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232 A P P E N D I X B Off-Ramp Queue Spillback Check The current methodology for Freeway Facilities analysis (HCM Chapter 10) evaluates the performance of each segment individually using standard 15-minute time periods. If any segment within the facility yields a LOS F and/or a v/c ratio greater than 1.0, the analysis continues with the oversaturated procedure, using smaller time steps. Similarly, in order to determine whether there is queue spillback from a freeway off-ramp, the analysis is first conducted using 15-minute time periods. If the analysis shows that any of the ramps are expected to experience queue spillback, the oversaturated procedure must be used to estimate the spillback impacts on the freeway mainline lanes, even if the segment-wide performance is not at a LOS F and/or a v/c ratio greater than 1.0. The methodology framework for conducting a spillback check at diverge critical points is presented in Figure B-1 and described in more detail in the remainder of this section.
233 Figure B-1. Procedure for identifying spillback occurrence at an off-ramp/weaving segment Step 1 - Capacity Checks The first step in the methodology determines whether capacity is exceeded at any of the critical points along the diverge section: Case A â Ramp proper Demand at the study diverge ramp (vR, as defined in HCM Chapter 14) is compared against the capacity of the ramp proper (cR) using HCM Exhibit 14-12, replicated in Figure B-2.
234 Source: HCM 6th Ed. Exhibit 14-12 Figure B-2. Capacity of ramp roadways (pc/h) Case B â Downstream intersection Demand at the downstream arterial intersection approach is compared against the estimated capacity of the approach. Depending on the type of intersection located at the end of the ramp proper, the respective capacities are obtained from one of the following chapters: Signalized Intersections (HCM Chapter 19); Two-Way Stop-Control Intersections (HCM Chapter 20); All-Way Stop Control Intersections (HCM Chapter 21); Roundabouts (HCM Chapter 22); Ramp Terminals and Alternative Intersections (HCM Chapter 23). The recommended approach for each case is as follows: Signalized Intersections. The operation of a signalized intersection will yield queues even when the operation is undersaturated. Although an oversaturated approach is expected to create longer queues that are growing in time and are more likely to spill back into the freeway diverge, it cannot be guaranteed that the queues at an undersaturated approach will not affect the freeway mainline. Therefore, the methodology estimates the queue length and compares it to the available storage length for each analysis period. The arriving demand at the intersection may be constrained by the ramp proper capacity, and for this reason the ramp proper capacity check must be conducted first. Unsignalized Intersections. Similar to signalized intersections, the approaches of an unsignalized intersection yield queues even during undersaturated conditions. Therefore, a LOS better than F at the intersection is not sufficient to guarantee that spillback will not occur. For unsignalized intersections (TWSC, AWSC and roundabouts) the user is advised to proceed to the second step of the check methodology (comparison of queue length). Case C â Downstream merge junction Queue spillback may also occur on freeway-to-freeway connectors, and this is a common issue in high- demand urban interchanges. In this case, the bottleneck is located at the downstream merge segment and occurs when the discharge rate into the downstream merge is lower than the off-ramp demand. Consequently, the queue may back up into the upstream freeway lanes. In this case, the merge capacity of the downstream freeway facility must be modeled using the current HCM methodology for freeway facilities. For oversaturated conditions, the methodology estimates the queue length at the on-ramp (as described in Chapter 25 â Freeway Facilities Supplemental). This queue length value should be used as input for queue spillback analysis as described below. Similar to arterial intersections, the arriving demand at downstream merge may also be constrained by the ramp proper capacity. Therefore, the entering ramp demand at the merge is the minimum value of the exiting flow rate at the diverge and the ramp proper capacity.
235 Step 2 â Queue Length Estimation In the second step, the procedure estimates the expected queue length for any conditions where demand exceeds capacity. Three cases may occur: Case A â Ramp proper In cases of demand exceeding capacity of the ramp proper, the bottleneck is the entry to the off-ramp, and the ramp proper would not necessarily have a queue present. If Case A occurs, bottleneck is expected to occur and no additional calculations are necessary at this step. Case B â Downstream intersection Spillback occurs when the resulting queues from the downstream intersection ramp terminal exceed the available ramp storage. For all cases, the first step is to estimate the maximum throughput v at the downstream intersection approach. That maximum throughput must not exceed the capacity of the ramp proper, cR under Case A: ð£ = min ð£ , ð Ã ð Ã ðð»ð¹ Ã ð (Equation B-1) Where: v = maximum entering flow rate for the intersection approach (veh/h) vR = offâramp demand for the period (pc/h) cR = capacity of the off-ramp roadway (pc/h) fHV = adjustment factor for heavy vehicle presence fp = adjustment factor for driver population If the off-ramp demand exceeds its capacity, the ramp proper acts as an upstream bottleneck, and limits the demand to the intersection approach. This step ensures that the incoming demand at intersection does not exceed the capacity of ramp proper. The calculations of throughput for each intersection type are described below. Signalized Intersections. The current methodology described in Chapters 19 and 31 evaluates the performance of individual lane groups for a subject approach. It also estimates the back of queue length Q (HCM Equation 31-149) or a percentile back-of-queue length Q% (HCM Equation 31-150). In some cases, only one high-demand movement at the intersection approach is the bottleneck that results in spillback, yielding an unbalanced lane usage pattern at the ramp. Field observations have shown that arterial intersection failures may occur at one lane group as drivers position themselves in a specific lane at the ramp to anticipate the downstream signal, the lane usage in the ramp becomes unbalanced, as shown in Figure B-3.
236 Figure B-3. Examples of unbalanced ramp lane usage: (a) Norfolk, VA and (b) Tampa, FL At off-ramps with two or more lanes, the estimated queue lengths for each intersection lane group must be associated with specific ramp lanes. Figure B-4 illustrates an example of a typical ramp terminal. It is expected that drivers that desire to take a left turn at the intersection will position themselves in the leftmost lane ramp (Ramp Lane 2), while drivers who intend to turn right will likely choose the rightmost lane at the ramp (Ramp Lane 1). Analyst judgement is required to define the grouping of intersection lane groups into ramp lanes. Figure B-4. Off-ramp geometry with additional lanes at the arterial approach By using the results of the queue estimation procedure, the number of queued vehicles in a given ramp lane n is estimated as follows: QL,k= â QLG,m = Q%, LGn x NLGm (Equation B-2) Where: QL,k = number of queued vehicles in ramp lane k, during a 15-min interval QLG,m = number of queued vehicles from lane group m associated with ramp lane k, during a 15-min interval Qn%,LGm = estimated back of queue length (nth percentile), as defined in HCM Equation 31-150 (measured in veh/ln) NLGm = number of approaching lanes for lane group m
237 Unsignalized Intersections. Each unsignalized intersection type has its own methodology to estimate queue length. The TWSC methodology estimates the 95th percentile queue length for minor movements with Equation 20-68, while the 95th percentile queue length for AWSC approaches is estimated with Equation 21-33. For roundabouts, the 95th percentile queue length for a given lane is provided by Equation 22-20. Regarding intersection lane groups and ramp lanes, the same procedure discussed above for signalized intersections is applied. Case C â Downstream merge For freeway-to-freeway connectors, the estimated queue length at the downstream merge is estimated using the freeway facilities oversaturated methodology, Equation 25-21. For this specific type of connector, the demand difference among ramp lanes can be considered negligible for the purposes of this analysis. Step 3 â Queue Storage Ratios and Spillback Checks The third step is to estimate the queue storage ratio (RQ) for the ramp proper queues. If RQ exceeds 1.00, then spillback is expected to occur. The calculations for each of the three possible cases is as follows: Case A â Ramp proper In cases of demand exceeding the capacity of the ramp proper, the bottleneck is the entry to the off-ramp, and the ramp itself would not necessarily have a queue present. This case estimates the impacts of the queue as it extends along the deceleration lane. The queue length upstream of the ramp proper (QSP) is estimated based on the âleftoverâ demand that is not served by the off-rampâs available capacity: ð = ð£ â ð Ã ð Ã ðð»ð¹ Ã ð Ã ð¿ Ã ð¡i (Equation B-3) Where: QSP = length of queue beyond ramp storage distance (ft) vR = offâramp demand for the period (pc/h) cR = capacity of the off-ramp roadway (pc/h) fHV = adjustment factor for heavy vehicle presence PHF = peak hour factor fp = adjustment factor for driver population ti = analysis period i (h) Case B â Downstream Intersection In cases of demand exceeding capacity at the intersection, the methodology considers the queues for all lanes from the ramp gore to the stop bar, as well as the channelization at the stop bar. The total storage length LR for the ramp can be estimated as the sum of lane lengths for i number of different sections (a section is defined as a uniform segment with a homogenous number of lanes) as follows: ð¿ = â ð ð¥ ð¿ (Equation B-4) Where: Ni = number of lanes in section i Li = section i length (ft)
238 The individual ramp storage for each of the k lanes in the off-ramp, LR,k, can be estimated by assigning the intersection lane groups to ramp lanes, as previously described: ð¿ , = â ð , ð¥ ð¿ (Equation B-5) Where: Ni,k = Number of lanes in section i that are associated to ramp lane k Li = Section i length (ft) Finally, the ramp queue ratio for every ramp lane k is obtained as: ð , = , , (Equation B-6) Where: QL,k = queue length associated to ramp lane k LR,k = available ramp storage for ramp lane k Next, the total storage length is calculated. Figure B-4 illustrates a common off-ramp geometry with three different sections from the stop bar to the gore point: â¢ Section 1: 4 lanes with length L1: two lanes (LG1) are associated with ramp lane 1, and two lanes (LG2) are associated with ramp lane 2 â¢ Section 2: 3 lanes with length L2: two lanes (LG1) are associated with ramp lane 1 and one lane (LG2) is associated with ramp lane 2, and â¢ Section 3: 2 lanes with length L3: one lane (LG1) is associated with ramp lane 1, and one lane (LG2) is associated with ramp lane 2 Therefore, the available ramp storage LR is calculated as: LR = (4 x L1) + (3 x L2) + (2 x L3) The ramp storage ratio for each ramp lane is as follows: LR,1 = (2 x L1) + (2 x L2) + (1 x L3) LR,2 = (2 x L1) + (1 x L2) + (1 x L3) Case C â Downstream Merge The queue storage ratio for freeway-to-freeway connections is estimated as follows: ð = â (Equation B-7) Where: ONRQ = downstream onramp queue length (veh) LR = available queue storage distance (ft/ln) Lh = average vehicle spacing in stationary queue (ft/veh) N = number of lanes in the diverge ramp
239 Example Problem 1 â Queue spillback from a downstream signalized intersection The exit ramp at I-95 SB to SW 25th Rd (Miami, FL) has a signalized intersection ramp terminal (Figure A-5). The off-ramp has two lanes and the signalized approach from the ramp (WB) has three lanes (one shared left-through, one through, and one shared through-right), as shown in Figure B-5. Figure B-5. Study site for example problem 1 (off-ramp queue spillback check - Miami, FL) The geometry of the approach, the channelization at the stop bar and the segment lengths are shown in Figure B-6. Figure B-6. Signalized approach geometry for example problem 1 (off-ramp queue spillback check - Miami, FL) Queues from each lane group are assigned as indicated in Table B-1: Table B-1. Assignment of lane group queues to ramp lanes Lane group Ramp Lane LG 1 (WB T-R) L1 LG 2 (WB T) L2 LG 3 (WB L-T)
240 The signalized intersection performance was estimated using HCM methods (Chapter 19 â Signalized Intersections), and the 95th percentile back-of-queue lengths were calculated as shown in Figure B-7. Figure B-7. Back-of-queue length estimation for intersection approach using HCM methodology (off-ramp queue spillback check â Miami, FL)
241 The 95th percentile queues to each ramp lane are: QL,1 = Q95%,LG1 = 1196.5 ft QL,2 = Q95%,LG2 + Q95%,LG3 = 1200.8 + 1532.3 = 2733.1 ft Available queue storage on each ramp lane are: LR,1 = = 400*1 + 1000*1 = 1,400 ft LR,2 = 400*2 + 1000*1 = 1,800 ft The ramp storage ratio for each of the two ramp lanes is: RQ,1 = 1,196/1,400 = 0.85 < 1 â No spillback expected RQ,2 = 2,733/1,800 = 1.51 > 1 â Spillback is expected It is concluded that spillback will occur due to the higher demand on ramp lane 2 (connected to the left and through movements). The expected queue length beyond the gore is 2733 â 1,800 = 933 ft. Given the length of the deceleration lane (LD = 450 ft), the queue will extend to the freeway mainline.
242 Example Problem 2 â Queue Spillback from a Downstream Merge (Freeway-to-Freeway) A freeway-to-freeway two-lane ramp is evaluated for queue spillback (I-75 SB to SR-826 SB â Miami, FL). The schematic of the study site is shown in Figure B-8. Figure B-8. Study site for example problem 2 (freeway-to-freeway queue spillback check, Miami-FL) This freeway-to-freeway connector is modeled as two separate freeway facilities. The upstream freeway (I-75) is modeled with a diverge section that is connected to the downstream freeway (SR-826). The detailed geometry, including turning movements and segment lengths, are shown in Figure B-9. Figure B-9. Geometry for the study site of example problem 2: (a) I-75 and (b) SR-826 A multi-period analysis considering AM peak hour traffic volume (6.00 AM-7.30 AM) is conducted for both facilities for six time periods (15 min each). The free-flow speed was measured as 63.5 mph for I-75 and 67.3 mph for SR-826. There are 12.1% trucks along the ramp, and the ramp length is 3,588 ft. The exiting demand from the diverge is equal to the entering demand at the merge for undersaturated conditions; however, the throughput at the two locations may not be the same if demand exceeds capacity at either location. The results of the analysis for the SR-826, where the queue originates, are shown in Figure B-10.
243 Figure B-10. Summary of analysis results for SR-826
244 As shown, segments 1 and 3 (boundary basic segments) in SR-826 are operating at LOS C and D respectively for the entire analysis period. On the other hand, the merge section operates at LOS F each during the third and fourth time periods. Thus, there is a queue present at the ramp starting from the third time period. The estimated on-ramp queue for each time period is provided using the Freeway Facilities method (Table B-2). The queue is assumed to be distributed evenly among the ramp lanes. The length of the queue along the ramp during each time period is estimated to be greater than the length of the ramp. As shown in Table B-2, the available queue storage length is insufficient (Queue storage ratio > 1), therefore queue spillback is expected to occur at the diverge segment of I-75. Table B-2. Estimation of queue length at the SR-826 on-ramp Time period Total Number of queued vehicles Number of queued vehicles in each lane Average vehicle length (ft) Queue length (ft) Ramp length (ft) Queue storage ratio Spillback occurs? [A] [B] = [A]/2 [C] [D] = [B]*[C] [E] [F] = [D]/[E] 1 0 0 27.4 0 3588 0.00 No 2 0 0 0 0.00 No 3 1002 501 13,727 3.83 Yes 4 1860 930 25,482 7.10 Yes 5 2065 1032.5 28,291 7.88 Yes 6 2099 1049.5 28,756 8.01 Yes