Evaluating the Performance of Corridors with Roundabouts (2014)

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Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-1 CHAPTER 3. MODELING This chapter describes the modeling framework and results for evaluating roundabout corridors in a Highway Capacity Manual (HCM) context. The chapter begins with a description of the modeling framework, including details on the sub models used in the HCM framework. The chapter then presents modeling results for each sub model, including details on the statistical model development and a discussion of implementation in the HCM. Last, comparisons to equivalent non roundabout (signalized or stop controlled) corridors are presented. 3.1. BACKGROUND The objective of this chapter is to enhance the Urban Streets methodology in the HCM 2010 to integrate the evaluation of one or more roundabouts along an urban street. The methodology as currently described in Chapter 17 of the HCM 2010 is primarily geared at evaluating the performance of an urban street with a signalized boundary intersection. The chapter does currently allow for the analysis of roundabouts in an urban street, but is limited in that regard to the capabilities of the roundabout node methodology described in HCM 2010 Chapter 21. That method is primarily used to estimate the average control delay and 95th percentile queues at roundabout approaches. However, the method does not currently allow for the estimation of segment specific aributes in roundabout corridors, including midsegment free flow speed or the extent of the roundabout influence area. This chapter presents a framework and models to fill that gap. An urban street segment in the HCM 2010 context is defined as a stretch of roadway between two intersections, including the downstream boundary intersection. In other words, the total delay of an urban street segment combines the control delay at the intersection with any midsegment delays resulting from queuing, driveway friction, or simply high vehicular volumes. The level of service (LOS) of an urban street segment is defined by the metric “Percent Free Flow Speed” (%FFS), which is calculated by dividing the average segment speed by the segment free flow speed. Several computational steps are necessary in the urban street chapter to arrive at the %FFS measure, which are replicated here for the case of roundabouts. These computational steps include the following: Step 1: Determine Traffic Demand Adjustments Step 2: Determine Running Time Step 3: Determine Proportion Arriving During Green Step 4: Determine Signal Phase Duration Step 5: Determine Through Delay Step 6: Determine Through Stop Rate Step 7: Determine Travel Speed Step 8: Determine Spatial Stop Rate Step 9: Determine LOS

Evaluating the Performance of Corridors with Roundabouts Page 3-2 Chapter 3 - Modeling Step 10: Determine Automobile Perception Score For the application to roundabout corridors, Step 1 is maintained. The Step 2 procedure for average running time is generally maintained, but certain components of that step, like the free flow speed estimation procedure, are updated for roundabout corridor operations. Steps 3 and 4 are not applicable to roundabouts. Step 5 is replaced with a roundabout specific delay estimation procedure. Step 6 remains as a gap in the literature, where no model for stop rates at roundabouts is available. Because this performance measure is not used in the determination of LOS for the urban street segment, it was not a focus in this research. Step 7 is maintained from Chapter 17 and uses earlier roundabout specific interim steps. Step 8 is again a gap in the methodology for roundabouts, as no stop rate–prediction procedure is available. Step 9 is maintained for roundabouts to estimate LOS. Step 10 represents another gap in the literature, as all studies to arrive at the automobile perception score were conducted at signalized intersections. The focus of this effort is on the calibration of Steps 2 and 5, while largely maintaining Steps 1, 7, and 9 to arrive at an urban street segment LOS for roundabout segments. Steps 3, 4, 6, 8, and 10 are either not applicable to roundabouts or do not have a roundabout specific model available. An example application of the methodology to the Old Meridian Road corridor in Carmel, Indiana, is presented at the end of the chapter to illustrate the computational steps. That particular corridor has four roundabouts and one signalized intersection. 3.2. MODELING FRAMEWORK The objective of the analytical framework is to develop sub models that can be used to estimate the performance of roundabout corridors. As a guiding principle, this framework is intended to be compatible with HCM 2010 methodologies for urban street segments (Chapter 17) and roundabouts (Chapter 21). The team developed four different sub models to characterize various aspects of corridor performance: 1. A Roundabout Influence Area (RIA) Model to estimate the spatial extents of the impact on speed of the roundabout node on the upstream and downstream urban street segments (HCM Chapter 17). This is especially important in the case of closely spaced roundabouts that may have overlapping influence areas. 2. A Geometric Delay Model for travel through the roundabout node, measuring that which is incurred by unimpeded drivers. This model is a potential addition to HCM Chapter 21, which currently does not include geometric delay in the methodology. 3. A Free Flow Speed Prediction Model for midsegment areas between two roundabout nodes under consideration of speed limit, intersection spacing, and other geometric aributes. This model is needed to

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-3 estimate free flow speed in the context of HCM Chapter 17, but is also needed as an input in the geometric delay model described above. 4. An Impeded Delay Model for the roundabout node, which is an exercise to verify the existing control delay model included in HCM Chapter 21 and to include any additional delay related to the roundabout node being part of a corridor. In addition, the team explored an Average Travel Speed Model for the segment between two roundabouts for prevailing traffic conditions, which includes interaction between vehicles in heavier traffic flow conditions. The first three models are considered site level models because they are not sensitive to time of day variability in traffic paerns (i.e., volumes). In other words, the RIA, geometric delay, and FFS models are considered to be fixed over time for a specific roundabout approach. On the other hand, the Impeded Delay Model and Average Travel Speed Model are operational level models that take traffic volumes and volume to capacity ratios into consideration. Conceptually, these laer two models may use one or more of the site level models as inputs, where, for example, the average travel speed may be a function of the free flow speed and roundabout influence area estimated in earlier models. In Chapter 17 of the HCM 2010, the average travel speed is estimated as a function of the segment running speed and the various sources of delay. The formulation of a separate travel speed model here is based on a desire to verify the applicability of the Chapter 17 method to roundabout corridors. Each model is described in more detail in the following sections. 3.2.1. ROUNDABOUT INFLUENCE AREA MODEL This model is used to estimate the length of the roundabout influence area (RIA). The concept of RIA assumes the roundabout corridor has a free flow speed (FFS) corresponding to the speed drivers would travel without the presence of the roundabout or other impedances such as other vehicles. With the geometric influence of the roundabout, all drivers then have to decelerate from that FFS to traverse the roundabout. This reduced speed is referred to as unimpeded speed because it is constrained by geometric effects only, without any interaction or impedance from other vehicles. The speed profile of this unimpeded speed relative to the free flow speed defines the length of the RIA. By definition, the beginning of the RIA is the point where the unimpeded speed trajectory begins to drop below the free flow speed. The end of the RIA is the point where the unimpeded speed recovers to the free flow speed downstream of the roundabout. Exhibit 3 1 illustrates the RIA for two adjacent roundabouts. Exhibit 3 1 assumes a midsegment distance between the two roundabouts where vehicles travel at an unimpeded midsegment speed. However, this may not always be the case, and the team identified cases of overlapping RIAs for several of the studied corridors with closely spaced roundabouts. The primary objective of the RIA model is to estimate whether the RIAs of two adjacent roundabouts overlap.

Evaluating the Performance of Corridors with Roundabouts Page 3-4 Chapter 3 - Modeling The existence of overlapping RIAs does not constitute a design flaw of the corridor. The studied roundabouts with overlapping RIAs appeared to perform normally. The overlapping RIA is merely a design aspect impacting modeling of operational performance. 3.2.2. GEOMETRIC DELAY MODEL This model predicts the geometric delay through the roundabout node. It includes the deceleration and acceleration delays of an unimpeded vehicle traveling through the roundabout. The geometric delay is defined spatially across the RIA, which encompasses the roundabout node and any upstream and downstream distance needed for deceleration from and acceleration to free-flow speed through the corridor. The geometric delay model is independent of the vehicular volume on the corridor or at the node. A geometric delay model for roundabouts exists from research performed in the UK (Kimber 1980), as well as in Australian analysis guidance (Austroads 1993). The objective of this effort, however, was to derive an empirical model based on US roundabouts and driving conditions. The total geometric delay for a corridor is calculated as the sum of individual node geometric delays and any midsegment geometric delays. For closely- spaced roundabouts, it is possible the RIAs of two roundabouts overlap. For larger spacing, a midsegment unimpeded speed is estimated to calculate travel times. If that midsegment unimpeded speed is equal to the roadway free-flow speed, no midsegment geometric delay is incurred. If the unimpeded speed is less than the free-flow speed, midsegment geometric delay is the product of segment length and the difference of the unimpeded trip time rate and the free- Exhibit 3-1: Concept of Roundabout Influence Area and Geometric Delay (TT = travel time, RBT = roundabout)

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-5 flow trip time rate: fu geom SS Ld 11 where dgeom = geometric delay (seconds); L = segment length (feet); Su = unimpeded speed (feet/second); and Sf = free flow speed (feet/second). The terms used in this discussion were shown visually in Exhibit 3 1. In the HCM, geometric delay is currently not calculated explicitly in HCM Chapter 21, although other approaches exist in literature to verify the field based measurements in this project. For Urban Streets, Equation 17 6 of the HCM 2010 predicts the segment running time for the auto mode, and the delay associated with acceleration and deceleration is included in this equation. The equation is principally used for signalized intersection delay, but also includes a term to accommodate yield controlled movements. Equation 17 6 is replicated below for reference. apN i iapv f xR ddfS L f L lt 1 other, 1 280,5 600,3 0025.0 0.6 Source: HCM 2010 Equation 17 6 with, (signalized or STOP controlled through movement) (uncontrolled through movement) (YIELD controlled through movement) where t R = segment running time (s); l1 = start up lost time = 2.0 if signalized, 2.5 if STOP or YIELD controlled (s); L = segment length (ft); fx= control type adjustment factor; vth = through demand flow rate (veh/h); c th = through movement capacity (veh/h); d ap,i = delay due to left and right turns from the street into access point Equation 3-1 Equation 3-2 ]00.1,/min[ 00.0 00.1 thth x cv f

Evaluating the Performance of Corridors with Roundabouts Page 3-6 Chapter 3 - Modeling intersection i (s/veh); Nap= number of influential access point approaches along the segment = Nap,s + p ap,lt N ap,o (points); Nap,s = number of access point approaches on the right side in the subject direction of travel (points); N ap,o = number of access point approaches on the right side in the opposing direction of travel (points); pap,lt= proportion of Nap,o that can be accessed by a left turn from the subject direction of travel; and dother= delay due to other sources along the segment (e.g., curb parking, pedestrians, etc.) (s/veh). The HCM Equation 17 6 does not include geometric delay within the roundabout. This geometric delay includes a difference in travel distance (i.e., the difference between traveling in the circulating lane versus travel along the center line distance for a signalized intersection), and a difference in travel speed (i.e., deceleration from free flow speed, travel at the geometrically constrained circulating speed, and acceleration to free flow speed). The geometric delay model was derived from field data collected in this project. The explanatory variables included in the model are free flow speed, circulating speed, and inscribed circle diameter. Other explanatory variables explored, but ultimately not incorporated into the geometric delay model, include central island diameter, lane width, median type, and other geometric components. 3.2.3. FREE-FLOW SPEED PREDICTION MODEL Both the RIA and geometric delay models incorporate the concept of midsegment free flow speed (FFS) between roundabouts. While the first two models use the field measured FFS directly, the objective of this model is to predict FFS as a function of the geometry of the segment characteristics between two roundabouts. This enables use of the first two models without field measurement of FFS. An equivalent for this approach exists in HCM Chapter 31 (for Urban Street Segments with signalized intersections), where a relationship is given between the base FFS and the prevailing FFS on the segment. The la”er is generally lower than the (theoretical) base FFS, especially for closely spaced intersections. In this project, a similar FFS prediction model was developed to estimate the prevailing FFS between two roundabouts. The explanatory variables included in the model are segment length, speed limit, central island diameter, and a dummy variable for the presence/absence of overlapping RIAs. FFS computed

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-7 with this model will be a required input for the geometric delay model and the average travel speed model. 3.2.4. IMPEDED DELAY MODEL This fourth model predicts the impeded delay at the roundabout, which is caused by interaction with other vehicles. The control delay methodology in HCM Chapter 21 provides an existing method for estimating the control delay for vehicles entering a roundabout. However, that methodology is limited to the upstream segments, and is therefore not applicable to the downstream segments in a roundabout corridor. For this project, the team estimated the impeded delay from prevailing conditions for both upstream and downstream segments, which includes the node control delay, as well as potential midsegment delays resulting from high vehicular flow rates. The key difference between this and the three prior models is that the RIA, geometric delay, and FFS are all based on unimpeded trajectories. In other words, they assume the scenario of a single vehicle traversing the corridor, and the data used to develop them were collected during low volume time periods. The impeded delay model now takes into consideration the interaction with other vehicles on the corridor. As traffic volumes increase, it is expected that the additional delay is incurred from the yield control operations at the roundabout entry and midsegment friction effects from prevailing traffic conditions. In particular, the control delay equation used in the roundabouts method (borrowed from two way stop controlled intersections) is, in its unadjusted form, based on the incremental delay term for signalized intersections (d2) shown in Equation 3 3. This equation is sensitive to the passage time seˆing at the signal controller (PT) as part of the incremental delay factor (k), and an upstream filtering adjustment factor (I) as described below. The passage time directly relates to the headways between vehicles, making it sensitive to arrival paˆerns. Source: HCM 2010 Equation 18 45 where d2 = incremental delay for signalized intersections (seconds); T = analysis period duration (seconds); XA = average volume to capacity ratio; k = incremental delay factor: Equation 3-3

Evaluating the Performance of Corridors with Roundabouts Page 3-8 Chapter 3 - Modeling PT = passage time seing on signal controller (seconds); I = upstream filtering adjustment factor: Xu = weighted v/c ratio for all upstream movements contributing to the volume in the subject movement group; and cA = available capacity (veh/h). In the application to roundabouts, the equation above has been modified in HCM Chapter 21 to add an estimate of service time (3600/c), add a base delay at the yield line (5*min[XA;1]), and set the incremental delay factor (k) and the upstream filtering adjustment factor (I) to a default value of 1.0. The equation simplifies to the following: Source: HCM 2010 Equation 21 17 where d = average control delay (s/veh); x = volume to capacity ratio of the subject lane; c = capacity of subject lane (veh/h); and T = time period (h) (T = 0.25 for a 15 min analysis). For roundabouts in a corridor, it is likely the variability of arrivals and the proportion of platooned vehicles (in green) are not random, and that further adjustments to the delay equation need to be made. A simple approach to do this when developing a model is to estimate the headway distribution of arrivals and to use that proportion to calibrate the k and I factors in the delay model based on field data (presumably a combined calibration factor, , can be defined as =k*I). Alternatively, the focus may be on the calibration of the upstream filtering adjustment factor, I, only. This factor describes the variation in arrivals during the analysis period, and HCM Chapter 18 includes an equation that can be used if the intersection upstream of the roundabout is signalized (HCM Equation 18 3). The team explored these various options for adapting Equation 3 4 above with consideration of these calibration factors, but while maintaining the roundabout specific estimates of minimum service time (3600/c) and base delay at the yield line (5*min[XA;1]). As an alternative, for estimating the total impeded delay, both the roundabout node control delay and any additional Equation 3-4

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-9 delays incurred over a segment from increases in volumes may be combined into one empirical model. Exhibit 3-2 shows the updated delay figure under consideration of control delay and other impediments to vehicles such as midsegment delay. The total impeded delay over a segment represents the sum of these two terms. The team ultimately decided to derive overall empirical impeded delay models that distinguish between upstream and downstream segments. These models will then be compared to the control delay models in HCM 2010 Chapter 21 for validation. 3.2.5. AVERAGE TRAVEL-SPEED MODEL This model predicts the average travel speed on a segment between two roundabouts. In Chapter 17 of the HCM 2010, the average travel speed is estimated as a function of the segment running speed and the various sources of delay. The formulation of a separate travel-speed model here is based on a desire to verify the applicability of the Chapter 17 method to roundabout corridors. HCM 2010 Chapter 17 predicts average travel speed as a function of various geometric and operational variables, with a full listing of the input data shown in Exhibit 3-3 (based on HCM Exhibit 17-5). In this project, the base methodology for average travel speed is maintained from the HCM 2010, but various sub-models are replaced with roundabout-specific models developed here. In addition, a stand-alone average travel speed model is provided for comparison and validation of the HCM 2010 method. Exhibit 3-2: Impact of Control Delay on Corridor Trajectories

Evaluating the Performance of Corridors with Roundabouts Page 3-10 Chapter 3 - Modeling Data Category Location Input Data Element Basis Traffic characteristics Boundary intersection Demand flow rate Movement group Segment Access point flow rate Movement group Midsegment flow rate Segment Geometric design Boundary intersection Number of lanes Movement group Upstream intersection width Intersection Turn bay length Segment approach Segment Number of through lanes Segment Number of lanes at access points Segment approach Turn bay length at access points Segment approach Segment length Segment Restrictive median length Segment Proportion of segment with curb Segment Number of access point approaches Segment Other Segment Analysis period duration Segment Speed limit Segment Performance measures Boundary intersection Through control delay Through-movement group Through stopped vehicles Through-movement group 2nd- and 3rd-term back-of-queue size Through-movement group Capacity Movement group Segment Midsegment delay Segment Midsegment stops Segment Notes: Movement group = one value for each turn movement with exclusive lanes and one value for the through movement (inclusive of any turn movements in a shared lane). Through-movement group = one value for the segment through movement at the downstream boundary intersection (inclusive of any turn movements in a shared lane). Segment = one value or condition for each direction of travel on the segment. Segment approach = one value or condition for each intersection approach on the subject segment. Source: HCM 2010 Exhibit 17-5. 3.2.6. SEGMENT AND VARIABLE DEFINITIONS Before proceeding to the individual modeling results, this section offers key definitions of analysis segments, as well as the dependent and independent variables used in model development. 3.2.6.1. Segment Definitions In the evaluation of roundabout corridors in an HCM context, some key challenges emerge related to definitions of analysis segments. In HCM Chapter 17, an urban street segment is defined spatially as extending from the stop bar of an upstream (signalized) intersection to the stop bar of the downstream intersection. For two adjacent roundabouts, the corresponding urban street segment definition would, therefore, be defined from the upstream yield line to the downstream yield line. However, in applying HCM Chapter 21, the spatial extent of the roundabout node for the purpose of estimating geometric delay would arguably include portions of the upstream and downstream segments. Exhibit 3-3: Input Requirement for Urban Street Segments in HCM

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-11 Assuming the roundabout analysis segment extends roughly from the midsegment point of the upstream link to the midsegment point of the downstream link, the result is that the HCM Chapter 17 segment is shifted approximately one half block in length from the HCM Chapter 21 segment. For analysis in this research, the team elected to use the lowest common denominator for segment definitions by applying all analysis to a segment equal to half of a link. In other words, each HCM Chapter 17 urban street segment is divided into two components at the midsegment point of the link between the two roundabouts. Exhibit 3 4 illustrates this approach to segment definition. The exhibit shows two roundabouts (RBT1 and RBT2) separated by (Urban Street) Segment B. For the purpose of analysis, Segment B is divided into sub segments B1 and B2, where B1 corresponds to the downstream influence of RBT1, and B2 corresponds to the upstream influence of RBT2. The upstream sub segment of RBT1 is consequently labeled A1 (portion of Segment A associated with RBT1), and the downstream sub segment of RBT is labeled C2 (portion of Segment C associated with RBT2). Conceptually, an urban street segment (HCM Chapter 17) is defined as the sum of the downstream and upstream sub segments of two adjacent roundabouts (e.g. B1 plus B2). Similarly, a roundabout segment (HCM Chapter 21) is defined as the sum of the upstream and downstream segment of the same roundabout (e.g., A1 plus B1). In the model development, the upstream and downstream sub segments are evaluated separately for two primary reasons: (1) this allows aggregation of model results from both HCM Chapters 17 and 21, and (2) the operational effects of the two are hypothesized to be different. To illustrate the laer point, Exhibit 3 4 shows as shaded areas the theoretical areas of geometric delay for upstream and downstream segments. Geometric delay in this case is defined as the difference between segment free flow speed and the unimpeded trajectory speed across the sub segment distance. The exhibit makes evident that geometric delay for the upstream roundabout sub segment (gray lines) is arguably much less than for the downstream sub segment (black crosshatch marks), as the laer includes significant travel at the geometrically constrained circulating speed. Consistent with these sub segment definitions, all variables are defined on a sub segment basis. This includes variables such as the free flow speed (FFS), with each roundabout having a potentially different upstream (A1) and downstream (B1) free flow speed. Coincidentally, the downstream FFS of RBT1 (B1) is the same as the upstream FFS of RBT2 (B2).

Evaluating the Performance of Corridors with Roundabouts Page 3-12 Chapter 3 - Modeling Exhibit 3-4: Segment Definitions for Modeling Framework

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-13 3.2.6.2. Variable Definitions Based on the segment definitions above, the following variables were extracted for each upstream and downstream sub segment (Exhibit 3 5): Variable Name Symbol Unit Description Roundabout Influence Area RIA ft The length of the corridor along which the geometric delay due to the roundabout is incurred Geometric Delay Delaygeo s The difference between the free flow and unimpeded trajectory travel times Total Delay - s The difference between the free flow and actual travel times (which vary by time of day) Free-Flow Speed (FFS) Sf mph The speed at which vehicles desire to travel while not encumbered by geometric elements or congestion Average Travel Speed - mph The average speed across the analysis segment measured under prevailing traffic conditions Segment Length L ft The length of the roundabout corridor segment, extending from the yield bar either upstream or downstream to the nearest midsegment point Spacing - ft The distance to the nearest upstream or downstream roundabout yield bar Access Points - N/A The number of driveways or side streets along the segment encountered in the direction of travel Curb Length Lcurb ft The total length of the segment where a curb is provided Median Length Lmedian ft The total length of the segment where a median is provided Approach Width ft The width of the travel way at the yield bar Central Island Diameter CID ft The central island diameter of the roundabout (including the truck apron) Inscribed Circle Diameter ICD ft The inscribed circle diameter of the roundabout Circulating Speed Sc mph The average speed at which unimpeded vehicles traverse the interior of the roundabout Speed Limit SL mph The posted speed Circulating Lanes - N/A The number of lanes that continue through the roundabout along the approach Midsegment Lanes - N/A The number of lanes at the midsegment point of the segment Acceleration Rate - ft/s2 The rate at which vehicles decelerate into (for an upstream segment) or accelerate out of (for a downstream segment) the roundabout Prop Curb - N/A The proportion of segment with curb Prop Median - N/A The proportion of segment with restrictive median Ratio Circulating Speed to Speed Limit - N/A The ratio of circulating speed to the posted speed limit Ratio Circulating Speed to FFS - N/A The ratio of circulating speed to free-flow speed Volume-to- Capacity Ratio v/c N/A The volume-to-capacity ratio of the roundabout In addition to the variables above, a combination variable (circulating delay) term is used to describe the geometric delay incurred while traveling within the circulatory roadway, as opposed to the deceleration and acceleration delays. This circulating delay term is estimated by the difference between FFS and circulating speed, multiplied by the travel distance along one third of the circle for a through movement. This concept is illustrated in Exhibit 3 6. Exhibit 3-5: Variable Definitions

Evaluating the Performance of Corridors with Roundabouts Page 3-14 Chapter 3 - Modeling The exhibit shows the expected portion of the delay incurred while traveling around approximately one third of the circle (distance “x” in the exhibit) at the circulating speed. That travel distance can be estimated as x = 1/3* Pi * ICD. The geometric delay in seconds is then calculated as the difference between the travel time at circulating speed (x/vcircle) minus the travel time at free flow speed (x/vff).This term is approximated by the following equation: dcircle = 1/3 * Pi * ICD / sc 1/3 * Pi * ICD / sf = 1/3 * Pi * ICD (1/sc 1/sf) where ICD = inscribed circle diameter (ft); Pi = the number Pi (approximately 3.14); sf = free flow speed (ft/s); and sc = circulating speed (ft/s). For free flow and circulating speeds given in miles per hour, the equation needs to be modified to the following: dcircle = 1/3 * 3600/5280 * Pi * ICD (1/sc 1/sf) = 0.714 * ICD * (1/sc 1/sf) 3.2.7. APPLICATION OF MODELS Exhibit 3 7 illustrates the calculation framework for applying the models within a given segment. The framework should be applied separately for each upstream and downstream sub segment, before eventually aggregating to the segment and facility levels. The framework is divided into computational steps A through L, with reference being made to the corresponding steps in HCM 2010 Chapter 17 for urban street segments at the appropriate time. Exhibit 3-6: Illustration of Circulating Delay Term Equation 3-5 Equation 3-6

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-15 First, the analyst gathers input data and calculates the FFS based on the posted speed limit, segment length, and an assumption that overlapping RIAs are not present. On a portion of a roundabout corridor between two roundabouts, such as Segment B in Exhibit 3 4, the calculation is performed for the downstream sub segment (B1 in Exhibit 3 4) and the upstream sub segment (B2 in Exhibit 3 4). Using the model predicted FFS and the circulating speed within the roundabout, the RIA length is calculated for both sub segments. Then the analyst must check whether the RIA lengths overlap. If so, this necessitates a recalculation of the FFS with the overlap (OL) term set equal to 1, which will cause the predicted FFS to decrease. With the final sub segment FFS being determined, the analyst selects the controlling FFS for that segment. Since the FFS is defined as being measured at the segment midpoint, the same FFS has to be used for the downstream segment and the next upstream segment. For that purpose, the lower of the two FFS values is selected as the controlling factor. From the FFS, the procedure uses HCM Chapter 17 Step 2 to estimate the segment running time, followed by roundabout specific models to estimate geometric delay and impeded delay. From these, the performance measures are aggregated to the HCM Chapter 17 segment level (Step K), and Chapter 17 Step 7 is used to determine the average travel speed on the sub segment. The team explored a separate, direct estimation of travel speed from the data collected in this project (between steps I and J), but for consistency use of the existing urban street segment method is preferred. From the average travel speed, the LOS is estimated for the urban street segment with roundabouts.

Evaluating the Performance of Corridors with Roundabouts Page 3-16 Chapter 3 - Modeling Note: After Step L, segments can be aggregated to facility level per HCM 2010 Chapter 16. Exhibit 3-7: Computation Process Step A: Gather Input Data: Sub segment length, posted speed limit, ICD, CID, circulating speed, entering flow, roundabout capacity, restrictive median length, curb length. Step B: Determine FFS for both sub segments using FFS model (assuming OL=0) Step C: Determine RIA length of both sub segments using RIA length model Step D: Do RIAs overlap? Step E: Recalculate FFS of both sub segments using FFS model (assuming OL=1) Step H: Determine geometric delay of each sub segment, adjust for negative estimates Yes No Step J: Aggregate sub segment performance measures to Chapter 17 segment level Step I: Determine impeded delay of each sub segment, adjust for negative estimates Step F: Select Controlling FFS from two sub segments (minimum) Step K: Determine segment average travel speed Consistent with HCM Ch. 17 – Step 7 Step G: Determine Segment Running Time Consistent with HCM Ch. 17 – Step 2 Step L: Determine LOS Consistent with HCM Ch. 17 – Step 9

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-17 Geometric delay, impeded delay, and (optional) average travel speed are calculated separately for upstream and downstream sub segments because the calculations use variables associated with either the upstream or downstream roundabout. Although it is not common for the FFS to vary from one sub segment to the next (i.e., within a length of roadway between two roundabouts), geometric differences of the upstream and downstream roundabouts may result in two different predicted FFS. In these cases, the lower of the two estimates is selected as the controlling FFS. The delays from the two sub segments are added to produce segment geometric delay and segment impeded delay. Calculations of travel time and travel speed as a percent of base FFS are done in the manner described in Chapter 17 of the HCM 2010 and are therefore not discussed in detail here. A sample application of the methodology to the Old Meridian corridor in Carmel, Indiana, is provided later in this chapter to illustrate the methodology. The following are the variables necessary to use the models: Sub segment length, defined in Exhibit 3 5, in feet; Posted speed limit, in miles per hour (mph); Inscribed circle diameter (ICD), in feet; Central island diameter (CID), including the truck apron if present, in feet; Circulating speed, in miles per hour (mph); Entering flow, in vehicles per hour (vph); Roundabout capacity, calculated using HCM Chapter 21, in vehicles per hour (vph); Length of sub segment where a restrictive median is present, in feet; and Length of sub segment where a curb is present, in feet. 3.3. MODELING RESULTS The team assembled a dataset by calculating geometric and operational parameters for each roundabout approach from the following seven roundabout corridors, leaving the two Carmel corridors out for validation purposes: MD 216, Scaggsville, Maryland (4 roundabouts) La Jolla Boulevard, San Diego, California (5 roundabouts) Borgen Boulevard, Gig Harbor, Washington (5 roundabouts) SR 539, Whatcom County, Washington (4 roundabouts) SR 67, Malta, New York (7 roundabouts) Avon Road, Avon, Colorado (5 roundabouts) Golden Road, Golden, Colorado (5 roundabouts) Each approach was partitioned into an upstream segment (extending from the upstream midsegment point to the yield bar) and a downstream segment

Evaluating the Performance of Corridors with Roundabouts Page 3-18 Chapter 3 - Modeling (extending from the yield bar to the downstream midsegment point). The total dataset included 62 roundabout approaches, with each providing an upstream and a downstream segment. Some approaches were excluded due to (a) overlapping influence areas, or (b) a too short upstream or downstream segment length at the end of the roundabout corridor. In the case of overlapping influence areas, these approaches were only excluded from the roundabout influence area models; these approaches were used in other models like the free flow speed prediction model. For the too short segments, the GPS travel time vehicles were not able to accelerate to their desired speeds (even in free flow conditions) because of a near by intersection or turnaround point. Detailed speed profiles of all seven corridors and for each direction are shown in Appendix N. The numbering and leƒering conventions for all corridors are shown in Appendix M. A list of excluded approaches is as follows: (a) Segments with Overlapping Influence Areas: Avon, CO: Segments D1 and D2 (Northbound and Southbound); Borgen, WA: Segments B1 and B2 (Eastbound and Westbound); MD 216, MD: Segments B1 and B2 (Eastbound and Westbound); SR 67, NY: Segments C2 and C3 (Eastbound and Westbound); and SR 67, NY: Segments D2 and D3 (Eastbound and Westbound). (b) Segments Excluded Because of Short Segment Length: Avon, CO: Segment A1 (Northbound and Southbound); Avon, CO: Segment F5 (Northbound and Southbound); Avon, CO: Segment C2 (Northbound, Interchange Unimpeded); Avon, CO: Segment B1 (Northbound, Interchange Unimpeded); Avon, CO: Segment B2 (Southbound, Interchange Unimpeded); Borgen, WA: Segment F5 (Eastbound and Westbound); Borgen, WA: Segment A1 (Eastbound and Westbound); Golden, CO: Segment A1 (Northbound and Southbound); Golden, CO: Segment F5 (Northbound and Southbound); SR 67, NY: Segment H7 (Eastbound and Westbound); and SR 539, WA: Segment A1 (Northbound and Southbound). 3.3.1. DESCRIPTIVE STATISTICS After excluding selected approaches, the remaining dataset included 49 upstream and 52 downstream roundabout “approaches.” Exhibit 3 8 and Exhibit 3 9 show the descriptive statistics of the variables collected for the upstream and downstream approaches, respectively. The exhibits show the site level descriptive statistics used for the first three models. The purpose of these exhibits is to show the range of variable values found in the dataset used to develop models. As with any models, the ones developed for this project may not be applicable for conditions beyond the range of the dataset. The descriptive statistics for the two operational level models are shown in Appendix L.

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-19 Variable Name Unit Mean St. Dev. Min Max Roundabout Influence Area ft 311.0 184.8 72.9 897.6 Geometric Delay sec 2.1 1.5 0.1 6.6 Free-Flow Speed (FFS) mph 38.1 8.5 26 53 Segment Length ft 971.8 936.9 244 3993 Spacing ft 1930.8 1907.6 238 8004 Access Points N/A 1.9 3.0 0 17 Curb Length ft 453.1 382.8 0 1627 Median Length ft 715.1 997.4 37 3993 Approach Width ft 22.0 6.0 11 38 Central Island Diameter ft 93.4 33.8 48 187 Inscribed Circle Diameter ft 142.1 39.7 84 245 Circulating Speed mph 18.0 2.6 12.4 23.6 Speed Limit mph 34.7 9.8 25 50 Circulating Lanes N/A 1.7 0.5 1 2 Midsegment Lanes N/A 1.6 0.5 1 2 Acceleration Rate ft/s2 -0.75 0.30 -1.40 -0.30 Prop Curb N/A 0.69 0.43 0.00 1.00 Prop Median N/A 0.72 0.38 0.04 1.00 Ratio Circulating Speed to Speed Limit N/A 0.5 0.1 0.37 0.94 Ratio Circulating Speed to FFS N/A 0.5 0.1 0.32 0.78 Exhibit 3-8: Descriptive Statistics for Upstream Segments – Site-Level Data

Evaluating the Performance of Corridors with Roundabouts Page 3-20 Chapter 3 - Modeling Variable Name Unit Mean St. Dev. Min Max Roundabout Influence Area ft 617.1 296.1 235.0 1446.2 Geometric Delay sec 3.0 1.9 0.1 9.5 Free-Flow Speed (FFS) mph 37.3 8.4 26 53 Segment Length ft 1049.3 910.6 270 3953 Spacing ft 1887.7 1861.0 416 8004 Access Points N/A 1.7 2.7 0 16 Curb Length ft 574.5 428.1 0 2031 Median Length ft 831.7 951.5 153 3953 Approach Width ft 22.2 5.7 11 36 Central Island Diameter ft 92.9 32.9 48 187 Inscribed Circle Diameter ft 141.7 38.6 84 245 Circulating Speed mph 18.0 2.6 11.0 23.6 Speed Limit mph 34.1 9.7 25 50 Circulating Lanes N/A 1.7 0.5 1 2 Midsegment Lanes N/A 1.6 0.5 1 3 Acceleration Rate ft/s2 0.51 0.18 0.20 1.20 Prop Curb N/A 0.74 0.39 0.00 1.00 Prop Median N/A 0.79 0.31 0.11 1.00 Ratio Circulating Speed to Speed Limit N/A 0.6 0.1 0.31 0.94 Ratio Circulating Speed to FFS N/A 0.5 0.1 0.26 0.81 3.3.2. ROUNDABOUT INFLUENCE AREA This section summarizes the methods used to develop a model for estimating the roundabout influence area (RIA), which the team defines as the length of the approach segment where geometric delay is incurred by travelers due to the presence of the roundabout. The premise of this exercise is that the factors that contribute to a larger RIA are also associated with an increase in geometric delay. A model for estimating the RIA is further useful to investigate planning decisions on spacing of adjacent intersections in a roundabout corridor, where closely spaced roundabouts may result in overlapping influence areas that prevent a driver from returning to FFS between adjacent roundabouts. The objective of the RIA model development is to predict the RIA with design and operational variables available to the analyst at the time of roundabout planning, including geometric and (design) speed parameters of the roundabout that could be obtained or reasonably approximated from concept plans. The model is restricted to the analysis of unimpeded vehicles, which traverse the roundabout without any interaction with other traffic. In other words, the data used for the RIA model development were limited to vehicles that experienced geometric delay only, with no interaction or impedance from other vehicles. The team hypothesized that the following factors would affect the RIA: Exhibit 3-9: Descriptive Statistics for Downstream Segments – Unimpeded

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-21 The inscribed circle diameter (ICD) and/or central island diameter (CID) were hypothesized to be associated with RIA. A larger circle would lead to increased circulating speeds, and consequently lower geometric delay, which is associated with a shorter RIA; The posted speed limit and/or the FFS along the approach were hypothesized to contribute to a larger RIA, as vehicles would need a longer distance to decelerate, or to recover to a high speed than a low speed; The ratio between the FFS and the circulating speed is expected to have an impact on the RIA, with a larger ratio (posted and circulating speeds similar) resulting in a lower RIA, as the amount of necessary deceleration and acceleration is reduced. The circulating speed can be field measured or estimated based on the radius of the R2 fastest path curve; and The RIA was hypothesized to decrease as the number of circulating lanes in the roundabout, the number of midsegment lanes, or the approach width increases—essentially, the team hypothesized that a wider roundabout or roundabout approach would lead to higher speeds within the roundabout due to the increased radii of fastest paths, thereby decreasing the RIA. 3.3.2.1. Modeling Approach The team examined the speed profiles for each roundabout corridor to get a sense of the FFS on each approach, as well as the length of the RIA. The speed profile in Exhibit 3 10 displays an example of the team’s method illustrated for one roundabout on the SR 539 corridor. The analysis steps were as follows: 1. The team used the TravTimeTM software to isolate the unimpeded runs by removing the trajectories appearing to be impeded by either heavy volume or conflicting traffic at the roundabouts. The remaining data consisted of unimpeded travel time runs from all times of day. 2. The team estimated an FFS based on the prevailing speed between roundabouts. In the case shown below, the FFS appeared to be constant (at approximately 53 mph) along the corridor, although many of the other corridors had changes in FFS between roundabouts due to changes in geometry, the posted speed, or other conditions. 3. The beginning and end points to each RIA were determined by estimating the points where the speeds started to deviate from FFS (upstream), or when the speed trajectories recovered to FFS. From these measurements, the team calculated various potential explanatory variables, as well as the dependent RIA variable as described below.

Evaluating the Performance of Corridors with Roundabouts Page 3-22 Chapter 3 - Modeling Exhibit 3-10: Roundabout Influence Area Example (Profiles for SR539 Site Northbound)

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-23 3.3.2.2. Variable Correlations The team investigated the relationships between RIA length and the remaining variables in Exhibit 3 5 by calculating the correlation coefficient (R2) between each pair of variables. This effort was done separately for the upstream RIA and for the downstream RIA. The correlation data for the two datasets are contained in Appendix L. A correlation coefficient close to zero corresponds to lile or no correlation between variables, while a coefficient close to +1.0 or 1.0 refers to a strong positive or negative correlation, respectively. The team made the following observations about the correlation between RIA length and the other variables: For the upstream and downstream datasets, RIA length was moderately positively correlated (r = +0.42 to +0.77) with segment length, spacing, and FFS. For the upstream and downstream datasets, RIA length was moderately negatively correlated with the ratios of circulating speed to speed limit and FFS (r = 0.63 to 0.41). The RIA length was not correlated with approach width, circulating speed, number of circulating lanes, number of midsegment lanes, or proportion of segment with median. Additionally, many of the potential explanatory variables were highly correlated with each other, including the following pairs of variables: Median length and number of access points; Median length, speed limit, and FFS; Approach width, number of circulating lanes, CID, and ICD; and Number of midsegment lanes and number of circulating lanes. Many of these trends are intuitive, but the team notes these relationships to avoid multicolinearity in the models. In general, if two independent variables are correlated, only one should be used in model development. The detail correlation coefficients are shown in Appendix L, with values greater than +0.5 and less than 0.5 emphasized in bold. 3.3.2.3. Model Results Building on the correlational analysis, the team developed several regression models using the Statistical Analysis Software (SAS) general linear model (GLM) procedure. The team strived to avoid using highly correlated variables in the same model. Models were developed separately for the upstream and downstream segment datasets. Appendix L shows a series of variable plots, followed by a full list of regression models considered for the RIA models. Based on the regression results, the team made the following observations: The models for downstream segment influence area length showed beer statistical fit than the upstream length, which is indicated by the higher levels of R2 for the downstream models (43 to 71 percent as

Evaluating the Performance of Corridors with Roundabouts Page 3-24 Chapter 3 - Modeling opposed to 16 to 38 percent). The R2 can be interpreted as the portion of variability in the dependent variable that is explained by the model. A low R2 for the upstream model, therefore, corresponds to more unexplained variability. Another way to look at this would be that driver acceleration behavior can be more consistently described than deceleration behavior at the different roundabouts. Several of the models indicated RIA length increases with the posted speed limit, FFS, median length, curb length, ICD, and CID. Several of the models indicated RIA length decreases as the approach width, number of midsegment lanes, circulating speed, and the ratio of circulating speed to FFS increase. Of these variables, those that had the greatest effect on RIA length were speed limit, FFS, circulating speed, and the ratio of circulating speed to FFS. This was indicated by the high Type III sum of squares and low p value for these variables, as well as the relatively high R2 of the models containing these variables. The models for upstream and downstream RIA are very different in parameter estimates. As a result, the two components should be estimated separately. From the results in Appendix L, it appears that models D8 and U8 have the highest model R2 for the downstream and upstream RIA, respectively. The RIA models are shown in Exhibit 3 11. Model Intercept Free-Flow Speed (mph) Circulating Speed (mph) R2 U8 165.9 13.8*** -21.1** 0.289 D8 -149.8 31.4*** -22.5** 0.714 * = p < 0.1 ** = p < 0.05 *** = p < 0.01 In equation form, Model U8 would be wri‡en as: RIAupstream = 165.9 + 13.8* Sf – 21.1*Sc where RIAupstream = upstream roundabout influence area (feet); Sc = circulating speed (feet/second); and Sf = free flow speed (feet/second). Some additional sensitivity analysis was performed on these two models to explore the behavior of the models. Exhibit 3 12 shows sensitivity of both Exhibit 3-11: RIA Models Equation 3-7

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-25 models by FFS and circulating speed. The field-observed data for the upstream and downstream RIA are superimposed on the final models. The exhibit intuitively shows RIA increases with greater segment FFS (x-axis), and decreases with faster circulating speed. The downstream RIA is generally greater than the upstream RIA. This may be a direct artifact of the segment definitions, which divide a segment at the yield line. Consequently, the downstream segment contains travel within the roundabout, which occurs at slow speeds. From these results, the total roundabout influence area can be estimated from the summation of upstream and downstream lengths, as follows: RIATotal = RIAupstream + RIAdownstream = Model U8 + Model D8 RIATotal = (165.9-149.8) + (13.8+31.4)*Sf – (21.1+22.5)*Sc RIATotal = 16.1 + 45.2 * Sf – 43.5 * Sc The total RIA estimation in Equation 3-8 is plo”ed in Exhibit 3-13. Exhibit 3-12: Sensitivity Analysis of RIA Models Equation 3-8

Evaluating the Performance of Corridors with Roundabouts Page 3-26 Chapter 3 - Modeling The model in Exhibit 3-13 shows the same trends as the individual segment models, with increasing RIA with higher FFS and lower circulating speed. The graph illustrates roundabouts on roads with a high FFS that are designed with a low circulating speed can have total RIAs greater than 1,600 feet or about 1/3 of a mile. 3.3.3. GEOMETRIC DELAY The team also modeled the geometric delay incurred to drivers at roundabouts as a function of several geometric elements. The purpose of this modeling effort is to predict the additional travel time caused by the curvature of the roundabout. A challenge in developing this model was to account for overlapping roundabout influence areas. In the case of closely-spaced roundabouts, for example, the geometric delay for each roundabout may not be easily discernible. 3.3.3.1. Modeling Approach For each upstream and downstream segment in the dataset, the team estimated the unimpeded and free-flow travel times based on the corridor space-time trajectories and speed profiles, respectively. This was accomplished using methods similar to those in the first two steps described in Section 3.3.2.1. Then the geometric delay was calculated by taking the difference between the unimpeded and free-flow travel times, as shown in Exhibit 3-6. The team used a similar approach to develop the geometric delay model as was used to develop the roundabout influence area model, with the advantage that now the influence area could be used as an explanatory variable. The SAS GLM procedure was used to develop separate models for the upstream and downstream segments, and several models were developed for each of these two datasets. Exhibit 3-13: Total RIA Based on Sum of Upstream and Downstream Lengths

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-27 3.3.3.2. Variable Correlations The team investigated the relationships between geometric delay and the remaining variables in Exhibit 3 5 by calculating the correlation coefficient between each pair of variables. This effort was done separately for the upstream geometric delay and for the downstream geometric delay. The correlation data for the two datasets are contained in Appendix L. The team made the following observations about the correlation between geometric delay and the other variables: The geometric delay was highly positively correlated (r = +0.76) with RIA length, which is expected due to the way the RIA is defined. However, it may be impractical to develop a geometric delay model based solely upon RIA length, as it is more cumbersome to determine than ordinary geometric elements of the roundabout. The geometric delay was moderately positively correlated (r = +0.41 to +0.46) with free flow speed and the central island diameter, which was intuitive based on how these elements should affect travel time at roundabouts. The geometric delay for downstream segments was highly positively correlated (r = +0.83) with the circulating delay term, which describes the difference in travel time around 1/3 of the inscribed circle diameter if traveling at the circulating speed versus the free flow speed. Like the RIA modeling effort, the team found several pairs of variables that were correlated with each other, including the FFS and central island diameter (r = +0.63) and the FFS and posted speed limit (r = +0.90). Two independent variables with high correlation should not be used within the same model. 3.3.3.3. Model Results Building on the correlational analysis, the team developed several regression models using the SAS GLM procedure. The team strived to avoid using highly correlated variables in the same model. Models were developed separately for the upstream and downstream segment datasets. Appendix L shows a series of variable plots, followed by a full list of regression models considered for the geometric delay models. Based on the regression results, the team made the following observations: The simplest models for the upstream and downstream datasets were based solely on the roundabout influence area, which yielded an R2 of approximately 60 percent. The models for downstream geometric delay showed consistently beer statistical fit than the upstream length, which is indicated by the higher levels of R2 for the downstream models (50 to 80 percent as opposed to 30 to 60 percent). Like the influence area models, another way to look at this would be that driver acceleration behavior can be more consistently described than deceleration behavior at the different roundabouts.

Evaluating the Performance of Corridors with Roundabouts Page 3-28 Chapter 3 - Modeling Several of the models indicated geometric delay increases with FFS and number of access points but decreases with the circulating speed. An interaction term between the FFS, circulating speed, and inscribed circle diameter (ICD) was also used to model geometric delay, with good results for the downstream geometric delay model. This circulating delay term, as shown in Exhibit 3-14, is based on the difference between FFS and circulating speed. Intuitively, this term applies to the downstream geometric delay, as it includes the geometric delay within the circle. From the results in Appendix L, it appears models U10 and D15 have the highest model R2 for the upstream and downstream geometric delay, respectively. The models for geometric delay are shown in Exhibit 3-14. Model Intercept Free-Flow Speed (FFS) Circulating Speed (mph) Circulating Delay**** R2 U10 1.57 0.11*** -0.21** n/a 0.315 D15 -2.632*** 0.0859*** n/a 0.7261*** 0.794 * = p < 0.1 ** = p < 0.05 *** = p < 0.01 **** Circulating delay is defined in Exhibit 3-6 Some additional sensitivity analysis was performed on these two models to explore the behavior of the models similar to the previous section. Exhibit 3-15 shows sensitivity of both models by FFS and circulating speed. The exhibit shows geometric delay increases with greater segment FFS (x-axis), and decreases with faster circulating speed. The downstream geometric delay is generally greater than the upstream portion, which is because the downstream Exhibit 3-14: Geometric Delay Models Exhibit 3-15: Upstream and Downstream Geometric Delay Model Sensitivity

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-29 segment contains a greater portion of travel around the circle (at a reduced speed). The downstream geometric delay graphs are shown for a fixed inscribed circle diameter (ICD) of 150 feet. A greater ICD would result in a further increase in downstream geometric delay because of additional travel distance around the circle. In a practical application, this increase in geometric delay would be offset by a faster circulating speed (resulting from the larger circle diameter), which reduces the effect of the circulating delay term in model D15. From these upstream and downstream results, the total geometric delay for a roundabout node can be estimated from the summation of upstream and downstream geometric delays, as follows: Delaygeom, total = Delaygeom, upstream + Delaygeom, downstream = Model U10 + Model D15 Delaygeom, total = (1.57-2.63) + (0.11+0.09)*Sf– (0.21)*Sc + 0.84 *0.714 * ICD * (1/Sc-1/Sf) Delaygeom, total = -1.06 + 0.20*Sf – 0.21*Sc + 0.625 * ICD *(1/Sc -1/Sf) The resulting total geometric delay for a roundabout node is shown in Exhibit 3- 16, again assuming an ICD of 150 feet. The general trend of this combined model is consistent with the earlier exhibit, as well as the shape of the roundabout influence area model. In future editions of the HCM, this model is most applicable in Chapter 21, with the individual upstream and downstream models most applicable in Chapter 17. 3.3.4. FREE-FLOW SPEED PREDICTION The next modeling effort concerned the FFS of each roundabout segment. The team proceeded to model FFS as a function of the geometric elements of the Equation 3-9 Exhibit 3-16: Combined Geometric Delay Model Sensitivity

Evaluating the Performance of Corridors with Roundabouts Page 3-30 Chapter 3 - Modeling corridor (e.g., segment length, spacing, and midsegment number of lanes), as well as the geometry of the roundabout itself (e.g., ICD). The team also hypothesized that the FFS would be highly correlated with the posted speed limit. The model allows the practitioner to estimate the FFS on an upstream or downstream roundabout segment in the absence of field data. From the modeling efforts described in previous sections, it is also useful to estimate the FFS since it emerged as a key model input to the geometric delay and roundabout influence area models. 3.3.4.1. Modeling Approach For each upstream and downstream segment in the dataset, the team estimated the FFS based upon the free flow trajectories. This was accomplished using a method similar to the second step described in Section 3.3.2.1. The segment by segment FFS measurements are documented in Appendix L. The FFS measurements were obtained from unimpeded trajectories through the roundabout corridors performed by members of the research team. While these unimpeded routes were intended to be free of the impact of other traffic, there was still some variability in the observed speed profiles shown in the appendix. The team initially used the average unimpeded midsegment speed as an estimate of FFS, but that definition proved challenging for multiple reasons: 1. From the trajectory data, it was unclear if all routes were truly unimpeded without interaction from other traffic; 2. The average midsegment speed in some cases was significantly lower than some of the individual unimpeded trajectories, which resulted in negative calculated travel times; and 3. The drivers collecting data were instructed to follow a “floating car” approach, which resulted in a significant portion of other drivers actually traveling faster than the data collection vehicle. In response to these challenges, the team defined the midsegment FFS as the maximum unimpeded trajectory speed recorded by the travel time vehicle. This guaranteed a positive and more realistic estimate of the geometric delay introduced by the roundabout. In an application of this method, this midsegment FFS can be interpreted as a realistic unimpeded speed of a driver familiar with the roundabout corridor but not overly aggressive in their travel behavior. Just as before, the analysis was performed separately for the upstream and downstream segments of each roundabout. While this is consistent with the approach taken for RIA and geometric delay, the interpretation of the resulting model is quite different. While in the previous two models, a combined model could be estimated by simply adding the component sub segment models, an additive approach is not realistic in this case. In fact, the downstream FFS for a roundabout is measured at the same point as the upstream FFS of the next roundabout along the corridor. Consequently, the team recommends interpreting the FFS prediction as estimated FFS resulting from the impact of a roundabout on the respective upstream or downstream segment. For a midsegment FFS between two

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-31 roundabouts, the prevailing FFS is defined as the minimum of the two sub segment FFS estimated for that segment. In other words, the analyst would calculate the downstream FFS for Roundabout 1 and the upstream FFS for Roundabout 2, and apply the smaller of the two numbers as the midsegment FFS for Segment B (see Exhibit 3 4 for numbering and leering conventions). The FFS model is considered to be a constraint model, in which the characteristics of the segment and adjacent roundabout impact driver FFS at the midsegment point. Since in a corridor the downstream FFS from Roundabout 1 is defined at the same location as the upstream FFS of Roundabout 2, the lower of the two would act as the constraint for that segment. Therefore, the team recommends using the minimum of the two estimated FFS as the prevailing condition for the segment in question. The SAS GLM procedure was used to develop separate models for the upstream and downstream segments, and several models were developed for each of these two datasets. 3.3.4.2. Variable Correlations The team investigated the relationship between FFS and the remaining variables in Exhibit 3 5 by calculating the correlation coefficient between each pair of variables. This effort was done separately for the upstream FFS and for the downstream FFS. The correlation data for the two datasets are contained in Appendix L. The team made the following observations about the correlation between FFS and the other variables: The FFS was highly positively correlated (r = +0.73 to +0.90) with the posted speed limit, segment length, spacing, and median length. The FFS was moderately positively correlated (r = +0.50 to +0.64) with the approach width, CID, ICD, and circulating speed. The FFS was moderately negatively correlated (r = 0.73 to 0.55) with the acceleration rate, the proportion of segment with curb, and the ratio of circulating speed to the posted speed limit. Like the geometric delay modeling effort, the team found several pairs of variables that were correlated with each other: the segment length and spacing (r = +0.97), the CID and ICD (r = +0.94), and the segment length and median length (r = +0.91). 3.3.4.3. Model Results Building on the correlational analysis, the team developed several regression models using the SAS GLM procedure. The team strived to avoid using highly correlated variables in the same model. Models were developed separately for the upstream and downstream segment datasets. Appendix L shows a series of variable plots, followed by a full list of regression models considered for the FFS models. Based on the regression results, the team made the following observations:

Evaluating the Performance of Corridors with Roundabouts Page 3-32 Chapter 3 - Modeling The simplest models for the upstream and downstream datasets were based on a combination of the segment length and posted speed limit. These models explained 80 to 90 percent of the variability in the data, which is a much beer statistical fit for either the RIA or geometric delay models. The models could be slightly improved by accounting for segments with overlapping roundabout influence areas. These segments were identified by the research team using the corridor speed profiles. If it appeared that drivers did not have enough distance to recover to FFS between two adjacent roundabouts, then these roundabouts were defined to have overlapping influence areas. The addition of a separate intercept term for these segments improved the model R2 by approximately 3 percent. Although the downstream segment models explained slightly more of the data variability, there did not appear to be as much discrepancy between the strength of the upstream and downstream models as there was in previous modeling efforts. Exhibit 3 17 summarizes the models for upstream and downstream FFS as a function of the segment length, posted speed limit, central island diameter, and a separate intercept term (or dummy variable) for the segments with overlapping influence areas (OL). Model Intercept Segment Length (ft) Speed Limit (mph) Central Island Diameter (ft) OL (dummy) R2 U10 15.1*** 0.0037*** 0.43*** 0.05*** -4.73*** 0.901 D10 14.6*** 0.0039*** 0.48*** 0.02** -4.43*** 0.926 * = p < 0.1 ** = p < 0.05 *** = p < 0.01 The sensitivity of these models is shown in Exhibit 3 18. The exhibit assumes a central island diameter of 100 feet, with a larger diameter resulting in a net increase in upstream and downstream FFS. The exhibit further assumes the upper limit of the overlapping influence area occurs within a segment length of 500 feet to 1,000 feet. This assumption is generally in line with the RIA models estimated above and was used here to illustrate an upward shift in free flow speed of about 4.4 to 4.7 mph once the RIAs no longer overlap. In a practical application of these models, the analyst should apply the RIA estimation equation above to assess whether the overlap condition is met or not. Exhibit 3-17: FFS Prediction Models

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-33 Note: Assumed Central Island Diameter of 100 ft 3.3.5. AVERAGE TRAVEL SPEED This section describes the development of a model to predict the average speed for the upstream or downstream sub-segment between roundabouts along a roundabout corridor. Unlike the previous models described in this report, this model is meant to include operational data that vary by time of day, such as entering traffic volumes and circulating flows, in addition to the geometric and operational data contained in the unimpeded models above. The purpose of this modeling effort is to allow a practitioner to estimate the operational performance along a midsegment portion of a roundabout corridor based on traffic data and geometric characteristics of the roadway. In the context of implementation in the HCM 2010 Chapter 17 Urban Street Segment procedure, this step is not needed, as the average travel speed is calculated from prior modeling steps, including the free-flow speeds and various delay terms. The average travel speed model presented here is optional and can be used to verify the predictions from the Chapter 17 methodology. 3.3.5.1. Modeling Approach For each upstream and downstream segment in the dataset, the team calculated the average speed along the segment during three time-of-day periods. For the average travel speed models, the team used all approaches and segments for which roundabout volumes were available from the data collection. Unlike the data used in the roundabout influence area, geometric delay, and FFS model development, these data included trajectories that may have been impeded by circulating traffic, as well as the unimpeded trajectories. Thus, these trajectories were much more variable than the unimpeded trajectories in the previous analyses, even when the data were broken down by time of day. The FFS measurements were obtained from unimpeded trajectories through the roundabout corridors performed by members of the research team. The team excluded a few segments that had resulted in negative total delay estimates as outliers. A negative total delay estimate may have occurred for Exhibit 3-18: FFS Model Sensitivity

Evaluating the Performance of Corridors with Roundabouts Page 3-34 Chapter 3 - Modeling segments that were very short and where the free flow speed estimate from the unimpeded routes was similar or somewhat less than the observed speed for other trajectories. Clearly, these negative delays were an aribute of driver behavior during field data collection—not an adequate reflection of roundabout performance—and would have introduced inconsistencies and bias in the model estimation. The same segments were removed from the average travel speed and impeded delay models for consistency across the two models. Like the other prediction models, this model is intended to be applied separately for upstream and downstream segment data. In the case of two adjacent roundabouts, the combined average travel speed may be estimated as the length weighted average of estimates for the downstream segment of Roundabout 1 and the upstream segment of Roundabout 2. The SAS GLM procedure was used to develop separate models for the upstream and downstream segments, and several models were developed for each of these two datasets. 3.3.5.2. Variable Correlations The team investigated the relationship between average speed and the remaining variables in Exhibit 3 5 by calculating the correlation coefficient between each pair of variables. This effort was done separately for the upstream speed and for the downstream speed. The correlation data for the two datasets are contained in Appendix L. The team made the following observations about the correlation between FFS and the other variables: The average speed was moderately negatively correlated with entering traffic flow, which is intuitive, as the speed should decrease as traffic congestion increases. The average speed was moderately negatively correlated with circulating traffic flow for the upstream segments, but uncorrelated with circulating traffic flow for the downstream segments. This is also intuitive, as congestion within a roundabout should be detrimental to speed along the upstream segment but should not affect the downstream speed. The average speed was also correlated with several of the same variables as the FFS, such as the posted speed limit and segment length, but these variables did not vary by time of day and are thus not included in the correlation summary. 3.3.5.3. Model Results Building on the correlational analysis, the team developed several regression models using the SAS GLM procedure. The team strived to avoid using highly correlated variables in the same model. Models were developed separately for the upstream and downstream segment datasets. Appendix L shows a series of variable plots, followed by a full list of regression models considered for the average speed models. Based on the regression results, the team made the following observations:

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-35 Several models for the upstream segment data were developed as a function of the circulating flow, entering flow, posted speed limit, and segment length, which were all significant (p < 0.021). The downstream segment models were similar, although the circulating flow was not significant (see discussion above). The models were successful in explaining 70 (upstream) to 79 (downstream) percent of the variability in the data. Exhibit 3 19 summarizes the models for upstream and downstream average travel running speed as a function of the FFS and the volume to capacity ratio of the approach. The full list of average travel speed models is shown in Appendix L. Model Intercept Free-Flow Speed (mph) Volume-to- Capacity Ratio R 2 U12 8.52** 0.73*** -18.20*** 0.76 D12 6.45*** 0.74*** -5.40*** 0.83 * = p < 0.1 ** = p < 0.05 *** = p < 0.01 In the application of the models in Exhibit 3 19, the FFS would be calculated from one of the earlier models, as a function of segment length, speed limit, roundabout central island diameter, and a binary variable checking for overlapping roundabout influence areas. That last term is a function of the RIA estimation models, which are in turn a function of FFS and circulating speed. The volume to capacity ratio is calculated using entering volume, and the theoretical roundabout capacity is calculated from the equations in the HCM. The sensitivity of these models is shown in Exhibit 3 20. The exhibit shows an increasing average travel speed with increasing FFS, and a reduction resulting from a higher volume to capacity ratio. Exhibit 3-19: Average Travel Speed Final Models

Evaluating the Performance of Corridors with Roundabouts Page 3-36 Chapter 3 - Modeling 3.3.6. IMPEDED DELAY The team’s final modeling effort included predicting the impeded delay at each roundabout due to the interaction among vehicles. This differs slightly from the control delay methodology in HCM Chapter 21 because the field data used to calibrate the models presented here was collected from roundabout corridors rather than isolated roundabouts and is based on empirical regression rather than analytical derivation. It further includes some corridor impedances resulting from curbs, medians, and the prevailing traffic volume. However, in a validation and verification exercise, the team compared the resulting impeded delay models to the current control delay models in the HCM 2010. 3.3.6.1. Modeling Approach The team began the model calibration effort by calculating the geometric and impeded delay for each upstream and downstream roundabout segment over each time of day. The geometric delay was computed using the same methodology described in Section 3.3.2.1., and the impeded delay was calculated by taking the difference between the average travel time and the free- flow travel time for each segment. Segments with incomplete data (e.g., a short segment on the end of a corridor of roundabouts between the last roundabout and where the driver collecting the data turned around) were excluded from the dataset. The time-of-day dependent variables such as entering and circulating flow were defined using the same methods described in Section 3.3.5.1. Additionally, the team calculated the capacity and volume-to-capacity ratio of the roundabout nearest to each segment (i.e. downstream of an upstream segment and upstream of downstream segment) using the roundabout capacity equations contained in the HCM Chapter 21. As with the other models, the team used the SAS GLM procedure to develop several models for the upstream and downstream segment datasets. Exhibit 3-20: Average Travel Speed Sensitivity Analysis Plots

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-37 3.3.6.2. Variable Correlations The team performed a correlation analysis similar to the analysis presented in Section 3.3.5.2., but using impeded delay as the dependent variable. The full correlation analysis results are presented in Appendix L. These operational data tables include time of day specific volumes, and are thus different from the site level correlation tables in Appendix L, which were used for the RIA, FFS, and geometric delay data. The team made the following observations about the data: The impeded delay for the upstream segments was positively correlated (r = +0.66) with the conflicting flow within the roundabout and negatively correlated (r = 0.66) with the capacity of the roundabout. The impeded delay for the downstream segments was positively correlated with the posted speed limit (r = +0.51), free flow speed (r = +0.64), and segment length (r = +0.55) but was not strongly negatively correlated with any of the variables. Additionally, several pairs of the possible explanatory variables appeared to be highly correlated with each other, including entry flow and volume to capacity ratio, posted speed limit and FFS, CID and ICD, and median length and segment length. During model development the team avoided using highly correlated explanatory variables within the same model. 3.3.6.3. Model Results The team then used the observations from the correlation analysis to develop several models for the upstream and downstream segment datasets under the SAS GLM procedure. Appendix L displays a series of variable plots, followed by a full list of regression models considered for the impeded delay models. Based on the regression results, the team made the following observations: The upstream and downstream delays were best modeled as a function of FFS and the volume to capacity ratio. The downstream delay was also related to the segment length, median length, and curb length. Although these three variables may be correlated to each other, the presence of these variables in the HCM Chapter 17 models motivated the team to still consider these variables. The models with the best predictive ability in either case explained 55 to 70 percent of the variability in the data. Exhibit 3 21 summarizes the models for upstream and downstream delay as a function of these elements. The upstream impeded delay is a function of FFS, volume to capacity ratio, and entering flow rate. The downstream impeded delay is a function of FFS, volume to capacity ratio, segment length, median length, and curb length across the segment.

Evaluating the Performance of Corridors with Roundabouts Page 3-38 Chapter 3 - Modeling Model Int. Free-Flow Speed (mph) Volume-to- Capacity Ratio Entering Flow (veh) R2 U7 -5.35*** 0.15*** 42.50*** -0.03*** 0.67 Model Int. Free-Flow Speed (mph) Volume-to- Capacity Ratio Segment Length (ft) Median Length (ft) Curb Length (ft) R 2 D6 -2.65** 0.07* 3.10*** 0.0020** -0.0010* 0.0014** 0.56 * = p < 0.1 ** = p < 0.05 *** = p < 0.01 The full list of impeded delay models is shown in Appendix L. The sensitivity of these models is shown in Exhibit 3-22. The exhibit shows increasing delay with greater FFS, as well as increasing volume-to-capacity ratio. The entering flow rate for Model U7 was set at 1,000 vehicles times the modeled volume-to- capacity ratio, resulting in 300, 600, and 900 vehicles/hour for the three volume- to-capacity ratios used in the graph. For Model D6, the three segment lengths were fixed at 1,000 feet for total length and 500 feet each for median and curb length (corresponding to 50 percent of segment with median and curb). Exhibit 3-21: Impeded Delay Final Models Exhibit 3-22: Impeded Delay Sensitivity Analysis Plots

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-39 3.4. MODEL VALIDATION AND APPLICATION This section presents a model validation and application exercise in two parts. First, the results of the various sub models will be validated internally against the field observed data. Specifically, the team compares model predictions to field observed performance data for FFS, roundabout influence area, geometric delay, impeded delay, and average travel speed. Second, the team presents an external validation of the methodology through application to the Old Meridian Road and Spring Mill Road corridors in Carmel, Indiana. Both corridors were excluded from model development, and thus represent a true validation of the methodology. The Old Meridian Road corridor is further presented in a step by step application of the HCM 2010 Chapter 17 Urban Street Segments method, integrated with modifications for the roundabout nodes. Because the Old Meridian corridor contains one signalized intersection, the application exercise further illustrates how the method can be applied to mixed corridors of signals and roundabouts. 3.4.1. INTERNAL MODEL VALIDATION To validate the various sub models developed in this research, this section compares the model predictions to the field-observed performance data for FFS, roundabout influence area, geometric delay, impeded delay, and average travel speed. The following sections use the data from the seven corridors used in model development, excluding the two Carmel, Indiana, corridors (which are evaluated separately in Section 3.4.2). 3.4.1.1. Free-Flow Speed The FFS prediction model is a function of the speed limit (mph), segment length (ft), central island diameter (ft), and a binary variable checking for overlapping roundabout influence areas. Plots for field measured versus predicted FFS are shown in Exhibit 3 23 for upstream and downstream segments. The plots show a wide observed range of free flow speeds from approximately 20 to 55 mph, and that the same range is predicted from the model. Further, the upstream and downstream models show an overall model R2 fit of 0.90 and 0.93, respectively, with intercept terms close to zero and a slope close to 1.0. Overall, these results point to a very good model fit to the field observed data.

Evaluating the Performance of Corridors with Roundabouts Page 3-40 Chapter 3 - Modeling 3.4.1.2. Roundabout Influence Area The roundabout influence area (RIA) model predicts the spatial extent of the speed-reducing effects of the roundabout measured upstream and downstream from the yield line. The RIA is predicted as a function of the segment free-flow speed and the circulating speed. Data plots for field-measured versus predicted free-flow speed are shown in Exhibit 3-24 for upstream and downstream segments. The plots show a model R2 fit of 0.24 and 0.57 for upstream and downstream RIA, respectively. Therefore, the resulting models do not fit as well as the free-flow speed models, which is directly attributable to the high variability of RIAs across the corridors. Nonetheless, the RIA models generally capture the range of field-observed data. 3.4.1.3. Geometric Delay The geometric delay upstream of the roundabout is predicted as a function of the free-flow speed and the circulating speed, just as the roundabout influence area. The downstream geometric delay further includes an effect of the inscribed circle diameter, which is combined with FFS and circulating speed into a circulating delay term. In Exhibit 3-25, the plots of field-observed data versus model prediction generally show a better fit for the downstream models (R2 = 0.50) than the Exhibit 3-23: Internal Validation – Free-Flow Speed Models Exhibit 3-24: Internal Validation – Roundabout Influence Area Models

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-41 upstream models (R2 = 0.24). Both models suggest having a somewhat “flat” slope, with the models over-predicting some low geometric delays, but underestimating high delays. 3.4.1.4. Impeded Delay The impeded delay model is the first model taking into account prevailing conditions and variations in volumes. The upstream impeded delay is predicted as a function of the FFS, the volume-to-capacity ratio, and the entering flow rate. The downstream impeded delay is predicted as a function of the FFS, the volume-to-capacity ratio, and three geometric terms (segment length, median length, and curb length). In Exhibit 3-26, the plots of field-measured versus predicted data show a better fit for the downstream impeded delay (R2 = 0.43) than the upstream model (R2 = 0.11). The model predictions generally follow an increasing trend relative to the field data, but are further subject to much scatter. The higher variability of delays is expected, as the data are representative of a much wider range of operating conditions than the free-flow speed models. Exhibit 3-25: Internal Validation – Geometric Delay Models Exhibit 3-26: Internal Validation – Impeded Delay Models

Evaluating the Performance of Corridors with Roundabouts Page 3-42 Chapter 3 - Modeling 3.4.1.5. Average Travel Speed As the final model, the team predicted the average travel speed on the segment as a function of the FFS and the volume-to-capacity ratio. Similar to the impeded delay model, the average travel speed model takes into account the prevailing conditions on the corridor, with the speed reducing with increasing volume (increasing volume-to-capacity ratio). In Exhibit 3-27, the data plots suggest a good fit with the field-observed values with R2 statistics of 0.55 and 0.75 for upstream and downstream segments, respectively. 3.4.2. EXTERNAL MODEL VALIDATION AND APPLICATION The previous section compared the estimates of the various sub-models with the field-observed data for seven of the roundabout corridors. The team collected additional data at two corridors that were not used in model development. In this section, the full methodology will be applied to these corridors in an effort to validate the overall methodology. The roundabout corridor methodology will be illustrated using the p.m. peak period in the northbound direction, which is the period with the highest travel time. Results for the a.m. peak period and the southbound a.m. and p.m. peaks will also be shown. The discussion presents the Old Meridian Street corridor in detail, followed by a presentation of the validation results for the Spring Mill Road corridor. 3.4.2.1. Application to Old Meridian Corridor The roundabout corridor on Old Meridian Street consists of five intersections with four roundabouts and one signalized intersection over a distance of approximately 1.25 miles. Old Meridian Street runs roughly southwest-to- northeast, though it will be referred to within this document as south to north. Exhibit 3-28 describes the five intersections from south to north. Exhibit 3-27: Internal Validation – Average Travel Speed Models

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-43 Number Cross Street # Legs Control ICD (ft) 1 Pennsylvania St. 4 Roundabout 220’ 2 Carmel Dr. 4 Signal n/a 3 Grand Blvd. 3 Roundabout 191’ 4 Main St. 4 Roundabout 211’ 5 Guilford Rd. 4 Roundabout 216’ All four roundabouts have two lanes along Old Meridian Street. The signalized intersection at Carmel Dr. has two through lanes (one with a shared right) and an exclusive left turn lane for both northbound and southbound approaches. STEP A: GATHER INPUT DATA The first step in the corridor analysis is to gather the necessary input data for the methodology. A summary of input needs for the roundabout corridor methodology by sub model is shown in Exhibit 3 29. The data below are collected for each upstream and downstream sub segment. The sub segment length is defined from the midpoint of each segment to the yield line (upstream), and then from the yield line to the next segment midpoint (downstream). D at a E le m en t U n it Sub-Model Step B, E, F Step C, D Step G Step H Step I Step L Fr ee -F lo w Sp ee d R ou nd ab ou t In flu en ce A re a Se gm en t R un ni ng T im e G eo m et ric D el ay Im pe de d D el ay Av er ag e Tr av el Sp ee d Speed Limit mph X Free-Flow Speed (FFS) mph X X X X Circulating Speed (1) mph X X Central Island Diameter ft X Inscribed Circle Diameter ft X Entering Volume veh Roundabout Capacity (2) veh Volume/Capacity Ratio - X Segment Length ft X X X X Median Length ft X Curb Length ft X Start-Up Lost Time (3) sec X Other - (4) (5), (6), (7) (8), (9) (1) – Can be estimated from Inscribed Circle Diameter (2) – Estimated from HCM 2010 Chapter 21 Roundabout Method (3) – Defaulted to 2.5 seconds from HCM Chapter 17 (4) – Binary Check for Overlapping Roundabout Influence Areas (5) – Proximity Adjustment Factor (fv) from HCM Chapter 17 (6) – Delay due to turns at Access Points from HCM Chapter 17 (7) – Other delay on segment from HCM Chapter 17 (8) – Segment Running Time (from Step G) (9) – Total Delay (from Steps H and I) Exhibit 3-28: Old Meridian Validation – Facility Summary Exhibit 3-29: Old Meridian Validation – Data Input Summary

Evaluating the Performance of Corridors with Roundabouts Page 3-44 Chapter 3 - Modeling STEP B: DETERMINE FFS FOR SUB-SEGMENT With all data collected, the FFS (Sf) is estimated for each upstream (US) and downstream (DS) segment from the speed limit (SL), central island diameter (CID), and segment length (L), using the following equation. In this initial step, it is assumed that the two adjacent ramp influence areas do not overlap (OL=0). Sf,US = 15.1 + 0.0037*L + 0.43 * SL + 0.05 * CID – 4.73 * OL Sf,DS = 14.6 + 0.0039*L + 0.48 * SL + 0.02 * CID – 4.43 * OL For the signalized intersection at Old Meridian Road/Carmel Drive, the FFS estimation procedure from HCM 2010 Chapter 17 is used (Equation 17 2), as a function of a speed constant (S0), a cross section adjustment (fCS), and an adjustment factor for access points (fA). Sf0 = S0 + fCS + fA Source: HCM 2010 Equation 17 2 Using the equations above, the FFS for each sub segment is estimated as shown in Exhibit 3 30. Seg. # Int. # Type US/DS Speed Limit (mph) Segment Length (ft) CID (ft) FFS (mph) A 1 RBT US 40 184 137 39.8 B 1 RBT DS 40 763 137 39.5 B 2 Signal US 40 763 n/a 42.2 C 2 Signal DS 40 628 n/a 42.2 C 3 RBT US 40 628 115 40.3 D 3 RBT DS 40 968 115 39.9 D 4 RBT US 40 1015 143 43.2 E 4 RBT DS 40 1075 143 40.9 E 5 RBT US 40 967 140 42.9 F 5 RBT DS 40 581 140 38.9 STEP C: DETERMINE ROUNDABOUT INFLUENCE AREA LENGTH In Step C, the roundabout influence area is estimated for each upstream and downstream segment from the FFS (Sf) and the circulating speed (Sc). RIAUS = 165.9 + 13.8* Sf – 21.1*Sc RIADS = 149.8 + 31.4* Sf – 22.5*Sc In the equations above, the circulating speed can be approximated using the following equation as a function of the inscribed circle diameter (ICD). Sc = 3.4614*(ICD/2) 0.3673 The RIA for each sub segment is estimated as shown in Exhibit 3 31. Equation 3-10 Exhibit 3-30: Old Meridian Validation – Step B Results

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-45 Seg # Int. # Type US/ DS FFS (mph) ICD (ft) Circle Speed (mph) RIA (ft) A 1 RBT US 39.8 220 19.5 303.1 B 1 RBT DS 39.5 220 19.5 653.2 B 2 Signal US 42.2 n/a n/a n/a C 2 Signal DS 42.2 n/a n/a n/a C 3 RBT US 40.3 191 18.5 331.0 D 3 RBT DS 39.9 191 18.5 686.7 D 4 RBT US 43.2 211 19.2 355.9 E 4 RBT DS 40.9 211 19.2 701.9 E 5 RBT US 42.9 216 19.3 347.9 F 5 RBT DS 38.9 216 19.3 635.8 STEP D: CHECK FOR OVERLAPPING INFLUENCE AREA After the downstream and upstream influence areas of two adjacent roundabouts have been calculated, this step checks whether the sum of the two influence areas is greater than the segment length between roundabouts, as shown in Exhibit 3 32. For the first and last segment, the RIA is simply compared to the sub segment length. If these conditions are met, the RIAs overlap and the FFS has to be re calculated with OL=1. Seg. # Int. # Type US/DS Segment Length (ft) RIA (ft) Overlap? A 1 RBT US 184 303.1 YES B 1 RBT DS 763 653.2 NO B 2 Signal US 763 n/a NO C 2 Signal DS 628 n/a NO C 3 RBT US 628 331.0 NO D 3 RBT DS 968 686.7 NO D 4 RBT US 1015 355.9 NO E 4 RBT DS 1075 701.9 NO E 5 RBT US 967 347.9 NO F 5 RBT DS 581 635.8 YES STEP E: RECALCULATE FFS FOR OVERLAPPING INFLUENCE AREAS In this step, the FFS equation from Step B is reapplied with OL=1 for roundabout segments with overlapping influence areas. On this corridor, the only “overlapping” influence areas are on the two sub segments that are external to the corridor, where the roundabout influence areas are longer than the sub segments, as shown in Exhibit 3 33. Exhibit 3-31: Old Meridian Validation – Step C Results Exhibit 3-32: Old Meridian Validation – Step D Results

Evaluating the Performance of Corridors with Roundabouts Page 3-46 Chapter 3 - Modeling Seg. # Int. # Type US/DS FFS (mph) - Initial Overlap? FFS (mph) - Adjusted A 1 RBT US 39.8 YES 35.1 B 1 RBT DS 39.5 NO 39.5 B 2 Signal US 42.2 NO 42.2 C 2 Signal DS 42.2 NO 42.2 C 3 RBT US 40.3 NO 40.3 D 3 RBT DS 39.9 NO 39.9 D 4 RBT US 43.2 NO 43.2 E 4 RBT DS 40.9 NO 40.9 E 5 RBT US 42.9 NO 42.9 F 5 RBT DS 38.9 YES 34.4 STEP F: SELECT CONTROLLING FFS In this project, the FFS has been defined and measured at the midpoint between two roundabouts; therefore, one FFS is defined for a downstream segment and the next upstream segment. Consequently, the lower of these two separate estimates is selected as the controlling free flow speed for both sub segments, as shown in Exhibit 3 34. Seg. # Int. # Type US/DS FFS (mph) - Adjusted FFS (mph) - Controlling A 1 RBT US 35.1 35.1 B 1 RBT DS 39.5 39.5 B 2 Signal US 42.2 C 2 Signal DS 42.2 40.3 C 3 RBT US 40.3 D 3 RBT DS 39.9 39.9 D 4 RBT US 43.2 E 4 RBT DS 40.9 40.9 E 5 RBT US 42.9 F 5 RBT DS 34.4 34.4 STEP G: DETERMINE SEGMENT RUNNING TIME Using Equation 17 6 in HCM 2010, the segment running time is calculated, as shown in Exhibit 3 35. The equation uses the start up lost time (l1=2.5 for yield control), segment length (L), start up adjustment factor (fx), free flow speed (Sf), a proximity adjustment factor (fv), additional delay from turns (dap), and other delay (dother). Exhibit 3-33: Old Meridian Validation – Step E Results Exhibit 3-34: Old Meridian Validation – Step F Results

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-47 apN i iapv f xR ddfS Lf L lt 1 other, 1 280,5 600,3 0025.0 0.6 Source: HCM 2010 Equation 17 6 with, (signalized or STOP controlled through movement) (uncontrolled through movement) (YIELD controlled through movement) For the Old Meridian corridor, the additional delay from turns (dap) and other delay (dother) were assumed to be zero because of minimal midsegment driveway activity and no other delay sources. Seg. # Int. # Type US/DS Segment Length (ft) FFS (mph) – Controlling Running Time (sec) A 1 RBT US 184 35.1 6.3 B 1 RBT DS 763 39.5 14.1 B 2 Signal US 763 39.5 15.4 C 2 Signal DS 628 40.3 13.3 C 3 RBT US 628 40.3 11.5 D 3 RBT DS 968 39.9 17.3 D 4 RBT US 1015 39.9 18.2 E 4 RBT DS 1075 40.9 18.8 E 5 RBT US 967 40.9 16.9 F 5 RBT DS 581 34.4 12.5 STEP H: DETERMINE GEOMETRIC DELAY Next, the geometric delay is estimated for each upstream and downstream segment as a function of FFS (Sf), circulating speed (Sc), and inscribed circle diameter (ICD), as shown in Exhibit 3 36. The circulating speed can be estimated from the central island diameter as discussed above. Delaygeom,US = 1.57 + 0.11*Sf – 0.21*Sc Delaygeom,DS = 2.63 + 0.09*Sf + 0.625 * ICD * (1/Sc 1/Sf) There is generally no geometric delay for a through movement at a signalized intersection; therefore, following guidance in HCM 2010 Chapter 17, the geometric delay is set to zero for Intersection 2. Equation 3-11 Exhibit 3-35: Old Meridian Validation – Step G Results ]00.1,/min[ 00.0 00.1 thth x cv f

Evaluating the Performance of Corridors with Roundabouts Page 3-48 Chapter 3 - Modeling Seg. # Int. # Type US/DS FFS (mph) – Controlling Circle Speed (mph) ICD (ft) Geom. Delay (sec) A 1 RBT US 35.1 19.5 220 1.3 B 1 RBT DS 39.5 19.5 220 4.3 B 2 Signal US 39.5 n/a n/a 0.0 C 2 Signal DS 40.3 n/a n/a 0.0 C 3 RBT US 40.3 18.5 191 2.0 D 3 RBT DS 39.9 18.5 191 4.3 D 4 RBT US 39.9 19.2 211 1.9 E 4 RBT DS 40.9 19.2 211 4.5 E 5 RBT US 40.9 19.3 216 2.0 F 5 RBT DS 34.4 19.3 216 3.4 STEP I: DETERMINE IMPEDED DELAY The next step is to estimate the impeded delay for each upstream and downstream roundabout segment under consideration of prevailing traffic conditions, as shown in Exhibit 3 37. The model is a function of free flow speed (Sf), volume to capacity ratio (x), entering flow rate (ventering), segment length (L), median length (Lmedian), and curb length (Lcurb). Delayimp, US = 5.35 + 0.15*Sf+ 42.50*x – 0.03 * ventering Delayimp, DS = 2.65 + 0.07*Sf+ 3.10*x + 0.0020 *L – 0.0010 *Lmedian + 0.0014 * Lcurb For the signalized intersection approach, the team used the HCM 2010 Chapter 17 methodology to estimate the control delay at the approach to the signalized intersection (upstream). In this case, Intersection 2 was assumed to operate under fixed time control with random arrivals from the upstream and downstream roundabouts. Signal timing parameters were obtained from the City of Carmel, Indiana, to complete this analysis. Seg. # Int. # Type US/ DS FFS (mph) Vol. (veh) Seg. Length (ft) Median Length (ft) Curb Length (ft) Imp. Delay (sec) A 1 RBT US 35.1 906 184 184 50 0.8 B 1 RBT DS 39.5 906 763 763 467 0.2 B 2 Sig. US 39.5 n/a n/a n/a n/a 26.3 C 2 Sig. DS 40.3 n/a n/a n/a n/a 0.0 C 3 RBT US 40.3 826 628 628 111 0.0 D 3 RBT DS 39.9 826 968 968 576 0.0 D 4 RBT US 39.9 872 1015 1015 965 2.0 E 4 RBT DS 40.9 872 1075 1075 845 0.0 E 5 RBT US 40.9 736 967 967 761 2.7 F 5 RBT DS 34.4 736 581 45 581 0.3 Exhibit 3-36: Old Meridian Validation – Step H Results Exhibit 3-37: Old Meridian Validation – Step I Results

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-49 STEP J: AGGREGATE PERFORMANCE MEASURES Up to this step, all calculations have been performed on the sub segment level, where upstream and downstream sub segments used different equations to estimate the various performance measures. At this stage, these performance measures need to be aggregated to the HCM 2010 Chapter 17 Urban Street Segments method. That methodology defines an urban street segment as the distance between two stop bars (or yield lines). In this project, that corresponds to the sum of one downstream and the next upstream segment. Aggregation should be performed as the sum of the sub segments for segment running time, geometric delay, and impeded delay, as shown in Exhibit 3 38. For the free flow speed, the controlling FFS has already been selected to apply for the entire segment. Seg. # Int. # Type US/ DS FFS (mph) – Controlling Running Time (sec) Geom. Delay (sec) Imp. Delay (sec) A 1 RBT US 35.1 6.3 1.3 0.8 B 1 RBT DS 39.5 29.5 4.3 26.5 B 2 Signal US C 2 Signal DS 40.3 24.8 2.0 0.0 C 3 RBT US D 3 RBT DS 39.9 35.5 6.2 2.0 D 4 RBT US E 4 RBT DS 40.9 35.7 6.5 2.7 E 5 RBT US F 5 RBT DS 34.4 12.5 3.4 3.4 STEP K: DETERMINE SEGMENT AVERAGE TRAVEL SPEED The average travel speed for each segment is calculated from HCM 2010 Equation 17 14 below, as a function of segment length (L), running time (tR), and total delay (dt), as shown in Exhibit 3 39. The total delay is calculated as the sum of geometric and impeded delay. Source: HCM 2010 Equation 17 14 Exhibit 3-38: Old Meridian Validation – Step J Results Equation 3-12

Evaluating the Performance of Corridors with Roundabouts Page 3-50 Chapter 3 - Modeling Seg. # Int. # Type US/ DS FFS (mph) Run Time (sec) Geom. Delay (sec) Imp. Delay (sec) Avg. Travel Speed (mph) A 1 RBT US 35.1 6.3 1.3 0.8 14.9 B 1 RBT DS 39.5 29.5 4.3 26.5 17.3 B 2 Signal US C 2 Signal DS 40.3 24.8 2 0 32.0 C 3 RBT US D 3 RBT DS 39.9 35.5 6.2 2 30.9 D 4 RBT US E 4 RBT DS 40.9 35.7 6.5 2.7 31.0 E 5 RBT US F 5 RBT DS 34.4 12.5 3.4 3.4 20.5 STEP L: DETERMINE LEVELS OF SERVICE (LOS) The LOS for an urban street segment is defined based on travel speed as a percent of free flow speed, which is calculated by dividing the segment travel speed from Step K by the controlling segment free flow speed from Step F. The LOS is then obtained from the thresholds given in HCM 2010 Exhibit 17 2, which is shown here in Exhibit 3 40. Travel Speed as a Percentage of Base Free- Flow Speed (%) LOS by Volume-to-Capacity Ratioa 1.0 > 1.0 >85 A F >67–85 B F >50–67 C F >40–50 D F >30–40 E F 30 F F Note: (a) Volume-to-capacity ratio of through movement at downstream boundary intersection. Exhibit 3-39: Old Meridian Validation – Step K Results Exhibit 3-40: Urban Street LOS Table (HCM 2010 Exhibit 17-2)

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-51 Seg. # Int. # Type US/ DS FFS (mph) Avg. Travel Speed (mph) Percent FFS LOS A 1 RBT US 35.1 14.9 42.6% D B 1 RBT DS 39.5 17.3 43.7% D B 2 Signal US C 2 Signal DS 40.3 32.0 79.3% B C 3 RBT US D 3 RBT DS 39.9 30.9 77.5% B D 4 RBT US E 4 RBT DS 40.9 31.0 75.8% B E 5 RBT US F 5 RBT DS 34.4 20.5 59.7% C 3.4.3. OLD MERIDIAN ROUTE VALIDATION The validation results above can further be aggregated to the roundabout corridor level, and those estimates compared to the field observed data. Exhibit 3 42 shows the facility average FFS, the total travel time, the average travel speed, and the percent FFS for the entire corridor compared to the field estimates. In addition to the results of the northbound p.m. peak data, the exhibit shows the northbound a.m. peak results, as well as the results for northbound a.m. and p.m. peaks. Exhibit 3-41: Old Meridian Validation – Step L Results

Evaluating the Performance of Corridors with Roundabouts Page 3-52 Chapter 3 - Modeling Exhibit 3-42: Old Meridian Validation – Summary Results

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-53 The validation results suggest a close match of the predicted FFS for both northbound and southbound, with an error of 0.6 mph and 1.2 mph, respectively. For the average travel speed estimation, the northbound results for the a.m. and p.m. peaks match the field observed data with an error of 2.1 mph (8.0%) and 0.2 mph (0.8%), respectively. For the southbound, the average travel speed estimates are lower than the field observed data by 5.4 mph (17.0%) and 2.5 mph (9.2%) for the a.m. and p.m. peaks, respectively. This difference in average travel speed translates to a difference in travel times of 0.0 and 0.2 minutes for northbound a.m. and p.m. peaks, and 0.6 and 0.5 minutes for the southbound routes. The final validation results are shown in Exhibit 3 43 in terms of the estimates of percent FFS and the corridor LOS. The results show the method predicted the correct LOS within one le‰er grade for all four tested routes. The validation generally performed be‰er for the northbound route than the southbound route. Route Time Field Data Model Data %FFS LOS %FFS LOS NB AM 66% C 72% B NB PM 63% C 64% C SB AM 83% B 66% C SB PM 72% B 63% C 3.4.4. SPRING MILL ROUTE VALIDATION Similar to the Old Meridian corridor, the team also performed the overall route validation for the Spring Mill corridor in Carmel, Indiana. The details are not shown here, as the steps are largely the same as described above. Further, the Spring Mill corridor does not contain any interim signals, which simplifies the analysis. The validation results have been aggregated to the roundabout corridor level, and those estimates compared to the field observed data. Exhibit 3 44 shows the facility average FFS, the total travel time, the average travel speed, and the percent FFS for the entire corridor compared to the field estimates. Exhibit 3-43: Old Meridian Validation – Route Validation Results

Evaluating the Performance of Corridors with Roundabouts Page 3-54 Chapter 3 - Modeling Exhibit 3-44: Spring Mill Route Validation – Summary Results

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-55 The Spring Mill corridor validation shows a close match between the model and field estimates. The model slightly overestimated the FFS and the average travel speed by about 2 to 5 mph across the four analyzed routes. This translated to a slight underestimation of travel time for three of the routes by 0.2 to 0.8 minutes. However, the resulting percent FFS measure proved to be within 10 percent of the field observed data for all routes, which is explained because the error in FFS and average travel speed was in the same direction. The final route validation results are shown in Exhibit 3 45. It is evident the method correctly predicted the route LOS for all four cases. Route Time Field Data Model Data %FFS LOS %FFS LOS NB AM 79% B 83% B NB PM 71% B 78% B SB AM 75% B 76% B SB PM 82% B 76% B 3.5. EQUIVALENT NON-ROUNDABOUT CORRIDORS A typical corridor operations evaluation involves comparing various control treatments at key intersections, typically roundabout versus signalized intersections. To gain insight into typical comparisons, the research team developed a non roundabout alternative for each of the study corridors. In most cases, the non roundabout alternative has signals in place of roundabouts. In a few cases noted in Section 3.5.2, stop controlled intersections were used in place of roundabouts. These comparisons are intended to provide insight from an operational perspective on the potential strengths and weaknesses that roundabouts and signalized intersections bring to a corridor. Because the corridors under study have already been built into a roundabout configuration, it is possible to use field based measurements of operational performance of the roundabout configuration and compare them to a predicted performance of the equivalent signalized corridor. These types of comparisons involve assumptions regarding the configuration of the equivalent non roundabout corridor (e.g., control, phasing, lane configurations) and the modeling tools employed (e.g., HCM based analytical analysis or simulation). The comparison presented here, like the data collected in the field for this project, is operations focused. A comprehensive evaluation of corridor alternatives, such as the process described in the Corridor Comparision Document (Appendix A), would incorporate many other elements, including safety. The Highway Safety Manual (HSM) contains safety performance functions (SPFs) for signalized and two way stop controlled intersections (AASHTO 2010). SPFs estimate the number of crashes expected in future years based on annual average daily traffic (AADT) and the basic geometric configuration. The HSM and a more recent study by Gross et al. (2012) provide crash modification Exhibit 3-45: Spring Mill Validation – Route Validation Results

Evaluating the Performance of Corridors with Roundabouts Page 3-56 Chapter 3 - Modeling factors (CMFs) for converting signalized intersections and stop controlled intersections into roundabouts. Through the use of SPFs and CMFs, the safety performance of non roundabout and roundabout alternatives can be compared on a planned corridor or on an existing corridor where a retrofit is being considered. Generally speaking, CMFs indicate that replacing a signalized or two way stop controlled intersection with a roundabout will reduce total and injury crashes. 3.5.1. METHODOLOGY The methodology for the operations comparison to equivalent signalized corridors consisted of the following steps: 1. Create an equivalent non roundabout corridor configuration. 2. Use a simplified simulation process to estimate the performance of the equivalent non roundabout corridor for the routes that were field measured for the roundabout corridor. 3. Compare the estimated performance of the selected routes between the equivalent non roundabout corridor and the roundabout corridor. 3.5.2. CORRIDOR CONFIGURATIONS Lane configurations, signal phasing, and coordinated signal timing parameters were developed to produce an equivalent non roundabout alternative that the research team believes could have been realistically considered in an alternatives analysis. Details for each equivalent non roundabout corridor configuration are provided in Appendix O. For maps of the corridors, refer to the site reports in Appendices B through J. In general, each equivalent non roundabout corridor was developed by replacing each roundabout with a signalized intersection so a pure roundabout only versus signal only comparison could be made. However, several corridor specific exceptions were made to adapt to local conditions: La Jolla Boulevard: The equivalent non roundabout corridor assumes three two way stop controlled intersections (Colima Street, Midway Street, and Camino de la Costa) and two signalized intersections (Bird Rock Avenue and Forward Street). Based on the data obtained by the research team, the three unsignalized intersections would function acceptably as stop controlled intersections and would not meet MUTCD signal warrants. Old Meridian Street: The existing roundabout corridor contains a signalized intersection (Carmel Drive) within the series of roundabouts. Therefore, the field measured roundabout performance includes the performance of a signalized intersection. SR 539: For the equivalent non roundabout corridor, only the central two intersections were assumed to be signalized. The intersections on each end were assumed to be two way stop controlled due to not meeting MUTCD signal warrants. Golden Road: For the equivalent non roundabout corridor, three intersections (Utah Street, Lunnonhaus Drive, and Jackson Street/Ford

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-57 Street) were modeled as two way stop controlled intersections. Utah Street and Lunnonhaus Drive were previously two way stop controlled intersections, and Jackson Street and Ford Street form a one way couplet extension of Golden Road. The remaining intersections (Ulysses Street and Johnson Road) were modeled as signalized intersections. 3.5.3. CORRIDOR TRAVEL-TIME EXTRACTION Each corridor was analyzing using six routes: Two routes conducted end to end. Four routes involving left turn movements at a selected intersection within the corridor. These routes capture the effect of major street left turns from the arterial and minor street left turns onto the arterial. A simplified method was employed to conduct the analysis of the equivalent non roundabout corridor. To generate travel time from the signalized/stop controlled intersection model that could be compared against the field data under roundabout control, the project team aggregated the intersection through movement average travel times reported in SimTraffic for each intersection along the corridor in each direction. This process was necessitated by the fact that SimTraffic does not provide a feature to collect the travel time for a segment or series of segments with a user specified origin/start point and destination/end point (such as the routes including a left turn onto or off the corridor). As SimTraffic is a stochastic simulation model, five runs were performed and the results were averaged to derive measures of effectiveness (MOEs) for the corridor under signalized/stop control. As a result of applying the performance measure aggregation methodology, the computed route travel time is similar to but not the same as taking the travel time of only those vehicles that travel the entire route. In other words, the travel time reported by SimTraffic is an average value for all vehicles traveling on the segment, including vehicles that are not traveling the route being studied. The methodology used here assumes the difference between the travel times of vehicles following and not following the studied route is negligible for the purpose of the comparison. Exhibit 3 46 provides a summary of travel time and intersection delay time comparisons for selected routes for each corridor. The table is sorted by travel time difference. The first route had the largest percentage decrease in travel time with the roundabouts. These values are extracted from the detailed analysis contained in Appendix O.

Evaluating the Performance of Corridors with Roundabouts Page 3-58 Chapter 3 - Modeling Corridor Route Route beginning with: 1 and 2 are through routes 3 and 5 are le turns deparng the corridor 4 and 6 are le turns entering the corridor E qu iv al en tS ig na liz ed Ro ut e Tr av el Ti m e (s ) Ro un da bo ut Tr av el Ti m e (s ) Tr av el Ti m e Di ffe re nc e Eq ui va le nt Si gn al ize d Ro ut e In t. Ap pr oa ch De la y (s ) Ro un da bo ut Ro ut e In t. Ap pr oa ch De la y (s ) In te rs ec o n Ap pr oa ch De la y Di ffe re nc e Eq ui va le nt Si gn al ize d Ro ut e N on In te rs ec o n Ti m e (s ) Ro un da bo ut Ro ut e N on In te rs ec o n Ti m e (s ) N on In te rs ec o n Ti m e Di ffe re nc e MD 216 3. East South, le turn at #4 NB US 29 103.7 48.0 54% 72.3 12.0 83% 31.4 36.0 15% Spring Mill (AM) 5. North East, le turn at #5 131st 295.1 166.8 43% 189.1 61.2 68% 106.0 105.6 0% Spring Mill (PM) 4. West North, le turn from #6 136th 139.1 81.0 42% 76.9 23.4 70% 62.2 57.6 7% MD 216 4. South West, le turn from #4 NB US 29 191.4 114.0 40% 101.2 24.0 76% 90.2 90.0 0% MD 216 5. West North, le turn at #2 Maple Lawn 77.5 48.0 38% 38.2 12.0 69% 39.3 36.0 8% Avon Road 3. South West, le turn at #3 Beaver Creek 104.0 68.4 34% 55.5 20.4 63% 48.5 48.0 1% Old Meridian (PM) 4. West North, le turn from #3 Main 104.0 68.4 34% 52.6 21.0 60% 51.4 47.4 8% Spring Mill (AM) 4. West North, le turn from #6 136th 135.5 90.0 34% 77.4 32.4 58% 58.1 57.6 1% Spring Mill (PM) 6. East South, le turn from #5 131st 577.6 390.0 32% 248.4 69.0 72% 329.2 321.0 2% Old Meridian (AM) 4. West North, le turn from #3 Main 92.6 64.8 30% 52.6 17.4 67% 40.0 47.4 19% Avon Road 6. East South, le turn from #4 Benchmark 88.3 62.4 29% 48.9 25.8 47% 39.4 36.6 7% Avon Road 4. West North, le turn from #3 Beaver Creek 99.4 72.0 28% 63.9 32.4 49% 35.5 39.6 12% SR 67 5. West North, le turn at #5 US 9 175.9 127.8 27% 75.1 33.6 55% 100.8 94.2 7% MD 216 6. North East, le turn from #2 Maple Lawn 188.2 138.0 27% 103.8 42.0 60% 84.4 96.0 14% Golden Road 4. West North, le turn from #4 Johnson 122.4 91.2 25% 30.1 9.6 68% 92.3 81.6 12% Spring Mill (PM) 5. North East, le turn at #5 131st 193.5 145.2 25% 88.7 39.6 55% 104.8 105.6 1% MD 216 2. East West 189.8 144.0 24% 86.1 30.0 65% 103.7 114.0 10% Spring Mill (AM) 2. North South 707.9 538.2 24% 304.9 139.8 54% 403.0 398.4 1% Avon Road 5. North East, le turn at #4 Benchmark 100.5 79.2 21% 53.2 35.4 33% 47.3 43.8 7% Old Meridian (AM) 6. East South, le turn from #2 Grand 119.5 94.8 21% 56.0 37.2 34% 63.5 57.6 9% Spring Mill (AM) 6. East South, le turn from #5 131st 490.8 394.2 20% 174.8 73.2 58% 316.0 321.0 2% SR 67 4. South West, le turn from #5 US 9 189.2 153.0 19% 81.4 51.0 37% 107.8 102.0 5% SR 67 6. North East, le turn from #5 US 9 151.1 124.2 18% 72.1 18.0 75% 79.0 106.2 34% SR 539 6. East South, le turn from #3 Wiser Lake 273.7 228.0 17% 66.7 46.8 30% 207.0 181.2 12% MD 216 1. West East 186.5 156.0 16% 81.8 42.0 49% 104.7 114.0 9% SR 539 4. West North, le turn from #2 Pole 245.8 207.0 16% 54.6 52.2 4% 191.2 154.8 19% Avon Road 2. North South 125.9 107.4 15% 56.3 40.8 28% 69.6 66.6 4% Old Meridian (AM) 5. North East, le turn at #2 Grand 117.2 100.8 14% 20.0 18.0 10% 97.2 82.8 15% Exhibit 3-46: Summary of Travel Time and Intersection Approach Delay Comparisons, Sorted by Travel Time Difference

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-59 Corridor Route Route beginning with: 1 and 2 are through routes 3 and 5 are le turns deparng the corridor 4 and 6 are le turns entering the corridor Eq ui va le nt Si gn al ize d Ro ut e Tr av el Ti m e (s ) Ro un da bo ut Tr av el Ti m e (s ) Tr av el Ti m e Di ffe re nc e Eq ui va le nt Si gn al ize d Ro ut e In t. Ap pr oa ch De la y (s ) Ro un da bo ut Ro ut e In t. Ap pr oa ch De la y (s ) In te rs ec o n Ap pr oa ch De la y Di ffe re nc e Eq ui va le nt Si gn al ize d Ro ut e N on In te rs ec o n Ti m e (s ) Ro un da bo ut Ro ut e N on In te rs ec o n Ti m e (s ) N on In te rs ec o n Ti m e Di ffe re nc e Spring Mill (PM) 2. North South 558.4 490.2 12% 154.8 91.8 41% 403.6 398.4 1% Spring Mill (AM) 3. South West, le turn at #6 136th 484.6 435.0 10% 139.6 78.6 44% 345.0 356.4 3% Old Meridian (PM) 5. North East, le turn at #2 Grand 111.6 100.2 10% 21.6 17.4 19% 90.0 82.8 8% Golden Road 6. East South, le turn from #4 Johnson 110.2 99.0 10% 33.2 31.2 6% 77.0 67.8 12% Avon Road 1. South North 133.8 120.6 10% 64.1 55.2 14% 69.7 65.4 6% Spring Mill (PM) 3. South West, le turn at #6 136th 558.6 508.8 9% 191.7 152.4 21% 366.9 356.4 3% Spring Mill (PM) 1. South North 602.4 556.8 8% 203.0 166.2 18% 399.4 390.6 2% SR 539 3. South West, le turn at #2 Pole 153.6 142.8 7% 12.7 32.4 155% 140.9 110.4 22% La Jolla Boulevard 5. West North, le turn from #4 Bird Rock 75.0 70.0 7% 29.5 6.0 80% 45.5 64.0 41% Golden Road 5. North East, le turn at #4 Johnson 107.1 100.8 6% 9.2 12.6 37% 97.9 88.2 10% Old Meridian (PM) 1. South North 202.5 192.0 5% 75.3 74.4 1% 127.2 117.6 8% SR 67 1. West East 246.1 233.4 5% 85.2 50.0 41% 160.9 183.4 14% Old Meridian (AM) 2. North South 164.4 162.6 1% 37.3 38.4 3% 127.1 124.2 2% Old Meridian (AM) 3. South West, le turn at #3 Main 139.5 138.0 1% 40.0 45.6 14% 99.5 92.4 7% SR 539 5. North East, le turn at #3 Wiser Lake 122.5 121.2 1% 11.1 25.8 132% 111.4 95.4 14% SR 539 1. South North 327.9 327.0 0% 30.2 74.4 146% 297.7 252.6 15% SR 539 2. North South 321.8 322.8 0% 23.4 63.6 172% 298.4 259.2 13% Golden Road 1. South North 161.7 163.2 1% 19.9 28.2 42% 141.8 135.0 5% Spring Mill (AM) 1. South North 492.6 497.4 1% 108.5 106.8 2% 384.1 390.6 2% Old Meridian (PM) 3. South West, le turn at #3 Main 153.7 156.0 1% 51.1 63.6 24% 102.6 92.4 10% Golden Road 2. North South 161.1 167.4 4% 22.5 30.0 33% 138.6 137.4 1% Old Meridian (AM) 1. South North 170.7 180.6 6% 52.4 63.0 20% 118.3 117.6 1% Golden Road 3. South West, le turn at #4 Johnson 91.9 98.4 7% 24.2 27.6 14% 67.7 70.8 5% Old Meridian (PM) 6. East South, le turn from #2 Grand 97.8 105.0 7% 50.5 47.4 6% 47.3 57.6 22% SR 67 2. East West 234.7 253.2 8% 79.4 69.6 12% 155.3 183.6 18% SR 67 3. East South, le turn at #5 US 9 121.6 138.6 14% 40.7 22.8 44% 80.9 115.8 43% Old Meridian (PM) 2. North South 142.7 175.8 23% 28.0 51.6 84% 114.7 124.2 8% La Jolla Boulevard 3. East South, le turn from #1 Colima 41.4 54.0 30% 11.8 6.0 49% 29.6 48.0 62% La Jolla Boulevard 4. South West, le turn at #4 Bird Rock 88.9 126.0 42% 32.8 6.0 82% 56.1 120.0 114 % Exhibit 3-46 Continued

Evaluating the Performance of Corridors with Roundabouts Page 3-60 Chapter 3 - Modeling Corridor Route Route beginning with: 1 and 2 are through routes 3 and 5 are le turns deparng the corridor 4 and 6 are le turns entering the corridor E qu iv al en tS ig na liz ed Ro ut e Tr av el Ti m e (s ) Ro un da bo ut Tr av el Ti m e (s ) Tr av el Ti m e Di ffe re nc e Eq ui va le nt Si gn al ize d Ro ut e In t. Ap pr oa ch De la y (s ) Ro un da bo ut Ro ut e In t. Ap pr oa ch De la y (s ) In te rs ec o n Ap pr oa ch De la y Di ffe re nc e Eq ui va le nt Si gn al ize d Ro ut e N on In te rs ec o n Ti m e (s ) Ro un da bo ut Ro ut e N on In te rs ec o n Ti m e (s ) N on In te rs ec o n Ti m e Di ffe re nc e La Jolla Boulevard 2. North South 110.7 162.0 46% 21.8 24.0 10% 88.9 138.0 55% La Jolla Boulevard 1. South North 110.2 162.0 47% 21.4 24.0 12% 88.8 138.0 55% La Jolla Boulevard 6. North East, le turn at #1 Colima 106.7 192.0 80% 24.7 36.0 46% 82.0 156.0 90% Int. = Intersection From this diverse set of corridors, the research team made a number of observations: Neither roundabout nor signalized/stop controlled corridor configurations consistently result in reduced travel time or intersection delays. Of the 20 through route combinations analyzed, approximately half resulted in lower travel time under a roundabout configuration and approximately half resulted in lower travel time under non roundabout configuration. The corridors having beer travel times under a roundabout configuration (MD 216, Spring Mill Road, Avon Road) also are notable for irregular intersection spacing. Corridors that can use two way stop controlled intersections in the place of roundabouts or signals generally produce beer end to end travel times, even if intersection delays are lower under a roundabout configuration. The corridor having the lowest travel times under an equivalent non roundabout configuration (La Jolla Boulevard) was designed with mixed signalized/unsignalized control. As a result, end to end travel times are more favorable under an equivalent non roundabout configuration, even though the roundabout configuration resulted in lower intersection delays. The corridor analyzed with large intersection spacing and higher speeds (SR 539) showed virtually no difference in travel time between the two alternatives, despite the observation that the intersection delay increases in a roundabout configuration. The analysis becomes more illuminating when including the travel time runs involving left turns to and from the arterial street. Of the 60 total corridor route combinations analyzed, approximately three quarters (44) of the corridor route combinations resulted in lower travel time under a roundabout configuration than under an equivalent signalized configuration. Approximately one third (21) of the analyzed combinations resulted in reduced travel time of 20 percent or more. In addition, approximately three quarters (44) of the corridor route combinations resulted in lower intersection approach delay for the routes studied under a roundabout configuration. Exhibit 3-46 Continued

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-61 Anecdotal observations about specific corridors or groups of corridors may explain some of the variability in the results: o Approach delay was lower with roundabouts for all intersections in both major street directions except for SR 539. o Through route travel time (average of both directions) increased with roundabouts on La Jolla Boulevard, Old Meridian Street, and Golden Road; decreased with roundabouts on MD 216, Spring Mill Road, Avon Road, and SR 67; and remained virtually unchanged on SR 539. The corridors on which through travel times decreased with roundabouts have irregular intersection spacing, changes in land use, and an interchange. They also have the highest peak hour major street and side street volumes among the corridors studied. SR 539 has the longest intersection spacing and highest speed limit; changes in intersection performance have a lower effect on overall corridor operations on SR 539 than on other corridors. o Travel time for routes with a left turn off the major street (average of both directions) increased with roundabouts on La Jolla Boulevard; decreased on MD 216, Old Meridian Street, Spring Mill Road, SR 539, Avon Road, and SR 67; and remained virtually unchanged on Golden Road. It is noted that Golden Road has the lowest 12 hour (7 a.m. to 7 p.m.) volume of all the corridors studied. o Travel time for routes with a left turn onto the major street (average of both directions) increased with roundabouts on La Jolla Boulevard and decreased on MD 216, Old Meridian Street, Spring Mill Road, SR 539, Golden Road, Avon Road, and SR 67. o The La Jolla Boulevard corridor performs quite differently from the other corridors studied in this project. It is the most urban of the corridors studied, with considerable pedestrian, bicycle, and on street parking activity. As a result, through vehicular traffic experiences more friction than was observed for other corridors. La Jolla Boulevard has the second shortest average intersection spacing (Avon Road has the shortest spacing), the lowest speed limit (La Jolla Boulevard and Avon Road are both 25 mph), and the highest pedestrian volume. It is the only corridor with angled on street parking. Over half of the length of the corridor lies within roundabout influence areas, or the areas upstream and downstream of roundabouts where drivers are accelerating or decelerating. Three of the five roundabouts on La Jolla Boulevard were modeled as two way stop control in the equivalent corridor because they did not meet signal warrants. Based on these observations, the research team believes a case by case evaluation is necessary to determine what is preferred operationally for a given corridor. The evidence suggests a roundabout corridor has a good likelihood of improving travel time performance, but site specific conditions may favor

Evaluating the Performance of Corridors with Roundabouts Page 3-62 Chapter 3 - Modeling signalized (or stop controlled) operation. The Corridor Comparison Document in Appendix A provides a framework for operations evaluations such as this in the context of a comprehensive corridor alternative analysis. 3.6. SUMMARY This chapter highlighted the key methods, observations, and conclusions of the modeling effort for this project. In this section, the five modeling results are summarized for roundabout influence area, geometric delay, free flow speed, average running speed, and impeded delay. The team began the study of roundabout corridors by developing a framework to investigate the effects of corridor design and operation on the speeds and delay incurred at the individual roundabouts. The first three models (RIA, FFS, and geometric delay) used a dataset with only geometric and speed data that did not change with the time of day, while a separate dataset containing time of day data was used for the last two types of models (average travel speed and impeded delay). 3.6.1. ROUNDABOUT INFLUENCE AREA MODEL The team investigated the spatial extent of each roundabout’s influence on the adjacent segments by determining the length of the segment along which geometric delay due to the presence of the roundabout is incurred. This length was denoted as the Roundabout Influence Area Length. The RIA was calculated using the unimpeded speed profile of each roundabout corridor and determining where the speed fell below free flow speed. Segments that the team suspected contained overlapping RIAs were excluded from the dataset. The team developed several regression models for the upstream and downstream portions of the RIA and found that it is primarily related to the free flow speed along the segment as well as the circulating speed (i.e., the minimum unimpeded speed) within the roundabout. For a given segment, as the free flow speed increases, the RIA length predicted by the model also increases, but this length decreases as the circulating flow in the roundabout adjacent to the segment increases. This is intuitive because it suggests roundabouts necessitating a greater decrease in speed (as indicated by a large difference between the free flow speed and circulating speed) should be associated with a longer RIA. While the downstream RIA models could explain up to 71 percent of the variability in the data, the upstream data were considerably more variable, and the preferred models only explained 29 to 38 percent of the variability in the data. 3.6.2. GEOMETRIC DELAY MODEL The HCM Chapter 21 methodology for determining roundabout delay only considers control delay and does not currently estimate geometric delay, which is incurred due to the presence of the roundabout and affects all vehicles regardless of the level of congestion. The team calculated the geometric delay for each upstream and downstream segment by taking the difference between

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-63 unimpeded and free flow travel times along each segment. Again, segments with overlapping RIAs were excluded from the dataset. Although the data were highly variable, the team found the geometric delay could be partially explained by the free flow speed along the segment and the circulating speed within the roundabout. These relationships were similar to those in the RIA models in that a higher free flow speed along a segment would cause the model to predict a higher geometric delay, but a higher circulating speed within the adjacent roundabout would lower the predicted geometric delay. This is also intuitive in that drivers should experience more geometric delay at a roundabout necessitating a greater decrease in speed. While the downstream geometric delay models could explain up to 66 percent of the variability in the data, the upstream data were considerably more variable; these models could only account for 30 to 40 percent of the variability in the data. 3.6.3. FREE-FLOW SPEED MODEL The third model aimed to predict the free flow speed along each roundabout segment based on planning and geometric data, before any traffic or operational data were considered. The team estimated the free flow speed within each segment by using the unimpeded speed profiles and examining the speeds in between the roundabouts. Several of the roundabouts were so closely spaced that the vehicles may not have been able to accelerate back to free flow speed (due to overlapping RIAs), so segments with this quality were denoted overlapping segments. The team found the free flow speed was primarily related to the segment length, the posted speed limit along the segment, and the central island diameter of the adjacent roundabout, as well as whether the segment was an overlapping segment. Specifically, the free flow speed was found to increase with the posted speed, segment length, and central island diameter, but the models assigned a significant penalty (minus 4.5 to 5.0 mph) to the free flow speed of these overlapping segments. The free flow speed models had the strongest fit of any of the models here; they explained more than 90 percent of the variability in the data. 3.6.4. IMPEDED DELAY MODEL The team investigated the average impeded delay incurred to each driver at each roundabout by calibrating a delay model for the time of day dataset. The team determined the impeded delay for each segment by taking the difference between the average travel time and the free flow travel time. The resulting models indicated that, for the upstream segments, the impeded delay is primarily related to the free flow speed along the segment as well as the entering flow and volume to capacity ratio for the downstream roundabout. The upstream models suggested drivers will experience more delay at a roundabout with a high level of congestion (indicated by a high volume to capacity ratio), but a roundabout with a higher level of entering flow will incur a lower amount of delay. This laer relationship may seem counterintuitive but

Evaluating the Performance of Corridors with Roundabouts Page 3-64 Chapter 3 - Modeling should be interpreted along with the volume to capacity ratio term. Like the geometric delay model, a segment with a higher free flow speed is associated with greater impeded delay. For the downstream segments, the free flow speed, segment length, curb length, and volume to capacity ratio all increased the delay, but an increase in median length led to a decrease in the model predicted delay. Again, this last relationship may be due to the sample size or range of median lengths. The resulting impeded delay models explained 55 to 70 percent of the variability in the data. 3.6.5. AVERAGE TRAVEL SPEED MODEL Finally, the team investigated the average speed along the sub segments of a roundabout corridor, under consideration of traffic characteristics such as the level of congestion. The average travel speed along each sub segment was calculated for the upstream and downstream segments to calibrate several models. This model is an optional step in the implementation of these models in HCM 2010 Chapter 17, as that procedure already contains a step to estimate the average travel speed under consideration of free flow speed, delays, and other factors. But the model developed here may be useful as a roundabout specific verification of the Chapter 17 model, which was calibrated from signalized intersection data. The team found the average travel speed was chiefly related to the free flow speed and volume to capacity ratio of the downstream roundabout. Thus, a segment with a higher free flow speed would experience a higher average speed, but an increase in volume to capacity ratio would lower the average speed within the segment. These models explained 75 to 85 percent of the variability in the data. 3.6.6. VALIDATION After completing the model development of all predictive models, the team performed two types of validation to the field observed data. The validation exercise was intended to document how well the various sub models match the field data, as well as verify that the proposed methodology results in satisfactory performance results. First, the results of the various sub models were validated internally against the field observed data for the seven roundabout corridors used in model development. A comparison of the model predictions to field observed performance data generally showed that the free flow speed model explained over 90 percent of the variability in the data for both upstream and downstream segments. The roundabout influence area models predicted 57 percent of the downstream variability, but only 24 percent of the upstream variability, which is aributed to high variability and some outliers in the field observed data. A similar model fit was observed for the geometric delay models, with downstream prediction ability being higher than upstream geometric delays. This may be explained by more consistent circulating and acceleration behavior across sites, with more variable deceleration profiles. This trend is similarly replicated for the impeded delay and average travel speed models. While not

Evaluating the Performance of Corridors with Roundabouts Chapter 3 - Modeling Page 3-65 used in the proposed methodology, the direct estimation of average travel speed is a viable model alternative to the HCM 2010 Chapter 17 method, explaining 55 percent and 75 percent of the upstream and downstream variability in average travel speed, respectively. Second, the team presented an external validation of the methodology through application to the Old Meridian Street and Spring Mill Road corridors in Carmel, Indiana. Both corridors were excluded from model development, and thus represent a true validation of the methodology. The Old Meridian Street corridor is further presented in a step by step application of the HCM 2010 Chapter 17 Urban Street Segments method, integrated with modifications for the roundabout nodes. Since the Old Meridian Street corridor contains one signalized intersection, the application exercise further illustrated how the method can be applied to mixed corridors of signals and roundabouts. The Carmel, Indiana, validation exercise showed the developed corridor methodology correctly predicted the LOS for all four analysis routes for the Spring Mill Road corridor, and it predicted LOS within one leer grade for the Old Meridian Street corridor. The resulting percent free flow speed estimates matched the field observed data within 10 percent for Spring Mill Road (all four routes) and for the northbound routes on Old Meridian Street. The Old Meridian Street southbound routes matched within a 20 percent difference. 3.6.7. EQUIVALENT NON-ROUNDABOUT CORRIDORS From this diverse set of corridors, neither roundabout nor signalized/stop controlled corridor configurations consistently result in reduced travel time or intersection delays. Of the 20 through route combinations analyzed, approximately half resulted in lower travel time under a roundabout configuration and approximately half resulted in lower travel time under a non roundabout configuration. The corridors having lower travel times under a roundabout configuration tend to have irregular intersection spacing, while those having two way stop controlled intersections tend to have lower travel times in the non roundabout alternative. The analysis becomes more illuminating when including the travel time runs involving left turns to and from the arterial street. For all routes analyzed, approximately three quarters resulted in lower travel time under a roundabout configuration than under an equivalent signalized configuration. Approximately one third of the analyzed combinations resulted in reduced travel time of 20 percent or more. Evaluating non operational elements such as safety would also help to differentiate more comprehensively between roundabout corridors and equivalent signalized corridors.