Loading...
HomeMy WebLinkAboutBozemanAtwell-TIS_2025-0310 P.O. Box 249 Bozeman, MT 59771 406.922.7300 www.406traffic.com M E M O R A N D U M To: City of Bozeman Engineering staff From: Nate Larson, PE, PTOE, RSP1 Date: 2/28/2025 Subject: Atwell Suites TIS: Baxter Queueing Analysis This memo addresses Engineering’s comment requirement for supplemental analysis of back-to-back queues on Baxter Lane between North 19th Avenue and the project’s proposed property access, shared with the existing Town Pump, opposite Commerce Way. This analysis has been conducted after the completion and review of the project’s Traffic Impact Study (TIS). To that end, this memorandum can be amended to, or filed with, that completed TIS for the project. There are multiple potential methods for estimating queue extents based on the detailed information in the TIS. Some data needed to complete these estimates is reproduced from the TIS in this memo. The following three methods have been employed, listed in increasing order of complexity: 1. a planning-level “Rule of Thumb”, 2. operations modeling results from the TIS’ Synchro analysis, and 3. stochastic queuing analysis based on foundational traffic flow theory principles. The Geometric Condition: Available Space and its Configuration The subject segment of Baxter Lane has a single left turn lane in each direction with a common striped taper joining them. This arrangement and the lengths available for (a) westbound storage back from 19th, (b) eastbound storage back from Commerce Way, and (c) the space between them are shown in in the figure on the following page. Note that the hotel will be situated starting near the upper right of the image, north is to the top of the page, and distances are approximate. Because the space between the two back-to-back left turn lanes is uniformly paved and has no curb or other raised median, it can physically be traversed and used for queue storage by left turning vehicles that number greater than the capacity of either left turn lane at drivers’ discretion—it might be considered “flexible” space in this sense. Drivers at this location have been observed doing so in the rare instances when it’s necessary or helpful, presumably in order to avoid blocking the single adjacent Baxter through lane. PTOE #1185, certified in 2003 406 Traffic and Transportation Consulting, PLLC Atwell: Baxter Queuing, 2/28/2025 2 General Queuing Assumptions and TIS Information The most important assumption driving queue estimates is the projected intensity (volume per hour) of traffic making each left turn movement. This information comes from Exhibit 11 of the project TIS submitted and reviewed in 2024. Peak hour total left turns after the hotel opens, including those not associated with the project (“background” traffic) have been estimated as follows:  AM: Westbound at 19th = 53, Eastbound at Commerce = 64  PM: Westbound at 19th = 70, Eastbound at Commerce = 74 Capacity, or the rate at which queued vehicles can be served, differs between the two directions. The signal at 19th controls westbound Baxter left turns, while eastbound Baxter drivers turning left into the project site must yield to opposing through traffic (and right turns) but do not face a traffic control device. For the potentially conflicting westbound and eastbound left turns in this segment of Baxter, capacities are identified by the timing of the 19th signal and the intensity of said opposing traffic, respectively. These capacities only matter for the second and third methods tested here. Quantitative analysis of queuing relies on the assumption that arrivals are generally random and how they are distributed in time. For westbound arrivals there are no signals or roundabouts upstream to meter traffic or create platoons, so the assumption of randomness is simple. Eastbound left turning traffic must originate from the 19th & Baxter intersection, but can be considered approximately equally likely to come from any of the three relevant traffic movements there: the northbound right, southbound left, and eastbound through, relative to their respective volumes. This also leads to a reasonable assumption of random arrivals. As with capacity, this assumption also matters only for the second and third methods tested here. WB 150’ Taper/Flex 120’ WB 50’ 406 Traffic and Transportation Consulting, PLLC Atwell: Baxter Queuing, 2/28/2025 3 Finally, the amount of space a queued vehicle occupies will define the relationship between certain queue parameters. Factors that affect the average spacing in queue include vehicle mix (especially as it relates to trucks), weather conditions, lighting, and roadway grade. Most passenger vehicles and pickup trucks are nominally 16-19 feet long, and bumper spacing for stopped vehicles is often in the range, though it can be longer in adverse conditions. Where heavy truck volumes are generally low, which tends to be more true in the PM peak hour, when design volumes often occur, a reasonable assumption for average spacing in queue is 25 feet. This also accounts for the fact that the last vehicle in the queue doesn’t need space behind it. Turn lane lengths are often rounded up to a value that represents a whole number of vehicles. These are often multiples of the average spacing in queue (25 feet). For example, a hypothetical average queue length estimate of 115 feet might result in a recommended turn lane length of 125 feet, such that it can accommodate five vehicles completely. Method 1: Rule of Thumb An older method of estimating design queue lengths stipulates that the minimum length of a turn lane, in feet, can be approximated by the traffic intensity itself as measured in vehicles per hour. This rule of thumb should only be considered in under-capacity conditions, and it does not consider the intensity of conflicting traffic or any information regarding traffic control at the intersection. With Method 1 and the lack of a physical median, each direction’s left turn volume in the PM peak (the busier of the two, listed on the previous page) translates to the need for a full width left turn lane that’s 75 feet long, or sufficient to store 3 vehicles at once. The total storage need of 150 feet is less than the combined length of about 320 feet, including taper/flex space, that’s currently available. This indicates that at the planning level, conflicts related to back-to-back left turn movements are not expected in the Atwell project’s buildout condition. Method 2: Synchro The traffic delay analysis conducted for the project and summarized in the TIS also included queue calculations at both intersections, although these were not included in the report. For the volume and geometric features of each scenario at signalized intersections, Synchro estimates the extent of both average queue, referred to as the “50th percentile” queue, and the queue at a higher theoretical level of traffic, which it refers to the “95th percentile” queue. At stop-controlled intersections only the 95th percentile queue is estimated. Many agencies that use Synchro interpret 95th percentile queue results to be reasonable for design, in part because that result is often roughly double the 50th percentile queue. This, in turn, stems from the traditional belief that designing for one standard deviation beyond the mean design hour condition is a prudent approach, and the application of various statistical distributions to arrivals at intersections left turn lanes (Erlang, Poisson, etc.) that result in 85-95% of expected results falling within that range. The relevant 95th percentile queue results from Synchro for this project are:  AM: Westbound at 19th = 38 feet, Eastbound at Commerce = 3 feet  PM: Westbound at 19th = 46 feet, Eastbound at Commerce = 5 feet Eastbound queues are substantially shorter than westbound in this segment because eastbound Baxter traffic at Commerce is uncontrolled: left turning drivers can proceed whenever there is a gap in opposing traffic that allows them to do so safely. Note also that these estimated measurements cover all potential times a queue could be measured throughout the peak hour, not just the maximum queue present during each signal cycle. These lengths fall well below available capacity. 406 Traffic and Transportation Consulting, PLLC Atwell: Baxter Queuing, 2/28/2025 4 Method 3: Foundational traffic flow theory has a well-developed set of mathematical relationships that allow the estimation of queue characteristics in a macroscopic way, similar to the estimation of average intersection delay. To apply these here, relevant information is adapted from the text Traffic Flow Fundamentals (Adolf D. May, Simon & Schuster, 1990), where Chapter 12, section 3 covers Stochastic Queuing Analysis. In the context of queuing analysis, traffic intensity is directly analogous to the commonly computed parameter “volume/capacity ratio”. This variable is assigned the letter ρ (rho), and it is the only one necessary, other than the number of vehicles that can fit in the space available, to analyze the Baxter segment in question. For westbound lefts at 19th, which are subject to “protected+permitted” control, capacity is driven by the amount of green time provided at the signal as well as opposing traffic that might be present during the “permitted left” part of the signal cycle. For eastbound lefts at Commerce Way into the Atwell site, capacity comes strictly from available gaps in opposing traffic. In both cases, the service of queued vehicles can be considered random for the purposes of this analysis. The applicable mathematical relationship here is the probability of a specific number of vehicles in queue (or fewer) that is equal to the left turn storage capacity. The equation for this probability is: P(n) = ρn(1 - ρ) where P(n) = probability of exactly n vehicles in the left turn lane, and ρ = traffic intensity (volume/capacity ratio) The table below indicates the probability of n or fewer vehicles being in each of the two back-to-back turn lanes as a function of traffic intensity that result from this equation, for the PM peak hour (again, the busier of the two). Parameter Westbound Eastbound Traffic intensity, ρ 0.29 0.07 Maximum vehicle storage, n 6 2 P(0 to n), cumulative 0.9998 0.9951 Spillover probability, 1 – P(0 to n) 0.0002 0.0049 The cumulative probability that the available striped queue storage will be exceeded is shown in the bottom row of the table. Furthermore, the combined probability that left turn queue storage is either blocked in one direction by several vehicles or simultaneously in both directions by 1-2 vehicles represents what would need to occur in order for the adjacent through lane on Baxter to be blocked by a queued left-turning vehicle. Such an event would be even more rare. Conclusion The examination of expected Baxter Lane queue conditions documented in this memo indicates that based on examination with three different methods, projected peak hour traffic is highly likely to function without blocking problems or related traffic conflicts. Not only is queue storage expected to be well within reasonable design limits, the presence of striped flexible space mid-block allows for an additional vehicle or two to be stored in very rare extended-queue situations without blocking through lanes. If you have any questions about these results, please feel free to reach out to me directly at 406.922.7300 or nate@406traffic.com, or to inquire through the appropriate applicant team contact.