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Page C-1 APPENDIX C ESTIMATION OF DESIGN LENGTHS OF ATL COMPONENTS Introduction A key design element of ATLs is the appropriate length of the ATLâs 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 âATL Volume Estimationâ 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 engineerâs 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 âATL Volume Estimationâ 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-2 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 âATL Volume Estimationâ 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-3 as sumption where a ll th ro ug h-mo v eme nt v ehicl es in the ATL are assumed to be contiguous in the queue an d no t separated intermittently by righ t- tur ni ng ve hi cl es in a shared lane, which would result in a larger separation b etwee n through -m ov em ent ve hi cl es. This procedure assume s th at th e effects of the two as sumptions will ba la nce. The downstre am stora ge cr iterio n is based on prov idin g suffici ent spaci ng be t ween ATL v ehicl es at the free flow speed or speed limit. Since v ehicl es acce le ra te from the stop lin e posi ti on , the downstream distance me asured from the far cur b can be sh ow n to be : Where: V = free fl ow speed or speed limit (in feet/second), A = acce le ra tion rate from stop line (i n feet/second2), L = spaci ng be t ween v ehicl es at stop (in feet), T = driv er reaction time (in seconds), an d INTW = in tersecti on width measure d from the stop ba r to the fa r cur b (in feet). The second criterion for est im at in g required downstre am l ength is based on gap av aila bi lity and acce pt ance un der uninterrupted flow conditions, especi al ly on high-speed approa ch es. The concept is that, after tr av el in g a reaction distance past the intersecti on , an AT L driv er must find an acce pt ab le merge ga p in the ne ig hb orin g CTL within the confines of the downstream ATL length. Using as sumptions on the head wa y distri b ution in the CTL and a minimum acceptab le merge he ad wa y value, the distance me asured from the far cur b ca n be show n to be: Where: NUM = the numb er of rejected gaps in the CT L. This could be ei ther the mean val ue of rejected gaps or a pre-specified percentile numb er of re ject ed gaps, as ex pl ai ned be lo w. G r = expected or av erage size of a rejected headway in the CT L (in seconds).
Page C-4 This model used to calculate DSL 2 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 ( t c ) , 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 λ is the flow rate in the CTL (in vehicles per hour). Then the probability of rejecting exactly i gaps is pi (1 â 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 â α) 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-5 Solving for I gives the condition for the percenti le rejected gap: For example, if the probability of a rejected gap p = 0.50 and a 95 th percentile confidence level on the number of rejected gaps is desired, then This compare s with a mean number of rejected gaps of In the remaining steps, the user may cho o se to apply either the percentile or mean value of rejected gaps. Step 2 . Determine the expected size of a rejected gap, E(t|t < t c ): 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-6 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: o r 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 o r in the case of the percentile gap, The computational engine d escribed in Appendix B provide s both a mean and percentile option for computing the design value of DSL 2 .
