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- 35 - Figure 31 â Procedure for identifying spillback occurrence at an on-ramp If spillback is detected, the queue length along the on-ramp is estimated and compared to the available storage. If the queue length is greater than the available storage length, then spillback is expected to occur. The analyst must then refer to the methodology described in Appendix E â On-Ramp Queue Spillback Analysis to evaluate the impacts of spillback on the performance of the arterial intersection. 7. Lane-by-Lane Speed and Flow Estimation Methods for Freeways Spillback into freeways results in uneven operations of mainline lanes, with some lanes blocked, while some operating in undersaturated conditions. Also, the development of trip-based travel time measures requires the evaluation of performance measures on individual lanes, as each O-D within a freeway system uses a specific lane or set of lanes. Therefore, estimating travel time measures in a freeway facility requires two key components: identifying the set of lanes selected for the trip, and estimating the operating speeds on each of these lanes.
- 36 - This section summarizes the framework developed for lane-by-lane analysis of freeway facilities. The full methodology for evaluation of lane-by-lane performance measures in freeway facilities is described in detail in Appendix F: Freeway Facilities â Lane-by-Lane Analysis. Lane Selection Framework Predicting lane selection by the traveler requires understanding of the dynamics of flow distribution among freeway lanes under varying operational conditions. For a given freeway segment, the percent of the total flow assigned to each lane is defined as the Lane Flow Ratio (LFR). Preliminary Field Observations This section briefly discusses and presents examples on the behavior of flow distribution along different freeway segments as a function of the demand-to-capacity ratio (v/c). For 2-lane freeway segments, Figure 32 demonstrates that flow distribution follows a âscissorsâ pattern, with the flow highly concentrated in Lane 1 during free-flow conditions. As the demand for the segment increases, flow gradually migrates to Lane 2. During near-capacity conditions, flow is higher in Lane 2. Figure 32(a) illustrates lane flows along a freeway segment of I-694 (Minneapolis/MN). At near-capacity conditions, lanes 1 and 2 carry 45% and 55% of total flow, respectively. Figure 32(b) provides lane flows for a segment of SR-67 (Salt Lake City/UT), where lanes 1 and 2 carry 40% and 60% of total flow when demand approaches capacity. As shown, the lane flow distribution varies between sites, and thus there are additional parameters that need to be considered in estimating lane-by-lane flows.
- 37 - Figure 32 â Comparison of lane flow distribution on two different 2-lane segments: (a) Minneapolis, MN and (b) Salt Lake City, UT Next, two different 3-lane freeway segments are compared (Figure 33). The lane distributions for these are different than those for 2-lane segments. At low demand most of the flow of 3-lane segments is concentrated in the center lane (lane 2), followed by lanes 1 and lane 3. As demand increases, lane flow distribution increases in lane 3 and decreases in lanes 1 and 2.
- 38 - Figure 33 â Comparison of lane flow distribution on two different 3-lane segments: (a) Tampa, FL and (b) St. Paul, MN As for 2-lane freeways, the values for boundary conditions at 3-lane freeways differ from one location to another. For example, Figure 33(a) shows that during near-capacity conditions lane 3 carries the majority of flow but it is similar to that of lane 2. However, in the location represented by Figure 33(b), the proportion of flow allocated to lane 3 is higher when compared to the other lanes. Finally, two 4-lane segments were examined. As shown in Figure 34, lane 4 is typically underused during free-flow conditions, but when demand approaches capacity it carries the majority of flow. However, in Figure 34(a), flow is highly concentrated on lanes 1 and 2 during free-flow, while Figure 34(b) shows that flow is more concentrated in lanes 2 and 3 for similar demand levels.
- 39 - Figure 34 â Comparison of lane flow distribution on two different 4-lane segments: (a) Salt Lake City, UT and (b) Tampa, FL Modeling of Lane Flow Ratio (LFR) Analytical models were developed to predict LFR for each lane as a function of the logarithm of the segment volume-capacity ratio (v/c): ð¿ð¹ð ð ðð ð (Equation 1) ð¿ð¹ð 1 â â ð¿ð¹ð (Equation 2) Where: LFRi = share of the total flow on lane i, where i ranges from 1 to n-1 (n = total number of segment lanes) LFRn = share of the total flow on the leftmost lane (lane n); a= multiplicative calibration parameter v/c = volume/capacity ratio b = additive calibration parameter
- 40 - The adjustment factors fa and fc are calculated as a function of a series of parameters, as follows: ð = ð + ðº Ã ð + ð¡ Ã ð + ð Ã ð (Equation 3) ð = ð + ðº Ã ð + ð¡ Ã ð + ð Ã ð (Equation 4) where: G = grade (%) a0 = empirical constant aG = empirical coefficient due to impact of grade cG = empirical coefficient due to impact of grade t = truck percentage (%) at = empirical coefficient due to impact of trucks bt = empirical coefficient due to impact of trucks n = access point density â number of ramps half a mile upstream and half mile downstream an = empirical coefficient due to impact of access point density b = empirical constant bn = empirical coefficient due to impact of access point density vR = ramp flow (vph) avR = empirical coefficient due to impact of ramp flow bvR = empirical coefficient due to impact of ramp flow Evaluation of speeds on individual lanes After the flows for individual lanes are obtained, the next step in the methodology calculates the speeds on individual lanes. HCM Chapter 12 (Basic segments) proposes the following equation to describe the speed-flow relationship of a basic segment: ð = ð¹ð¹ð â (Equation 5) Where ð = segment speed (mi/h) ðµð = breakpoint value (pc/h/ln) ð = segment capacity (pc/h/ln) ð¹ð¹ð = segment free-flow speed ð£ = demand flow rate for the segment (pc/h/ln) The same speed-flow relationship is used to predict speeds on individual lanes, as long as the free-flow speed (FFS) and capacity (c) inputs can be provided on an individual lane basis. Appendix F provides a procedure to estimate these values based on the segment-wise average values of FFS and capacity. Figure 35 illustrates the field data and the resulting speed-flow relationship of each lane for a 2-lane basic freeway segment.