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APPENDIX E ARTERIAL WEAVING SPEED MODELS E.1 WEAVING SPEED MODEL This section describes the development of a methodology for evaluating the performance of selected traffic movements in weaving sections on arterial cross streets in interchange areas. This performance was evaluated in terms of the speeds of both the weaving and non-weaving movements. The weaving maneuver that was examined in this study was the off-ramp right-turn movement that weaves across the arterial to make a left-turn at the downstream signalized intersection. Although several other weaving maneuvers exist in interchange areas, the off-ramp weave maneuver was generally found to have the largest volume and to be the most disruptive to arterial traffic flow. Henceforth, the weaving problem described in this appendix is referred to as "arterial" weaving. This terminology is adopted to clearly indicate that the weaving studied in this research occurs on streets whose traffic flow is periodicallyinterruptedby traffic signals, as compared to the more extensively studied weaving that occurs on uninterrupted flow facilities (such as freeways). The following sections provide a brief overview of the weaving problem, a description of He weaving database, and the results of a mode} development and calibration process. Two maneuver speed models were developed. One mode! predicts the maneuver speed of weaving vehicles. The other mode! predicts He maneuver speed of arsenal vehicles as they travel Trough the weaving section. The maneuver speed referred to here is effectively a running speed, as it represents the ratio of travel distance to travel time within the weaving section. Edit.! Background cat , The weaving maneuver studied in this research is somewhat comparable to a two-sided Type C Leeway weave, as described in Chapter 4 of the Highway Capacity Manual (HCM) All. As shown in Figure 4-5 ofthe HCM, the two-sided Type C weave maneuver entails an entry via a ramp, a weave across two or more through lanes, and an exit via a lefc-hand off-ramp. The off-ramp weaving maneuver considered in this study also enters via a ramp, weaves across two or more through lanes, and exits from the major street by Lining left at the downstream intersection. However, there are some fundamental differences between freeway and arterial weaving. Freeway weaving sections operate under uninterrupted flow conditions while arterial weaving sections operate under interrupted flow due to upstream and downstream traffic signals. Another difference is that a freeway weaving section has a fixed length that is based on the distance between its entry and exit points while an arterial weaving section has a varying length as a result of downstream queues. Weaving Section Classification. Maneuver (or travel path), weave type, and movement type are used in this research to denote different aspects of travel through a weaving section. An arterial weaving section can be classified according to the various maneuvers that pass through it. Maneuver denotes the path a vehicle takes from its point of entry to the point where it first experiences stopped delay or exits the weaving section. In other words, the maneuver begins when E-l

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the vehicle enters the weaving section and ends when the vehicle stops in a queue, stops at Me stop line, or exits the weaving section, whichever event occurs first. Therefore, the maneuver distance vanes from vehicle to vehicle depending on traffic conditions. An arsenal street segment bounded by signalized intersections has ten possible travel paths (or maneuvers), as defined by all possible or~gin-dest~nation pairs in one travel direction through it. These ten paws are listed in Table E-. Table E-1. Classification of an arterial weaving section based on maneuver and weave type Path No. Maneuver (Entry to Exit) Right-Turn to Left-Turn Left-Turn to Right-Turn Right-Turn to Inside Through Lane Left-Turn to Outside Through Lane Outside Through Lane to Left-Turn Inside Through Lane to Right-Turn Through to Adjacent Through Lane Weave Turns Lane Changes2 Present in | Typel | ],Iade - - Sections Weaving-Related Paws l Non-Weaving-Related Paws 11 8 _ 10 Right to Outside Through (or Right) Left to Inside Through Lane (or Left) Through to Same Through Lane _ 1 (or 2) 1 (or 2) O 0 | 0 | Yes 1 none 0 | 0 | No | none O | O | Yes 1 Artenal Notes: 1 - Weave Type is determined by the number of tums and lane changes required (i.e., level of difficulty). Type 1 = maximum difficulty, Type 2 = medium difficulty, Type 3 = minimum difficulty. 2 - Number of arterial lanes crossed during we weave (excluding lane changes from acceleration lanes or lane changes to deceleration lanes or turn bays). 3 - Number of arsenal lanes in the subject direction (excluding acceleration lanes, deceleration lanes, and turn bays). 4 - "Yes" indicates we paw is present in arterial weaving sections in interchange areas. 5 - Applicable maneuver speed model. The arterial segments considered in this research were bounded by art upstream off-ramp terminal and a downstream signalized intersection. Due to the nature of the off-ramp terminal, only seven of the ten possible paths existed. The seven travel paths that were present in these study sections are indicated by a "Yes" in Column 7 of Table E-] . Travel paths that include a weave (i.e., change lane) are further categorized by their type. The weave type is defined by the difficulty of the weaving maneuver as expressed in terms of the number of turns and lane changes each weaving vehicle must make. Turns and lane changes increase We difficulty of negotiating a path because they have Me most potential for reducing the E-2

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vehicle's speed by inducing periods of deceleration, acceleration, and merging. The Type 1 weave is He most difficult because it entails He most tutus and lane changes. In contrast, the Type 3 weave is least difficult because it entails no turns and the fewest lane changes. The study sections considered for this research contain all three weave types. However, only the Type ~ weave was studied because of its characteristically high traffic volume In interchange areas. Further classification of weaving-related maneuvers is possible by including secondary characteristics such as the type of movement required at each end of the path and its associated traDic control, angle of entry, and the Dequency of significant acceleration or deceleration (due to a large speed change). Movement type describes how a vehicle enters or exits the weaving section (e.g., left, through, right). As shown In Table E-2, the type of traffic condom in combination with He angle of entry (or exit) has a different effect on He speed of the corresponding movement. Specifically, He speeds associated with a weaving maneuver paw will varsr depending on whether the path always, sometunes, or never requires acceleration at its entry or exit. -- ~a ~~ a Table E-2. Classification of weaving-related maneuvers based on movement type [:ntry/Exit Movement Left Right Through Traffic Controli Signal Signal Angle of EntrylExit: Sharp Frequency of Accel. at Entry Always Frequency of Decel. at Exit Always Flat Sharp Sometimes Always Sometimes Always Sometimes Flat Sometimes Stop Yield Uncontrolled Signal Uncontrolled Sharp Always Always Always Sometimes Always Flat Sharp Flat Sharp Always Never Flat Never Sometimes Never Sometimes Never ~ .1 Notes: 1 - Traffic control for Me entry or exit movement under consideration only. Dependent of the traffic control for Me other movements at the associated intersection. 2 - Angle of entry or exit is Me deflection angle in Me Gavel paw. Shard angles are about 90-degrees (turning radius of about 7.6 meters). Flat angles are about 30-de~ees or less (turning radius of about 30.5 meters or more). Through movements are considered to be straight (no angle). As indicated in Table E-2, some combinations of movement and control do not generally exist. In particular, stop and yield-controlled right-sum exits usually do not exist on arterials (a mining roadway for a r~ght-t~n exit is considered to be an ur~conholled exit). E-3

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Two maneuver speed models were developed In this research. A weaving speed mode] was created for predicting Path ~ speeds. An arterial speed mode} was created for predicting the speeds of Paws 5, 6, 7, and 10 combined. The weaving path, Path I, is a Type ~ weave from the off-ramp to the arterial Intersection left-turn exit. The arsenal paths, Paths 5, 6, 7, and 1 0, are arsenal through movement entries and are considered together despite the fact that technically three paths have a weaving component. Paws 3 and ~ were not studied in this research because they were not as problematic as the Path ~ weaving maneuver. Literature Review. Many researchers have conducted studies of weaving sections on freeways and highways 62, 3, 4, 5, 69, but little research has been done conceding arterial weaving. A weaving section is defined by Me HCM (~) as being formed by the crossing of two or more traffic streams where a merge is closely followed by a diverge. While the HCM acknowledges the existence of arterial weaving, it does not explicitly provide analysis procedures for this type of weaving, however, it does suggest that the freeway procedures can be used as an approximation. In a recent study of single-point urban interchanges, Messer and Bonneson (79 noted the turbulence Mat occurs on the arsenal cross street due to the high volume of weaving vehicles associated with interchange areas. They noted that this turbulence often restricted the capacity of bow the cross street and Me off-ramp. Schoppert et al (89 devised a methodology for quantifying the level of service In arterial weaving sections. Their methodology was based on the travel tunes (or speeds) of arsenal vehicles _ _- ~ , , . ~ ~ . ~ ~ ~a ~ passing through the weaving section. They proposed quantifying this level of service using origin- destination tables to quantify the number of large changes occurring In a weaving section. They hypothesized Mat Me number of lane changes would be directly related to the ramp volume. If so, the number of lane changes could be directly related to the travel times (or speeds) of arterial vehicles. No field data were collected by Schoppert to calibrate this methodology. Equal (99 studied weaving operations on arterial sections that were not bounded by signalized intersections and Hat had uncontrolled entry and exit maneuvers. He collected width, length, angle of approach, alignment deflection angle, speed, and volume data at twenty arsenal weaving sections and used this data to calibrate weave and non-weave speed models similar to those in HCM. He demonstrated how his models yielded better estimates ofthe weave and non-weave speeds than did He Leeway models provided In the HCM, even after he calibrated the HCM models wad his data. E.~.2 Data Collection The data for this study were collected at six study sites In four states. Each study site consisted of a section of urban arterial located between a freeway off-ramp and a closely-spaced signalized intersection. During each field study, flow rates, travel tines, travel distance, and stopped delays were measured for each of He seven paths identified by a "Yes" in Column 7 of Table E-1 . Three of the four types of traffic control (i.e., signal, yield, and uncontrolled) are represented in the database for He off-ramp r~ght-turn movement. E-4

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A video camera, elevated ten meters above the ground, was positioned at each end of the weaving section. The cameras faced toward each other in order to provide continuous surveillance of each vehicle entering the study section. The upstream camera was used to measure the entry time and movement type of each vehicle entering the study section. It was also used to measure the entry speed of each arterial vehicle. The downstream camera was used to measure the queue position arid exit time all vehicles at the downstream arterial Intersection. The cameras were synchronized In time to facilitate matching the entry and exit times for each vehicle. The field studies were conducted during the evening peak hour at each of the six sites. The study section was surveyed prior to each study to obtain its length and the width of venous cross section elements. The details of the data collection effort are provided in Appendix B. E.~.3 Mode' Development The weaving database was analyzed using We Statistical Analysis System (SAS) (109. In all cases, the speed and flow rate data were aggregated into averages based on 15-minute analysis intervals. The analysis of the aggregated data consisted of using linear regression techniques to calibrate several candidate maneuver speed model formulations. Two models were ultimately identified as having the best fit to the data. One model predicts the weaving maneuver speed (i.e., Path 1 speed) and the other model predicts the arterial maneuver speed (i.e., average speed of Paths 5, 6, 7, arid ~ 0~. The components of these two models are described below. Maneuver Speed Models. The speed models developed for this research were based on empirical formulations that adhered to logical boundary conditions. The form of each model is similar; however, there is some variation In the model variables due to the differences In the priority assigned to Me two vehicle classes (i.e., major and minor movement). The weaving speed model is: U = b U 1 e ( b2 (1 - Mu) ~w/3600) m,w O a where: U,72 w = average maneuver speed for weaving vehicles, m/s; Ua = average arterial speed entering the weaving section, m/s; Pa = probability of a weaving vehicle being unblocked (i.e., able to change lanes freely); If = average weaving flow rate, vph; arid bo' b,, b2 = regression coefficients. (Em) This mode} relates the weaving maneuver speed to Me average speed of arterial vehicles entering the weaving section. This latter speed was measured as a spot speed at the point of entry to the arterial weaving section. Hence, it represents He "desired" speed of arterial drivers for the given arterial volume conditions when Here is no weaving activity. In theory, He weaving maneuver arid arterial entry speeds would be similar when the weaving flow rate is negligible. However, the weaving speed would decrease as the weaving flow rate increases or when the arterial flow rate increases such Hat crossing opportunities decrease. The E-5

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mode! formulated In Equation E-] Incorporates this speed boundary and arterial flow rate sensitivity (via Pu). The regression coefficients ho and b' would logically be equal to unity; however, they are Included in the mode! to allow for slight deviations from theory in light of practical differences in Me speeds of weaving and arterial vehicles. The arterial maneuver speed model is similar in form to that of the weaving speed model. Its form is: U = b Ub4 e ( bs Fa/3600) m,a 3 a where: U', a = average maneuver speed for arterial through vehicles, m/s; Ua = average arterial speed entering We weaving section, m/s; Va = average arterial flow rate entering the weaving section, vph, and b3, b4, b5 = regression coefficients. (E-2) Like the rationale for the weaving maneuver speed model, the arterial maneuver speed mode} is based on the assumption Mat weaving speed should equal the arterial entry speed when the weaving flow rate is negligible. The variable for arterial flow rate is included ~ Me mode] rawer than weaving flow rate because it was found to be more strongly correlated with arterial maneuver speed. Logically, the two flow rates are positively correlated such Hat an Increase in the arterial flow rate would likely be associated with an Increase In weaving flow rate. Hence, He use of a surrogate van able for weaving flow rate that improved He quality was determined to be acceptable. Dependent Variable. The dependent variable considered in these models is the maneuver speed. Maneuver speed is defined as the average rutting speed and represents the ratio of travel distance to travel time within the study section. The distance (and timed are measured from the point of entry to point where the vehicle first stops in a queue, stops at the stop line, or crosses the stop line and exits the study section, whichever is shortest (or occurs first). Therefore, the corresponding maneuver distance (and timed vanes from vehicle to vehicle. It also vanes among He two maneuver types as He weaving maneuver often has to accelerate Dom a stopped (or slowed) condition whereas the arterial maneuver generally enters He weaving section at speed. The maneuver speed for a weaving or arterial vehicle is calculated as follows: d . m, U = . m,l where: = u,72 i = maneuver speed for vehicle i' m/s; cl,n i = maneuver distance for vehicle i, m, m,l L - ~ w q,i (texittent~y)i (texit tStop) E-6 ~-3)

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tin i = maneuver time for vehicle i, see; [a = distance between the off-ramp entry point and Me stop line ofthe downstream Intersection (i.e., the length of the weaving section), m; it i = length of queue joined by vehicle i, m; and tj = time of eventj for vehicle i (I = entry, stop, exit), sec. It should be noted that the maneuver speed is based on We tune and location of the vehicle when it stops for theirst time. No subsequent periods of motion, such as when moving up in or discharging Tom a queue, are incorporated into the maneuver speed. The maneuver speed computed with Equation E-3 does not explicitly account for the extra time used during acceleration or deceleration at the beginning or end of the maneuver. This distinction is particularly important for the weaving maneuver. As indicated in Table E-2, the weaving movements considered in this analysis cart "always," "sometimes," and "never" experience acceleration (or deceleration) upon entry (or exit), depending on their traffic control and angle of entry. As a result, there is more variability in the weaving maneuver speed data than In the arsenal maneuver speed data. Independent Variables. One of the independent vanables used in the weaving maneuver speed mode! is the "probability of a weaving vehicle being unblocked" Pu. This variable relates to the portion of tune Nat the end of the off-ramp (i.e., the beginning of the weaving section) is not blocked by the passing of the arsenal traffic stream or the spilIback of a downstream queue. Blockage by He passing stream is represented by the formation of platoons in the arterial traffic stream (induced by signalization or random bunching) which can delay the weaving vehicle. A distinction is made in the computation of Pu based on the length of the weaving section. Specifically, weaving sections are referred to as "short" or "Ion"" depending on the nature of the weaving maneuver. A "Ion"" weaving section is defined as a section Hat has sufficient length to allow a weaving driver to weave across the arterial one lane at a tune. The minimum length of a "Ion"" section is computed as the product of He length needed for a s~ngle-lane lane change (estimated as 90 meters) and the number of arsenal traffic lanes being crossed (excluding He first). If this miIiimum length is not available, then the section is referred to as "short." This designation implies Hat the weave maneuver requires the simultaneous crossing of all arterial larles (in the subject direction) using more of a "crossing" than a "lane-changing" action. Based on He preceding definitions, Pu for short weaving sections is based on there being a gap In the arterial traffic stream Hat is sufficiently large that the on-ramp driver can cross all arsenal traffic lanes at one time. For long sections, Pu is based on there being an acceptable lane-charlge gap in each lane as it is crossed one lane at a time. An equation was derived to estimate Pu based on the preceding definition using an expected value approach and art assumed random arrival distribution; however, the resulting equation was intractable and felt to be overly complicated. Thus, a simplified form of the mode} was developed based on a queueing theory representation. This equation is: E-7

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/ p = a where: 1 _ _| (1 -I ) + | 1 --| I 2 0 (E,-4) Pu = probability of a weaving vehicle being unblocked; Va = average arsenal flow rate entering the weaving section, vph, 51 = saturation flow rate per lane under prevailing conditions (~ 1,800), vphpl; N. = number of arsenal through lanes In the subject direction, lanes; IL = indicator variable (1.0 if D,,, W > 90 (Nt - 1)' 0.0 otherwise), Do w = average maneuver distance for weaving vehicles (= [a - [q a), m; arid [q w = average length of queue joined by weaving vehicles, m. It should be noted that Pu is equal to 0.0 when the average queue length equals Me length of the weaving section (i.e., when Dn w is effectively zero). In this study, the length of the queue Mat was joined was measured for each weaving vehicle. In most cases. the Queue was joined when it was near its cyclic maximum because most weaving , , ,, ,, ~ .. .. . ^. .. . . . .. . .. . .. .. ^^ ~ ~ .. actlvlcy occurred alter the arsenal through movement nao passed by the on-ramp. ot course, me queue would continue to grow as other weaving vehicles joined it. For practical applications of Equation Em, [q w cart be conservatively estimated as Me average maximum queue length per cycle at the downstream intersection based on the arsenal flow rate entenug the weaving section Va. In this regard, the following equation cart be used to estimate the average queue length joined by a weaving vehicle: where: V r L a v L = x q,w V 1 - a slN, 3600 r = effective red time for the downstream intersection through movement; see, and [v = average lane length occupied by a queued vehicle (see Equation C-45), mJveh. (Ens) A second independent variable used in the weaving speed model is the average weaving flow rate Vw. This flow rate represents the number of vehicles that perform Me Path ~ weave during the analysis period, it is a subset of the number of vehicles that enter the arterial via Me off-ramp. The probability of Mere being a brocade condition (i.e., ~ - Pu) and the average weaving flow rate Vw are multiplied together to obtain the expected number of weaving vehicles that will be blocked by arterial traffic. This product was included in the weave maneuver speed model because the maneuver speed was found to decrease as the number of blocked vehicles increased. E-8

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E.~.4 Database Summary Table E-3 shows the range of values In the weaving database for the independent arid dependent variables included in the maneuver speed models. The variables are listed according to Me applicable model. This table demonstrates the range over which each mode} is considered valid. In general, the models were calibrated with sites having two or three arterial Trough farces fin Me subject direction), closely spaced intersections, and a wide range of arsenal flow rates. Table E-3. Range of independent and dependent variables Model | Variable | Variable Name| Units | Minimums | Maximum] Both' | N. Arterial through lanes: the subject direction | | 2 | 3 1. | Lw Length of the weaving _ | U., Average arterial entry ~ reed | rn/s | 8.9 | 21.8 | | Va Avg. arterialflow rate Itering the weaving section | vph | 640 | 1,924 | V`,/N, Average arterial flow rate per lane vphpl 320 676 Weaving | Iq,, w Queue length joined b' _ 60.0 ~ | Pu Probability of a weaving ~[ | Vw Average weaving flow ate | vph | 88 | 270 |[ | dm w Maneuver distance for . weaving vehicle |[ | tm w Maneuver time for a u aving vehicle | s | 4 | 62 |[ Am w Weaving maneuver speed m/s 2.8 18.7 Arterial | Ida 1 Queue leng~ljoinedb an artenalvehicle | m | 0.0 | 209.7 |[ Am' a Maneuver distance for an arterial vehicle m 18.0 265.2 | tm, a Maneuver tune for an ~[ | Am, a Artenal maneuver spe 1 | m/s | 1.9 | 23.4 | Notes: 1 - Variables used by bob Me weaving and arterial maneuver speed models. 2 - All average values are based on a 1 5-minute intervals. Table E-3 illustrates the wide range of conditions over which the maneuver speed models are applicable. Specifically, the weaving maneuver speeds range from 2.8 to 18.7 mJs and the arsenal maneuver speeds range from I.9 to 23.4 m/s. These ranges do not contain zero because, by definition, a vehicle could not complete the subject maneuver without having some speed. The low speeds In these ranges were observed during spilIback conditions where the subject vehicle creeps forward to join the queue (and thus complete its maneuver). The maxim speeds in the two aforementioned speed ranges are about equal to the maximum arterial entry speed. This agreement was generally observed during low off-ramp volume conditions. The maximum arterial maneuver speed, a running speed, is slightly higher Mail Me E-9

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maximum arterial entry speed, a spot speed, because unimpeded arsenal vehicles could enter the study section at speed and then accelerate along We length of the section to a speed higher than Me entry speed. The minimum value of the arterial entry speed range was observed Ruling conditions of extensive downstream queuing such Mat the arsenal vehicles were moving slowly as they decelerated to join the back of queue. E.~.5 Calibrated Models The model forms developed in a previous section were calibrated using Me weaving database, as summarized in Table E-3. The SAS analysis regression procedure was used to determine the regression parameter coefficients for each model. The resulting calibrated weaving maneuver speed mode! is: U = 3 .74 1 U 0 408 e (~~ l-04s (~ - pub Fw/36oo) m,w a The resulting calibrated arterial maneuver speed model is: U = 1 986 U0.717 Ed m,a a {-0.634 Fa/3600) where: U,72 w = average maneuver speed for weaving vehicles, m/s; and U,72 ~ = average maneuver speed for arterial through vehicles, m/s. (E-6) (Elk Table E-4 lists several statistics that indicate the quality-of-fit for each maneuver speed model. As these statistics suggest, Me weaving maneuver speed model (i.e., Equation E-6) accounts for 16 percent of Me variability in Me maneuver speed data Likewise, Me arterial maneuver speed mode! (i.e., Equation E-7) accounts for 22 percent of the variability in the data. In all cases, Me independent variables included In Me model were fourth to be strongly correlated with maneuver speed. All tests were conducted with a 95 percent level of confidence. The root mean square error (or standard error) of each model, combined with the number of observations, yields a minimum precision of+0. 10 and ~t0.16 m/s for estimates of Me average weaving arid arterial maneuver speeds, respectively. Table Em. Maneuver speed mode! statistics Maneuver Speed Model | Observations | R2 | Root Mean Square Error | Precision | Weaving 1 421 1 0.16 T 2.02 m/s T to 10 Is ~ Artenal | 324 | 0.22 7 2.94 m/s | +0.16 m/s | d E-10

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The low R2 values listed in Table E-4 are due partly to limitations of Me models and partly to random sources. As discussed previously, these models do not include the acceleration or deceleration component of the maneuver in the maneuver speed calculation. This omission has a larger impact on the weaving maneuver speed model because many weaving vehicles accelerate from the off-ramp (i.e., they arrive on the red indication or have to yield) while others enter at speed. In contrast, arterial vehicles almost always enter the study section at speed. Another factor that affects the R2 of the arterial maneuver speed model is the inclusion of vehicles on several paths (i.e., Paths 5' 6' 7, arid 10). Future enhancements to these models to account for acceleration' deceleration' and individual paws would likely improve We quality-of-fit. Figure E-1 compares the weaving maneuver speeds predicted by Equation E-6 with Rose measured in the field. Each data point represents the average often observations (sorted by predicted speed) in order to reduce the overlapping density of 421 observations. It should be noted that individual observations were used in the regression analysis whereas the averaged data were used only for the graphical examination of trends. The data in Figure E- 1 indicate that there is a general trend of agreement between the predicted and measured speeds over the range of measured speeds. Predicted Maneuver Speed (m/s) (Legend: A = 1 obs, B = 2 obs, etc.) ~ (Each data point represents the average of 10 obs) 11 + 10 8 + A AA A A A AA A A AA A A B AAA A B A A A A AA B A A AA A A A A AA A A 4 6 8 10 12 14 Measured Maneuver Speed (m/s) Figure Eat. Predicted versus measured weaving maneuver speed. Figure E-2 compares Me arsenal maneuver speed predicted by Equation E-7 with that measured in the field. Each data point represents the average of ten observations (sorted by predicted speed) in order to reduce the overlapping density of 324 observations. As with the preceding figure, there is a general trend of agreement between the predicted and measured speeds. In fact, the trend of agreement is probably a little better Man Mat for Me weaving speed model. Em!

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Predi cted Maneuver Speed (m/s) (Legend: A = 1 obs, B = 2 obs, etc. ) ~ (Each data point represents the average of 10 obs) 14 + A 12 + 10 + 8 + A | A 6 + A A AA A A AB A AA A AA A A AAA A AA A A A A A A A 6 8 10 12 14 Measured Maneuver Speed (m/s) Figure E-2. Predicted versus measured arterial maneuver speed. E.~.6 Sensitivity Analysis The effects of arterial flow rate, weaving flow rate, arterial traffic lanes, and weaving section length on maneuver speed are examined In this section. Initially, the two maneuver speed models are compared to one another. Then, a sensitivity analysis is conducted for each model. Figure E-3 illustrates Me elect of arsenal flow rate on weaving and arterial maneuver speed. This figure shows the behavior of both models when all over factors are held constant. The values selected for these factors represent their respective average values as found in the database. The range of flow rates over which the two models are compared is larger than We corresponding range In the database. This extension was undertaken to show the overall behavior of each mode] when extrapolated to extreme (but realistic) values. The trends in Figure E-3 show that bow models predict art exponentially decreasing maneuver speed with Increasing arsenal flow rate. This trend is somewhat consistent with Me traditions speed-flow relationship for uninterrupted traffic streams in un congested conditions. This figure also shows Mat Me arsenal maneuver speed is always higher than Me weaving maneuver speed for Me same flow rate. This trend is reasonable since Me arterial vehicles enter Me weaving section at speed while Me weaving vehicles often must accelerate hom a stopped (or sIowed) condition when departing Me off-ramp. The trend toward convergence of the two models at higher flow rates is also reasonable as the weaving maneuver speed should approach Me arterial maneuver speed as the capacity of Me weaving section is neared. E-12

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Maneuver Speed, m/s 12 10 8 4 2 Ua = 13.4 m/s It- 2 1~=0 Vw = 170 vph 0 500 1000 1500 2000 2500 3000 3500 Average Arterial Flow Rate, vph Figure E-3. Effect of arterialflow rate on weaving and arterial maneuver speeds. Figures E4, E-S, and E-6 illustrate Me effect of arterial lanes, weaving flow rate, and section length, respectively, on weaving maneuver speed. In each figure, one factor is vaned while all others are held constant. In all cases, We average arsenal entry speed Sa is held constant at 13.4 m/s. Also, the range of flow rates used in these figures is representative of Mat found In the database. Figure E4 illustrates Me relationship between weaving maneuver speed and arterial lanes. This comparison applies to the situation where Me weaving section can be described as "short" relative to Me distance available for the weaving maneuver. In general, the weave in a short section is descnbed as a simultaneous crossing of all arterial lanes at one time. As Figure EM indicates, the weaving maneuver speed is higher for arsenals with Tree lanes In Me subject direction, as compared to those with two lanes. This trend is the result of two effects. First, it reflects the elect of the acceleration component relative to the distance traveled. In general, the average speed will be higher when the distance traveled during the weave (i.e., three lanes versus two lanes) is longer such that the effect of Me initial acceleration becomes less significant on the overall travel dine. Second, it reflects the elect of lower arterial lane flow rates. Presumably, the lower lane flow rates yield larger headways which would be less of a hindrance to a weaving vehicle. Figure E-S indurates the relationship between weaving maneuver speed and weaving flow rate. All other factors being equal, the higher the weaving flow rate, the lower the average weaving maneuver speed. This trend is reasonable and suggests that the capacity of the weaving section is dependent on the combined arsenal and weaving flow rates. E-13

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10 9 8 7 Weaving Maneuver Speed, m/s Ua = 13.4 m/s 1'=0 Vw = 170 vph 3 Lanes 600 800 1000 1200 1400 Average Arterial Flow Rate, vph Figure E-4. Elect of number of arterial lanes on weaving maneuver speed. Weaving Maneuver Speed, m/s 8 7 6 1600 1800 Ua= 13.4m/s Nt = 2 lL=o 600 800 1000 1200 1400 1600 1800 Average Arterial Flow Rate, vph Figure E-S. Effect of weaving flow rate on weaving maneuver speed. E-14

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Figure E-6 illustrates the relationship between weaving maneuver speed and the length of the weaving section. All other factors being equal, the weaving maneuver speed is higher In a "long" weaving section than it is in a "short" section. This trend is reasonable since a vehicle can attain a higher speed when it has a longer distance In which to maneuver. Weaving Maneuver Speed, m/s ~ t~n9~, an 9 8 6 Ua = 13.4 m/s No = 2 Vw= 170vph 1 - 90~_ 600 800 1000 1200 1400 1600 1800 Average Arterial Flow Rate, vph Figure E-6. Effect of weaving section length on weaving maneuver speedl. E.~.7 Summary An arsenal weaving section Carl be classified by the maneuver (or travel path) Trough it, the type of (or difficulty associated with) the weave, and the characteristics of entry and exit movements for the weave-related travel paths. These factors can be used to explain the behavior of vehicles In the different travel paths and their corresponding maneuver speed. The results of the literature search indicated that relatively little research has been devoted to the problem of arterial weaving. While the HCM (1) methods may have application to the analysis of arterial weaving sections with uninterrupted flow conditions, they do not appear to be sensitive to the effects of up and downstream signals on arterial weaving performance. This research was undertaken to quantify the effects of traffic signals on the speed of weaving and arterial traffic streams. The results of this research are focused on a type of weaving Mat is commonly found on Me arterial cross street in interchange areas; however, Me modeling anDroach is also applicable to any arterial weaving section in the vicinity of traffic signals. E-IS --I err

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Two models were developed in this research to predict the maneuver speed of vehicles passing through an arsenal weaving section. Both of these models include the average arterial entry speed as an independent variable. This speed represents the "desired" speed of arterial drivers for the given arterial volume conditions. It is the speed that would be maintained when there are no weaving vehicles. The mode] calibration revealed that both the weaving and arterial maneuver speeds are dependent upon the arterial flow rate. The mode} calibration also indicated that weaving maneuver speed is dependent on the weaving flow rate, weaving section length, and the probability of Me weaving vehicles being blocked. Separately, both models show strong correlations with the measured maneuver speeds and can be used to estimate the mean maneuver speed with a precision of less than +0.2 m/s. A sensitivity analysis using the calibrated models indicated that both weaving and arterial maneuver speeds decreased with increasing arterial flow rate. This trend reflects the increased turbulence between the arsenal and weaving movements associated with an increase in arterial flow rate. The sensitivity analysts also indicated that weaving maneuver speed decreased with increasing weaving flow rate and shorter weaving section length. These two models can be used to predict Me operational performance of other weaving sections in interchange areas with characteristics similar to those studied. While these models are limited to a particular weave maneuver (i.e., Path ~ ), similar models could be developed for different paths and characteristics. It is recommended that future research be conducted to enhance the models developed in this research to include other travel paths and the effects of acceleration and deceleration at the entry and exit points. E-16

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REFERENCES I . Special Report 209: Highway Capacity Manual, 3rd ea., TRB, National Research Council, Washington, D.C. (1994~. 2. 3. Ostrum, B.K., Lehman, L., arid May, A.D., Suggested Procedures for Analyzing Freeway Weaving Sections. In TransportationResearch Record 139S, TRB, National Research Council, Washington, D.C. (1993) pp. 42-48. Vermijs, R., and Schuu~man, H., "Evaluating Capacity of Freeway Weaving Sections and On- Ramps using the Microscopic Simulation Mode} FOSIM." In Proceedings of the Second International Symposium on Highway Capacity, Volume 2, (Ed: Akcelik, R.), ARRB Transport Research Ltd. Vermont South, Victona, Australia (1994) pp. 651-671. Windover, J.R., and May' A.D., Previsions to Level D Methodology of Analyzing Freeway Ramp Weaving Sections." In Transportation Research Record 1457, TRB, National Research Council, Washington, D.C. (1994) pp. 43-49. Fazio, J. "Geometnc Approach to Modeling Vehicular Speeds through Simple Freeway Weaving Sections." ITE Journal Institute of Tran~nortation Fn~ineer~ Washington n (April ~ 988) pp. 41-45. ~--D- - ----- ~--O~ _ _ __ _ 6. Wang, M., Cassidy, M.J., Chan, P., and May, A.D., "Evaluating the Capacity of Freeway Weaving Sections." Journal of Transportation Engineering, Vol. 119, No. 3, American Society of Civil Engineers, New York, New, York (1 993) pp. 360-384. 7. Messer, C.J., Bonneson, J.A., Anderson, S.D., and McFarland, W.F., NCHRP Report 345: Single Point Urban Interchange Design and Operations Analysis, TRY, National Research Council,Washington,D.C. (1991). 8. Schoppert, D.W., Kittelson, W., and Shapiro, S., Quality of Flow in Urban Arterials Phase I. Report No. FHWA-RD-78-l99,Federal Highway Administration, Washington, D.C. (1978). 9. Iqbal, M. S., "Analytical Models of Weaving Area Operations Under Nonfreeway Conditions." ITE Journal, Vol. 65, No. 7, Institute of Transportation Engineers' Washington, D.C. (July 1995). 10. SAS/STAT User's Guide, Version 6, 4~ ea., SAS Institute, Cary, Norm Carolina (1990). E-17

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