mes . Arr DettaPhi Max Min Comp Adj New Rate ValueValue Hdwy Hdwy- Ext Ext Hdwy 0.06 1.500.95 3.59 3.59 8.69 7.42 3.59 0.17 0.500.96 3.59 3.59 9.99 3.88 3.59 0.01 1.500.99 3.59 3.59 6.50 6.50 3.59 0.14 0.500.97 3.59 3.59 9.70 9.70 3.59 0.08 1.500.93 3.59 3.59 9.19 3.63 3.59 0.08 0.500.98 3.59 3.59 9.19 9.19 3.59 0.03 1.500.98 3.59 3.59 7.91 7.91 3.59 0.07 0.500.98 3.59 3.59 9.08 9.08 3.59 Computed Phase Times Including Extension Intervals RING 1 2(EBT) 3(NBL) 4(SBT) 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-~. Worksheet 4 of iteration 5 for the example of compoun~i left turn protection Appendix E: Page 43

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Llorksheet 3a: T raf f i c -Actuated T imi ng Computat i ons I terat i on A B Totat A Tota ~ R i ng 1 PH Swap?No No - - - - - - - -NoNo Movts tJBL EBT -------- NBL SBT PH Time 20.00 50.00 70.00 12.76 47.44 R i ng 2 PH Swap? 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. 1 180. 1 182.71 70.0082.760.0020.00100.38 Cycte convergence has been achieved at 130.2 NBT 30.38 0.00 30.38 26.38 99.82 1 03 .82 99.85 70.00 Figure E-19. Worksheet 3a of the last iteration for the example of compoun~i left turn protection Appendix E: Page 44

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+ ~ - - - - - - - + - - - - - - - + - - - - - - - + - - - - - - EXAMPLE2 1 2 3 4 Cycle: 130.2 UBL EBT NBL SBT EBLLIBT Phase Time 20.00 50.00 12.76 47.4420.0050.00 Sat Green 12.58 46.12 6.27 37.74 16.37 20.09 SBL 29.82 0.00 LG 1 Mov' ts Volune fit Final Sat 1710.00 Eff g16.00 Finat g/C0.12 Capaci ty210.13 v/c Rat ~ o0.59 QAP du37.95 xO0.64 fd11.15 kd0.76 Delay d143.68 Delay d24.72 Tot Delay48.40 LLL 123.20115.2043.23 0.950.230.95 411.921710.00 50.008.76 0.380.07 158.18115.11 0.730.38 7.5449.31 0.640.64 1.191.17 1.050.07 8.9857.60 8.990.00 17.9757.60 77. 10184 .8076.8022.906. 77 0.460.950.080.950.23 825 201710.00144.001710.00410.34 13 6216.0050.0029.8217.62 0.100.120.380.230.14 86.31210.1355.30391.6555.52 0.890.881.390.060.12 42.6931.1724.830.008.81 0.640.640.640.640.64 1.211.161.291.101.21 0 181.050.760.180.07 51 :n36.0731.910.0010.64 0.008.994.720.000.00 51.7345.0636.630.0010.64 LT Vot LT Cap LT v/c LT QAP du Ll xO LT kd LT d1 LT d2 LT Delay 0.00300.00 0.00368.31 0.000.81 0.0022.09 0.000.64 0.001.05 0.0025.67 0.008.99 0.0034.66 0.00100.00 0.00477.96 0.000.21 0.0032.91 0.000.64 0.000.18 0.0039.88 0.000.00 0.OO39.88 + + + + + + . LG 2 Mov'ts Volume fit Final Sat Eff 9 Final g/C Capac i ty v/c Rat ~ o QAP du xO fd1 kd DeLay d1 DetaY d2 Tot telay TR 0.00600.00 0.001.00 0.001747.00 0.0046.00 0.000.35 0.00617.20 0.000.97 0.0041.47 0.000.79 0.001.12 0.001.27 0.0046.50 0.0019.04 0.0065.54 ~R 0.00500.00 0.001.00 O. 001737.00 0 0043.44 0.000.33 0.00579.51 0.000.86 0.0040.59 0.000.79 0.001.12 0.00t.OO 0.0045.54 0.003.07 0.0048.60 + ++ ~+ _~ v/c Ratio 0.590.970.38 0.89 + ~+++ + 0.00200.00 0.00265.43 0.000.75 0.0032.91 0.000.64 0.000.76 0.0039.16 0.004.72 0.0043.88 ~+ TR TR 0 00300.000.00250.00 0 001 .000.001 . 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

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APPENDIX E REFERENCES Courage, K. G. and R. Ak~elik, "A Computational Framework for Modeling Traffic- Actuated Controller Operations," Working Paper NCHRP 3-48-1, Transportation Research Center, University of Florida, Gainesville, May 1994. Courage, K. G. and P-S. Lin, "A Computational Framework for Modeling Traffic- actuated Controller Operations," Working Paper NCHRP 3-48 - , Transportation Research Center, University of Florida, Gainesville, August 1994. Courage, K. G., D. B. Fambro, R. Ak~elik, P-S. Lin, M. Anwer, "Capacity Analysis of Traffic-Actuated Intersections," NCHRP 3-48 Draft Interim Report, TRB, National Research Council, Washington D.C., January, 1995. Ak~elik R. arid E. Chung, "Calibration of the Bunched Exponential Distribution of Arrival Headways," Road and Transport Research, Vol. 3, No. I, 1994, pp. 42-S9. Ak~elik, R. "Extension of the HEM Progression Factor Method for Platooned Arrivals," Working Document WD TO 95/! I, ARRB Transport Research, Australia, August 199S. Appendix E: Page 46