Guidelines on the Use of Auxiliary Through Lanes at Signalized Intersections (2011) / Chapter Skim
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Appendix C - Estimation of Design Lengths of ATL Components
Appendix C - Estimation of Design Lengths of ATL Components
Pages 78-83
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From page 78... ...
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.
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From page 79... ...
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)
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From page 80... ...
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
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From page 81... ...
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 – α)
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From page 82... ...
: 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:
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From page 83... ...
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)
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