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APPENDIX C ESTIMATION OF DESIGN LENGTHS OF ATL COMPONENTS Introduction A key design element of ATLs is the appropriate length of the ATL's upstream and downstream components. Although it may be hypothesized that a longer ATL promotes higher ATL use, extensive field observations of ATLs tend to contradict this theory. In fact, some of the ATL sites used to develop the operational models in the "ATL Volume Estimation" section in Chapter 3 had high ATL utilization and short downstream lengths. Instead, the primary motivator for using the ATL appears to be a defensive one: avoiding a cycle failure when traffic in the adjoining CTL is moderately to highly congested. Based on the above premise, the required ATL upstream length is predicated on the provision of adequate storage for and access to the ATL from the neighboring CTL. The downstream length, on the other hand, is predicated on servicing the queued vehicles in the ATL so that they can accelerate to the approach free flow speed and smoothly merge before reaching the end of the downstream taper. Gap availability and acceptance in the CTL for ATL vehicles operating under relatively high-speed, uninterrupted conditions must also be considered. Therefore, the recommended minimum downstream length is the greater of the lengths determined from these two operating conditions. Note that the lengths determined from this method represent minimum design requirements for ATLs. Poor downstream sight distance, lack of proper signage (or existence of overhead lane signs), presence of downstream driveways, and significant right-turn-on-red (RTOR) flow from cross-street traffic may all necessitate adjustments to the minimum length to accommodate those effects. Finally, the minimum ATL lengths developed in this section are predicated on the assumption that an ATL will in fact be built. This is a strong assumption, but it is one that relies on the engineer's judgment on the practical need for such a lane. Because one of the major outputs of these guidelines is the predicted ATL through flow rate under various conditions, it is incumbent on the practitioner to decide whether the estimated ATL volume indeed warrants the additional lane, especially if the anticipated flow is only one to three vehicles per cycle on average. However, if the decision is to proceed with an ATL installation, then the procedure described in the next section can be followed. ATL Length Estimation Procedure This procedure is built around the ATL flow rate estimation models described in the "ATL Volume Estimation" section in Chapter 3. Since there are separate models for one-CTL and 2-CTL cases, the same reasoning applies to the ATL length estimation process. The procedure is implemented in two Microsoft Excel spreadsheets that estimate minimum ATL length and provide other important performance measures as outputs. The starting point of the analysis has no ATL presence. For the one-CTL case, the procedure considers an approach with a single shared through-right continuous lane, while the 2-CTL Page C-1

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case assumes an exclusive through-movement lane and a shared through-right continuous lane. In all cases, left turns are assumed to operate from an exclusive lane or pocket and therefore are not part of the analysis. An outline of the procedure as it relates to the ATL upstream length determination is explained in the following steps: 1. Identify whether the one-CTL or 2-CTL case applies. 2. Supply the data required for ATL flow rate estimation including: a. Total approach through and right-turn flow rates, b. Cycle length and effective green time for the subject approach, and c. Saturation flow rate for both through and right-turn movements. 3. Estimate the ATL flow rate based on the one-CTL or 2-CTL model in the "ATL Volume Estimation" section in Chapter 3. 4. Calculate the ATL through flow rate assuming equal lane volume-to- adjusted saturation flow rate (v/s) based on the HCM 2010 shared or exclusive lane-group volume distribution. 5. Take the predicted ATL flow rate as the lower estimate from steps 3 and 4. 6. Calculate the ATL and CTL volumes, capacity, control delay, and back of queue using the HCM 2010 signalized intersection procedures. For shared ATLs, include the right-turn flow rate in the lane flow computations. 7. Estimate the 95th percentile queues in both the ATL and CTL (for one CTL lane in the case of two CTLs) using HCM procedures. 8. Select a storage length based on the greater of the 95th percentile queues in the ATL and CTL. Queue storage or access distance is calculated based on an estimate of average vehicle spacing in a stopped queue. The determination of the requisite downstream length requires a further set of input parameters, some of which may be defaulted as shown in parentheses, namely: Approach free flow speed or speed limit, Average acceleration rate from a stop on the ATL (10 feet/second2), Intersection width measured from the stop line to the far curb (40 feet), Minimum acceptable headway in CTL traffic stream (6 seconds), and Driver reaction time (1 second). The downstream length estimation based on storage of vehicles at the desired spacing in the downstream length (DSL1) proceeds as follows. Estimate the average uniform, random, and oversaturation back of queue (BOQ) for ATL through traffic only (Q1 + Q2 in HCM terminology). This approach incorporates two opposing and simplifying assumptions. The first is that the required length will be based on the average BOQ as opposed to the 95th percentile value as was done in the upstream case. This is offset by another Page C-2

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assumption where all through-movement vehicles in the ATL are assumed to be contiguous in the queue and not separated intermittently by righ t-turning vehicles in a shared lane, which would result in a larger separation between through-movement vehicles. This procedure assumes that the effects of the two assumptions will balance. The downstream storage criterio n is based on providing sufficient spacing between ATL vehicles at the free flow speed or speed limit. Since v ehicles accelerate from the stop line position, the downstream distance me asured from the far curb can be shown to be: Where: V = free flow speed or speed limit (in feet/second), A = acceleration rate from stop line (in feet/second2), L = spacing between vehicles at stop (in feet), T = driver reaction time (in seconds), an d INTW = intersection width measure d from the stop bar to the far curb (in feet). The second criterion for est imating required downstream length is based on gap availability and acceptance under uninterrupted flow conditions, especially on high-speed approaches. The concept is that, after tr aveling a reaction distance past the intersection, an ATL driver must find an acceptable merge gap in the neighboring CTL within the confines of the downstream ATL length. Using assumptions on the headway distribution in the CTL and a minimum acceptable merge headway value, the distance me asured from the far curb can be shown to be: Where: NUM = the number of rejected gaps in the CTL. This could be either the mean value of rejected gaps or a pre-specified percentile number of rejected gaps, as explained below. Gr = expected or average size of a rejected headway in the CTL (in seconds). Page C-3

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This model used to calculate DSL2 is based upon a gap acceptance procedure with the following assumptions: Drivers begin searching for gaps as soon as they pass the stop bar, Drivers have reached the operating speed of the arterial, Drivers are homogeneous with regard to a critical headway or gap (tc), and Traffic in the adjacent CTL follows an exponential headway distribution. The following steps describe the model development: Step 1. Determine the number of rejected gaps encountered until an acceptable gap is found. Let p be the probability of rejecting a gap in the CTL, tc be the size of the critical headway, and h be the time headway between vehicles in the CTL. Then where is the flow rate in the CTL (in vehicles per hour). Then the probability of rejecting exactly i gaps is pi (1 p) and the expected number of rejected gaps is: An alternative approach to using Nr is to design the downstream length to accommodate the 95th number of rejected gaps, as opposed to the mean value. In this case, we would like to determine the number of rejected gaps that would only be exceeded at most (1 ) percent of the time. In other words, find I such that the number of rejected gaps X is such that or conversely which can be then expressed as Page C-4

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Solving for I gives the condition for the percentile rejected gap: For example, if the probability of a rejected gap p = 0.50 and a 95th percentile confidence level on the number of rejected gaps is desired, then This compares with a mean number of rejected gaps of In the remaining steps, the user may choose to apply either the percentile or mean value of rejected gaps. Step 2. Determine the expected size of a rejected gap, E(t|t < tc): where using integration by parts, and after simplifying gives: Since Step 3. Calculate the expected waiting time for an acceptable gap, which is equal to the product of the number of rejected gaps and the expected size of a rejected gap: Page C-5

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Optionally, if one selected the percentile gap approach, then the waiting time for the (alpha) percentile rejected gap would be Step 4. Calculate the distance traveled before an acceptable gap is found: or in the case of the percentile gap: where V is the operating speed in feet per second. Incorporating the reaction time T, the total distance traveled (in feet) is given by or in the case of the percentile gap, The computational engine described in Appendix B provides both a mean and percentile option for computing the design value of DSL2. Page C-6