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CHAPTER 2 FINDINGS 2. 1 SUMMARY OF EXISTING CONDITIONS A comprehensive evaluation of the state-of-the-artin areas related to interchange design and traffic operations was conducted as part of this research. This evaluation consisted of a survey of practitioners and a review of existing traffic models. The focus of this evaluation was on issues underlying the design and operation of interchanges in urban or suburban areas. More specifically, the focus was on issues related to the signal-controlled ramp terminals and traffic flow along the cross street through these terminals. Consideration was also given to the relationship between the interchange ramp terminals and any adjacent, closely-spaced signalized intersections. 2.1.! Survey of Current Practice The intent of this survey was to gain insight into the current practices arid concerns of engineers who are responsible for interchange traffic operations. The survey was conducted in two stages. The first-stage survey was intended to obtain basic types of interchange-related infonnation such as common interchange types, traffic flow problems, and operational analysis techniques. The second-stage survey was designed to obtain more detailed information about interchange operations. This survey asked the respondent to select one interchange that they were familiar with and then respond to detailed questions about its operation and any steps taken to alleviate flow problems at this interchange. The respondent was also asked to describe the analysis techniques (or computer models) Hat they had successfi~ly used to evaluate interchange operations. The findings from these two surveys are summanzed in this section. A more detailed discussion of He survey findings is provided in Appendix A. Distribution. The first-stage survey was sent to more than 2,400 transportation engineers in the U.S. and abroad. The members of the American Association of State Highway and Transportation Officials' (AASHTO) subcommittees on traffic engineering, on design, and on transportation systems operation were specifically targeted. A large number of the Institute of Transportation Engineers ' (ITE) Urban Traffic Engineers Council and its Consultants Council were also included in the survey. In addition, several hundred surveys were sent to over selected members of ITE. After a review of each returned questionnaire, a total of 350 first-stage questionnaires were deemed completely responsive and valid for furler processing. Overall, there were 146 responses from the public sector which included state, city, and county highway agencies. Seventeen responses were received from outside of the United States. Responses were also received from ~ 87 consultants in 23 states. 2
The second-stage survey was sent to 1 90 individuals who responded to the first survey. A total of 3 1 completed surveys were returned, representing a 16 percent response rate. Of these surveys, 29 were deter~ninedto be valid responsesin the context that they addressed the interchange types and issues described in the survey. Overall, 21 states are represented among the 29 valid returned surveys. Findings. The first-stage questionnaire consisted of six questions that were primarily of the multiple-choice type. The second-stage questionnaire consisted of eleven questions, several of which had follow-up questions. In general, these questions inquired about the kinds of interchanges being used or constructed, the type of signal control used, the types of operational problems found at existing interchanges, and the methods used to evaluate and mitigate these problems. The responses to the questions on both questionnaires are summarized in the following paragraphs. The diamond interchange was found to be the most commonly used interchange configuration. This trendis likely due to the reduced right-of-way end construction costs associated with diamond interchanges relative to other configurations (e.g., partial cloverleaf). The distance between the diamond interchange ramp terminals can vary from 60 meters in densely-developed urban areas to 240 meters in suburban areas. In contrast, the distance between ramp terminals associated with a partial cloverleaf interchange generally range from 180 to 280 meters. Regardless of configuration, the interchanges that tend to experience operational problems are those with relatively short distances between the ramp terminals or between one terminal and an adjacent signalized intersection. These close spacings often lead to problems such as queue spillback, flow turbulence due to weaving, and left-turn bay overflow. Queue spillback represents the blockage of an upstream intersection by a traffic queue from a downstream intersection. The interchanges described by the survey respondents as having operational problems had ramp terminal distancesin the range of61 to 410 meters. The distance to the adjacent intersection for these same interchanges was in the range of 46 to 436 meters. The survey indicated that most interchanges have two semiactuated signal controllers, one controller for each ramp terminal. The two controllers are typically coordinated to facilitate progressed traffic flow along the arterial and minimum queuing on the street segment between the two terminals. Some interchanges have pretimed control with either one or two controllers. The few diamond interchanges that were pretimed and had one controller used four-phase-with-overlap phasing. Only a few interchanges had fi~ll-actuated, uncoordinated control. The distribution of operational problems found in interchange areas is shown in Figure 2. As this figure indicates, the operational problem that occurred most frequently is queue spillback at some junction on the cross street. This problem was generally related to the spilling back of a queue from a downstream ramp terminal or intersection into an upstream terminal or intersection. This spillback tended to significantly reduce the car acitY of the upstream junction. Also included in this ~Or i- - -a category is spillback stemming from a left-turn bay overflow. 2 - 2
Percent of Responses Spillback on Cross Street Other Spillback Poor Signal Timing Weaving-related Unbalanced Lane Volumes 0 10 20 30 40 50 Figure 2. Distribution of operational pro bZems in urban interchange areas. The reported flow problems related to queue spillback between the ramp terminals were generally associated with tight or compressed diamond interchanges. Flow problems related to queue spillback between a ramp terminal and adjacentintersection were more commonly associated with conventional (wide) diamond interchanges and partial cloverleaf interchanges. The wide spacing between ramp terminals for these interchanges tends to be associated with shorter distances between these terminals and the adjacent intersections. By design, the single point diamond configuration does not experience spillback between its terminals; however, it can experience spillback between it and the adjacent intersection during high-volume conditions. Other frequently cited problems at interchanges include unbalanced large volumes on the ramp terminal approaches, flow turbulence due to weaving, and a lack of effective signal coordination between the ramp terminals. The unbalancedlane volume problem stems from frequent driver propositioning for downstream turns in interchange areas. Drivers desiring to turn left (right) at a downstream intersection tend to move into the inside (outside) lane of a multilane lane group at the upstream intersection. This propositioning effectively reduces the capacity of the lane group by leaving some traffic lanes underutilized, even during high volume conditions. The weaving maneuver that is predominate in interchange areas is the off-ramp right-turn movement that weaves across the arterial to make a left-turn at the next downstream signalized intersection. This maneuver typically has a high volume associated with it such that considerable turbulence is created on the cross street. This turbulence results in significant speed reductions to the nonweaving traffic movements. 2 - 3
The lack of effective signal coordination along the cross street in interchange areas occurs for a variety of reasons. These reasons generally include incompatibility ofinterchar~ge phasing with the cross street system coordination plan and institutional barriers (i.e., the state operates He interchange and the city operates the adjacent intersection). The lack of efficient signal coordination can lead to increased delays and stops and precipitate the occurrence of spillback when the ramp terminals or intersections are closely spaced. A wide range of methods were described by the respondents for alleviating the aforementioned operationalproblems. Geometric improvements were most commonly cited. These improvements included adding a second left-turn lane or an additional through lane to the cross street. Many respondentsindicated that improved or updated signal timing and coordination helped mitigate some operationalproblems. These latterimprovements were often obtained through the use of existing software-based traffic analysis models. In general, software programs are more frequently used than manual methods for evaluating interchange traffic operations. The most commonly used software program is the signalized intersection analysts procedure included in the Highway Capacity Software (HCS). In general, this procedure was used to evaluate the individual ramp tenninals after appropriate calibration of the progression adjustment factors to account for nearby intersections. The popularity ofthis program may be due to its widespread acceptance by transportation engineers, its consistency with the methods described in Chapter 9 ofthe Highway Capacity Manual (HCM) (3j, and the relative ease with which it can be used. The most frequently cited strength of this program is that it is easier to use than multiple-intersectionsoftware programs (e.g., PASSER II, TRANSYT-7F,NETSIM, etch. Ofthe various software programs available, TRANSYT-7F was cited by nearly half of all the respondents as being used! for analyzing interchange operations. This finding may be due to the fact that TRANSYT-7F is sensitive to the proximity of adjacent ramp terminals or signalized intersections in its signal timing optimization routine. Another software model, PASSER- was also cited by many of the respondents as being a usefi~] too] to analyze arterial traffic flow through interchange ramp terminals. In the case of this latter model, the large response may be due to the fact that PASSERS optimizes signal phasing based on progression analysis. NETSIM was used by some of the respondents. This program was noted to be the only one that modeled queue spilIback and congested flow conditions. The respondents also noted that the existing software programs had some weaknesses that limited their ability to accurately mode} interchange traffic operations. The weaknesses cited for the HCS program (i.e., the HCM Chapter 9 procedure) were that it did not accurately model the effect of closely-spaced upstream intersections and that it did not yield queue length estimates. The weaknesses cited for PASSER Il were Hat it did not provide progression solutions for left-turn movements, did not consider queues when determining progression, did not allow the user to enter some types of interchange phasing, and did not fillly consider right-turn demand. NETSIM was noted to be very time consuming to use due to its microscopic simulation formulation. A couple of respondents nosed that none ofthe programs dealt explicitly with the coordination of a downstream 2 - 4
ramp meter with the ramp terminal. Further evaluations of these computer-based models, primarily for research applications in this project, watt be presented later in this chapter The survey found that the most commonly selected measure of effectiveness (MOE) for evaluating interchange traffic operations was traffic signal delay, followed by spilIback frequency, and volume-to-capacityratio. Delay was likely chosen by the practitioners because it represents the most tar~gible measure of effectiveness that is also comprehensible by the motoring public. After delay, queue spilIback frequency was the next most frequently cited MOE by the respondents. 2.~.2 Field Survey of Interchange Operations The research team studied over a dozen service interchanges dunug the field studies and spent marry hours observing traffic operations at the sites. Comparisons could be rapidly made among interchange types, types of operational problems observed, and the hypothesized probable cause of these problems. Our summary of these field sites having congested operations are noted below: Designlife of interchange probably exceeded, overall traffic demand exceeded interchange capacity during rush hours. Due to growth in suburban areas, older four-lane crossing arterials now need to be six lanes. The average daily traffic on many of We four-lane crossing arterials exceeded 30,000 ADT. Many "next" downstream signalized intersections along Me crossing arterial experience high access demands toffrom the Leeway (interchange) and are routinely too closely spaced to provide good operating conditions. Better access management, intersection spacing and design policies are needed. Traffic management of quelling and spilIback is difficult at interchanges due to high volumes and high percentages of turning traffic having typical lane distribution problems. Some approaches along the crossing arsenal and within the interchange can have almost constant demand within Me cycle, so queuing can not be mitigated using traditional signal coordination techniques. Four-quad parclos would seem to be more susceptible to constant demand conditions within the interchange because oftheir free flowing loop ramps. All parclo interchanges,including the four-quad AB that exits both left and right turns from the same side of a cross arterial approach, may experience high lane imbalances ofarrival flow on that side ofthe street, even at intersections along the crossing arterial upstream of the interchange. Many ofthe congested interchanges noted above had a predominant number of single-lane left turn bays within the interchange and/or have single lanes assigned on approach ramps 2 - 5
at ramp terminals to serve left and/or right turning movements. Many approach ramps were single lane with only a modest flare to a two-lane approach at the ramp terminal. 6. e Traffic actuated operations on high-volume, single-lane movements appear to result in excessively long cycles that reduce the overall input capacity of the interchange. Protected- permissive left-turn operations, while reducing delays during moderate traffic, loses capacity during rush-hour conditions and, consequently, cannot be depended upon to provide significant capacity increases during these critical times. 7. Most traffic control strategies employed appear to be based on undersaturated flow conditions and may lose efficiency when oversaturated conditions arise. Management of queue spillback to mitigate the onset of congestion is needed together with the need to transition to downstream bottleneck control strategies once oversaturation has occurred. 2.2 SURVEY OF EXISTING TRAFFIC MODELS The first-round survey inquired about the types of analysis methods used to evaluate (not optimize timing) signalized interchange traffic operations. In general, software models were more frequently used than manual methods. The most commonly used software method is the Highway Capacity Software (HCS). PASSER II and TRANSYT-7F were also found to be frequently used in practical engineering applications. However, research applications usually require more complex computer simulation models than application-specific models like HCS and PASSER II. Computer simulationis a viable method with which to analyze situations which may occur at signalizedinterchanges,but for whatever reason are difficult to witness or collect date from field studies. This investigation was primarily based on literature and manuals for each model, and discussions withindividuals familiar with the models. Experience with each model is arguably the most informative method of discovering what a program can and cannot do. Time constraints always limit the depth with which each ofthese models can tee investigated. A list ofthe simulation models investigated is included in Table l. Simulation models can be described by their analysis approach, basis, objective and outcome. A model's analysis approach is either macroscopic or microscopic. A macroscopic simulation model is one in which the traffic stream is moved as one homogenous aggregate group, whereas a microscopic simulation model is vehicle specificin which each vehicle moves as its ownidentifiable entity. A simulationmodel's analysis basis is either empirical or analytical. The analysis basis refers to the algorithm on which the model is based. An empirical model is based on field observations or data and\or previous experience. Analytical models use mathematical formulas based on theoretical relationships. The analysis objective refers to the purpose of the simulation model. Models simulate traffic given certain geometric constraints, and/or optimize some specific traffic parameter. Lastly, a simulation model is described by its analysis outcome, which is either stochastic or deterministic. A stochastic model attempts to model human behavior by providing a 2 - 6
degree of randomness to its methodology. In this way the output is never the same given a set of inputs. Given the same Inputs, a detennin~stic model would have the same output every time the same data is input. Each model's analysis is also given in Table I. Table I. Simulation Models Examined Model FREFLO . . l _ Analysis i| Description ~Approach | Basis | Oboe ctive | Outcome ' 1 Freeway Macroscopic | Analytical | Sim ration Simulation Freeway and Microscopic Analytical Simulation or Surtace Street Optimization Network Model Freeway and Macroscopic Analytical Simulation Surface Street Network Model Freeway and Microscopic Analytical Simulation or Surface Street Optimization Network Model Urban Street Microscopic Analytical Simulation Network Model Signalized Macroscopic Analytical Optimization Diamonci Interchanges Signalized Multi- Macroscopic Analytical Optimization ~ Intersections | Signalized Multi- Macroscopic Analytical Simulation or Intersections Optimization Isolated Microscopic Analytical Simulation Intersection ~Analysis r COmplete Macroscopic Empirical Simulation Implementation of 1985 HCM Freeway Weaving Macroscopic Empirical Simulation Analysis , 1 Deterministic INTRAS 1 980 Stochastic CORFLO Deterministic INTEGRATION Version 1 5 Unknown · 11 NETSIM Stochastic PASSER 111 1 990 Deterministic PASSER 11 1 990 TRANSYT-7F TEXAS Version 3.11 HCS Deterministic Deterministic Stochastic Deterministic FREWEV Version 1.1 Deterministic 2 - 7
2.2.1 Input and Output Obviously, each mode} has a required amount of input. Mar~y models have options that may or may not be important to ~is project, and therefore ~e input for some data is optional. An abbreviatedlist of model inputsis included~n Table 2. The table indicates~e inputs (bosh requ~red and optional) by each model. The list is not all-~nclusive. Model names were abbreviated in Table 2, but they are presented in ~e same order as they are listed in Table I. t Table 2. Mode! Inputs Input Model | FRE | INT | COE. | ITG | NET | PIII | PII | T-7F | TX | HCS | WEV lus Stop Delay 2apaciiy ~X ~ X ~X ~ X ~ X ~river & Vehicle X X 'haractenstics l l l l l l I :: ~rades ~X Horiz. Curve Data X Incident Data X ntersection Spacing l ~l ~I X | X ,ink Lengths | X | X | X | X | X | X | ,oad Factors Numb~er of X X X X Approaches Numb~er of I ~neS X X XX X X X X X X )-D Travel Pauerns l l l | X | X l l 'edestrianAcolation l l l | X X 'ercentageof l ~X l l l l l X |Vehicle Types Ramp Metering Rate X X Rte. Detouring Data X Saturation Flows X X X Signal & Sign ~| X l | X | X X ~ X X ~ X X Control Parameters Simulation X X X X X X X peed l l l l l l | average X X X X free flow X X X X X Through Volumes X X X X X X X X X X r~ng percentages ~ x ~ ~ x ~ ~ ~ ~ ~ ~ F ~Turning Volumes X X X X X X X X . Vertical Curve Data l | X l l l l l l I | X X X X X X 2 - 8
The ou~ut available for each model investigated is ~ncluded ~n Table 3 The table does not include all output for every model. FREFLO, INTRAS, CORFLO, INTEGRATION, NETSIM, and TRANSYT-7F display most of its output on a link specific basis. TEXAS Model provides output by lane, approach, and for the ~ntersection as a whole. Table 3. Model Outputs OIl~Ut ~ _ Degree of Saturation | I r | | x | x | x | I I queue X X X X X smpped l l l l | X | l l | X Density I X _ L x I x ~ || uel Consumpd m | | X | l | | X | X | I I [ Graphical Simulation ll X T I x Level of Service L _ Il l X := Lane Changes l l l l l l l l l I 3-D Chart T | x I 1 X I I I ! I I I 11 Optimal Ti~ng X X X _ Person tmiPleSSes | X l | X ~1010 Queue Length l | ? I rX | X | | X | X | Saturation Flow l l l l l l | X | | X | ime mean X X X space ~nean | l l I ~ ~ ~ ~ 11 rime Space Diag. I I I I I I x I x I I I I Il rrave1 T v~eear~gveehm | X | X |~ 1 1 L 11 ~s XX X X X X ~ Volume 1 l I X TX I I I I x I I I ~ 2 - 9 x x
2.2.2 Summary of Mode! Capabilities An important decision in this project is what models should be used and how should they be used for research purposes. All the models investigated have some link to interchange and arterial operations. However, they may be used to develop relationships for situations where it would be difficult to collect field data. As a result, a list of geometric and operational characteristics, as well as other concerns, typical of interchange operations has been compiled in Table 4. Each model was then investigated as to its capability to model the stipulated geometr.c or operational characteristic. The results were shown in Table 4, and a brief discussion of the results follows. An interchange ramp terminal/frontage road operates differently from an arterial street due to the effect of the freeway and its ramps. For this reason, a model capable of simulating traffic on both arterial streets and freeways would be advantageous. INTRAS and CORFLO are the only two models investigated in this initial study capable of interacting freeway vehicles and arterial street vehicles. Because INTRAS is a microscopic model, a greater level of detail can be both input and extrapolated from INTRAS than from CORFLO. Weaving is another Important factor. A level of service can be assumed from FREFLO output (and CORFLO) for weaving areas such as an entrance ramp closely followed by an exit ramp. For INTRAS, entrance/exit ramp weaving is not specifically addressed in the manual; however, TTI has used INTRAS for freeway weaving analysis and has found the model to operas adequately. However, it is improbable that the logic used in FREFLO and INTRAS for a freeway weaving analysis can be applied to a Interchange ramp terminal weaving sections. Other weaving scenarios Involve the interaction of vehicles exiting the freeway and requiring a right turn at the ramp terminal intersection or vehicles turning out of a driveway and requiring a left turn at the first downstream intersection. These scenarios cannot be specifically modeled in INTRAS; however, INTRAS output does contain O-D charts which can quantify those maneuvers, and the output also quantifies the number of missed maneuvers. In other words, if a vehicle was destined to exit the freeway and turn right at the next intersection on the frontage road, but could not complete the maneuver, INTRAS includes this information in its output. NETSIM, on the other hand, is capable of traffic assignment parameters which could require a certain percentage of freeway exiting vehicles to turn right at the frontage road intersection. This process is, however, very complex and careful attention must be made to keep percentages of vehicle movements at each link equal to 100 percent. PASSERIII deals specifically with diamond interchanges at which such a weaving maneuver would take place, however, simulationof weaving in the vicinity of the intersection is beyond its scope. With interchanges being an integral part of freeway traffic management systems in some states, and with ramp metering becoming more prevalent, the issue of queue length could play an important role in freeway corridor operations. Queue length would aid in determining an adequate distance between a ramp exit or entrance and the interchange. Therefore, it would be desirable 2- 10
Table 4. Computer Simulation Model's Capabilities Computer Model Model Constraints ~ FREFLO ~INTRAS ~CORF~O ~ NETSIM ~PASSER III ~ PASSER II ~ TRANSY ~ TEXAS freeway Simulation ~Yes ~Yes ~Yes ~n/a ~n/a ~n ~n/a Frontage Road n/a Yes Yes Yes No No No Simulation nterchange Simulation ~No ~Yes ~Unknown ~Yes ~Yes ~Y s ~Yes driveways ~n/a ~Yes ~Yes ~Yes ~No ~it; ~No Type of Traffic Control No Ramp Stop, Yield, Stop, Yield, Stop, Yield, Pretimed or Signals Pre-timed Metering Fixed, Actuated Pretimed Signal Fixed Traffic- Signals or Control, 3 types Control, Some Control, Responsive Unsignali of Ramp Actuated Actuated Fixed Sequence zed Metering, Merge Control Control Signals and Diver e freeway Weaving ~LOS ~Yes ~ LOS Provided ~n/a ~n/a ~n' ~n/a Analysis _ Provided l rterial Weaving | n/a | Yes l No | nknown | n/a | n/ | n/a Analysis Caused by Two Closely Spaced Ramps arying Distance of | Yes | Yes l Yes | Yes | n/a | n/ | n/a ! I Weaving Area | rterial Weaving | n/a | O-D quip l No | Yes | No | N | No | Analysis Caused by Either Vehicle Exiting Freeway and Turning Right at Interchange, or Vehicle Turning From Driveway and Turning Left at Intersection . Varying Distance n/a Yes Yes Yes Yes No No Between Exit Ramp Terminal and Downstream Arterial | Inter sect ion U-Turn Area at n/a Yes Unknown Yes Yes No Unknown | Interchanges Exit Ramp Vehicles n/a Yes. All lanes Unknown Unknown No No No Able to Yield to Cross yield Arterial Traffic l I 'rediction of Queue | n/a | Unknow | Unknown | Yes | No | Ye | Yes Length at Intersections . sadistic Output At or ~No ~Yes ~Unknown ~ 1; Known ~No ~No t Unknown Near Capacity Levels ~ at V/C > 0.95 n/a No Yes No No Control, Stop, Yield, Pretimed, Semi actuated, or Full Actuated n/a n/a n/a Unknown Yes Yes No No Unknown 2- 11
to have queue length as an output from a model. Sources irdicate a discrepancy regarding queue length output for INTRAS. The PASSER ~ model does not estimate queue length. However, PASSER it, although not specifically designed to handle diamond interchanges, can be used to evaluate a diamond interchange and produces similar results to PASSER HI, with He added advantage of queue analysis output. In addition, NETSIM and TRANSYT-7F are bow capable of producing queue lengths, whereas TEXAS is not. High volume operations are critical conditions to be studied in this project. The elects of queue spilIback on impeding and blocking output flow at an upstream intersection must be assessed. None of the models except INTRAS and NETSIM appear to perform as desired at oversaturated volume levels. PASSER II and PASSER III were not designed to operate at or near capacity, and may not produce realistic results when the v/c ratio is greater than 0.95. The literature does not say whether TEXAS produces realistic results when the v/c ratio nears one. 2.2.3 Other Considerations Other considerations not included in Table 4, yet found in the literature and/or manuals that may be important in determining which modelers) to use in this project, are summarized in this section. One important factor associated with urban freeway ramp terminals that cannot be simulated by FREFLO is ramp metering. Also, the model deals with operations on freeways, whereas ramp terminals/arterial systems are important in this project. The main reason FREFLO was investigated is for its role in CORFLO and as a possible weaving analysis tool. Other considerations regarding INTRAS not being included in Table 4 are that the manual is difficult to understand, and modeling a complex freeway/interchange systems could be very time consuming. Many inputs are required for any simulation run, which may require significant time for data preparation and processing. It is interesting to note that one study that compared results of an analysis of a single point diamondinterchange using several different models found that PASSER TII and the TEXAS Mode} resulted in data most similar to the field data. PASSER II is somewhat more limited in its abilities than PASSER III with regard to frontage roads in that it cannot simulate U-b~n lanes. Some additional disadvantages of the PASSER II program is that it does not allow for separate right turning lanes and the user cannot input the clearance interval of each phase. In addition, the TEXAS Model can only simulate one interchange/intersection at a time. Therefore a network evaluation of intersections would not be possible using TEXAS. Both PASSER models, He TEXAS Model, and TRANSYT-7F would be advantageous for this project to assess existing conditions at signalized interchanges, however, they do not take the whole interchange/arterial "experience" (driveways, weaving, etc.) Into consideration. 2- 12
2.2.4 Findings All the models investigated are notable, respectable models that have their specific purposes. Because Me geometric and operational charactensticsofthe interchange/artenalsystem are complex, each model investigated has its advantages and disadvantages for use. However, this investigation indicated that, in ranked order: TRAF-NETSIM, TEXAS, and TRANSYT 7-F were the more attractive operational models for potential research use in this project. NETSIM was selected because it can simulate almost all aspects of interchange/arter~altraff~c operations desired. Its capability to view the simulation process gives the analyst an added sense of the fidelity ofthe simulationin progress. NETSIM offers the traffic assignment option which may also be helpful in analyzing arterial weaving caused by the interaction of turning vehicles and ramp- to-intersection spacing. 2.3 FIELD STUDIES Several analytic models were developed during this study to facilitate Me evaluation of interchange ramp terminal capacity and level of service. This section provides a description of the traffic flow problems for which models were developed, a descnption of the field study sites, and some summary statistics from the field study database. A more detailed discussion of He data collection and reduction activities is provided in Appendix B. 2.3.1 Traffic Flow Problems Associated With Interchange Ramp Terminals This section describes traffic flow problems commonly found in interchange areas as related to the objectives of this research. Problems of primary interest were those occurring on the cross street at or between the interchange ramp terminals and any adjacent, closely-spaced intersections. The findings from the survey of practitioners indicated that there were several types of traffic flow problems associated with signalized interchange ramp terminals. These flow problems were broadly categorized as: (~) midblock turbulence (i.e., weaving) and unbalanced lane volumes that stem from high-volume turn movements in the interchange vicinity, and (2) flow restriction or impediment to discharging queues due to a relatively near downstream traffic queue. Four models were developed to facilitate the evaluation ofthese flow problems. The vanables included in these models were used to identify the data needed for mode] calibration. These four models are descnbed in the remainder of this section. Capacity Model. This mode! quantifies the effect ofdownstream traffic conditions on the tragic character~sticsused to estimate the capacity of left-turn and through movements at interchange ramp terminals and adjacent intersections. These character~sticsinclude start-up lost time, saturation flow rate, and clearance lost time. The capacity of an upstream signal phase has been found to be adversely effected by the close proximity of a downstream queue, particularly when the queue spills back into the upstream intersection. 2- 13
Approach Lane Utilization Model. This model quantifies the extent of unbalanced large use in multi-lane lane groups. On a cycle-by-cycle basis, many drivers in the interchange area tend to use one lane of a multi-lane lane group more than the others, they rarely choose the lane with the fewest vehicles in it. One possible reason for this unbalanced lane use in interchange areas may be driver desire to "preposition" for a downstream turn. As a result of this behavior, some lanes in a lane group are underutilized which effectively translates into a reduced lane group capacity. Queue Length Model. This model can be used to convert a predicted queue length from Me number of queued vehicles into units of distance (e.g., meters). This queue length conversion model was found to be an important component of the capacity model. Arterial Weaving Model. This model quantifies the effect of weaving activity on Me efficiency of arterial traffic flow. The weaving maneuver that is predominate in interchange areas is the off-ramp right-turn movement that weaves across the arterial to make a left-turn at the downstream signalized intersection. This maneuver has been observed to cause significant turbulence in the arterial traffic flow resulting in significant increases in travel time and, in some cases, lengthy queues on the off-ramp. Figure 3 illustrates extent of queuing that is commonly found during peak hours at many interchanges in urban areas. The queue shown in this figure extends back from the downstream intersection to the ramp terming in the foreground. The proximity Osiris queue to the ramp junction was observed to significantly slow Me discharge of arterial Trough traffic at the ramp terminal. It also caused the off-ramp drivers that desired to make a downstream left hun to cross the arterial at nearly right-angles in order to join the back of queue. Figure 3. Queue growth between an interchange terminal ant! a downstream intersection. 2- 14
Figure 3 also illustrates the field of view obtained from one of the two trailer-mounte~video recording systems used dunng the field study. Figure 4 shows one of these systems. It was deployed at this location to record arsenal weaving activity. The video camera for this system is mourned atop a 30-foot telescoping mast built into the two-wheeled trailer shown. -.:. : i,: ,, ~.,. ~. - . ~ Figure 4. Video recording system used during the field study of queue interaction and weaving. 2.3.2 Field Study Site Description The data collection plan was developed to obtain calibration data for the four models descnbed in the preceding section. An initial step in developing this plan was the identification of sites that exhibited one or more of the four flow problems. It was also desired that the study sites collectively offer some diversity in their geometric design and geographic location. This section describes the characteristics used during the study site selection process and provides a brief description ofthe traffic and geometric characteristicsofthe twelve interchanges ultimately selected. study Site Characteristics. The study sites were selected to collectively include the two basic forms of service interchange commonly used in suburban and urban areas: the diamond and the partial cloverieaffor parclo) interchanges. Vanations of these two interchange forms stem Tom variations in the distance between the ramp terminals and from the routing of the tmff~c movements malting the equivalent of a left or right-turn movement at the interchange. An a assessment of the correlation between interchange type, the extent of its operational problems, and its frequency of application in urban areas led to the following six interchange types being identified as the most appropriate candidates for the field studies: 2- 15
Diamond Interchange I. Compressed Diamond 2. Tight Urban Diamond (without frontage roads) 3. Tight Urban Diamond (with frontage roads) 4. Single Point Urban Diamond Partial Cloverleaf (Parclo) 5. Parclo B (2-quad) 6. Pareto AB (2-quad) In addition to having one of the six interchange forms listed above, the interchange study sites were selected to have characteristics that would promote the four operational problems to be studied. Thus, sites were selected that had ramp terminal spacings of 275 meters or less; ramp-to- intersection spacings of 275 meters or less, average daily traffic demands in excess of 20,000 vpd, and generally unconstrained geometries (i.e., 3.6-m lanes, no curvature, minimal grade, etc.~. In addition to these charactenstics,the study sites were selected to have frequent and recurring traffic queues on the arterial dunng the peak traffic periods. Study Site Locations. In addition to the aforementioned characteristics, there was a need for geographic diversity in the collective list of study sites. In this regard, study sites were identified in six geographic regions ofthe U.S. Within these regions, highway agencies in the states with large metropolitan areas were contacted and inquiry was made as to potential study locations. Interchanges that had the desired characteristics were identified as candidates for a preliminary site visit. Based on the results ofthe preliminary visit to the candidate sites, twelve interchanges were identified as being most suitable for field study. Table 5 describes the traffic and geometric characteristics of these twelve interchange study sites. Of these sites is provided in Appendix B. 2.3.3 Data Collection Details of the traffic signalization at each The data collection activities focused on the collection ofthe basic characteristics describing traffic flow at and between signalized ramp terminals and adjacent intersections. The data collected at the terminals and intersections included discharge headways, speeds, driver use of the yellow interval, and lane utilization. The data collected between the ramp terminals and the adjacent intersections included the speed and volume of weaving and non-weaving vehicles. The equipment used to collect the field data included video cameras and computer-mon~tored tape switch sensors placed in the traffic lanes. The equipment deployment followed one of two study types (i.e., a capacity or weaving study). All data were collected during weekday, daytime periods between the hours of 7:00 a.m. and 7:00 p.m. The typical data collection setup for a capacity StUdY is shown in Figure 5. ~_ As indicated by this figure, a trailer-mounted video camera was located at the upstream end of each of two street segments. The data collection setup for a weaving study was similar to that for the capacity study; however, the video cameras were located at both ends of the arterial segment between the adjacent intersection arid nearest interchange off-ramp. 2- 16
Table S. Tra ff~c and geo m etric charactenshcs of the study sites Ramp to Ramp to Interchange Arterial City, Arterial Arterial Ram p Intersection Speed Type StateAADT Thru Distance Distance Limit Lanes (meters) ~(metered (km/h) Compressed ~MetcalfAve Overland Park, ~ 58,600 T 6 ~200 ~204 Diamond 110th to I-435 Kansas |75th Street |OverlandP~k, ~ 32,000 ~4 T 174 ~155 I-35 to Frontage Kansas Maple Street ~Omaha, ~34,200 T 4 ~268 ~198 ~72 ~ 102nd to I-68( Nebraska Tight Urban Peoria Road Phoenix, 34,400 6 107 276 64 . Diamond 125th Ave.to I- 7 1 Arizona l l l I I Mathilda Ave Sunnyvale, 34,540 6 87 110 72 SR-237 to Ross Califomia Texas Arapaho Road Richardson, 39,000 6 99 265 64 Diamond US75 to Greenville Texas . Towneast Blot ~Mesquite, T 35,000 ~6 T 137 T 223 ~ 1 1. IEmporiumto I 635 ITexas l l l I I :1 arclo AB |60th Street 1 Omaha, 1 31,800 1 4 259 1 216 1 64 (2 quad) I-80 to Grover Nebraska Pareto B Somersville Rd Antioch, 39,700 4 265 119 56 (2 quad) Delta Fair to SR-4 Califomia . |StevensonBlv'1 ~Newark, T 55,600 ~4 r 264 ~157 ~56 Balentine to I-880 Califomia -| ingle Point | 7th Street l Phoenix, | 42,000 | 6 78 | 331 | 56 l[ Urban I-10 to McDowell Arizona ia~nond ndian School Rd Phoenix, 54,500 6 91 316 ~ ~I 16th St. to SR- 1 | Arizona l l l l 1 23 Notes: 1 - Distance measured from stop line to stop line in the same direction, except at SPUI's. At SP13I's, the "same direction" concept is also applied but the opposing direction Trough stop line is used as the reference point at the second ramp terminal (since the through stop line at the second ramp terminal does not exist at the SPUI). 2 - 17
Downstrea m Case .,,.,.,,'.~. . - of:::::::: . ~......... ;`r , . ~, 7' ~- _ ~,.~ ', .......... - ~- r ^ ~1 ~ Upstream Case . -_ ~ Boundary of / | Study Zone LEGEND Video Camera I "< end field of view ~ Tape Switch Sensor Camera 2 Boundary of / Study Zone ~ Photocell Sensor `p Tape Switch Speed Trap Figure 5. Capacity study data collection setup for a diamond interchange. 2- I~ 1 1 , 1 , . - r _' A.. :: .:~B.:; . ..~, - : _ _ ~-
During each ofthe capacity studies, the video and tape-switch equipment were deployed in a manner consistent with that shown in Figure S. Data collected during the capacity studies were used to calibrate the capacity and lane utilization models. The tape switches were used to record traffic flow behavior in two traffic lanes on three intersection or ramp terminal approaches. The video recorders were positioned to provide a visual record of traffic crossing the tape switches as well as information about queuing conditions on the downstream street segment. 2.3.4 Database Summary Statistics The data reduction effort proceeded on a model-by-model basis. For all models, the data reduction procedures were defined, documented, and tested on a sample portion of the collected data prior to their full-scale implementation. Following data reduction, and prior to model calibration, relevant summary statistics for each of the data bases were computed and reviewed. This review included the computation of sample statistics for selected traffic characteristics and performance measures. These statistics are categorizedby j unction type and traffic movement where appropriate. The findings ofthis review are surnmarizedin this section; a more detailed examination is provided in Appendix B. Capacity. The collected data were used to create a database of traffic characteristics and performance measures for use in calibrating the capacity model. This database included vehicle- related data (i.e., discharge headway, speed, acceleration)and phase-relateddata (i.e., phase duration, cycle length, distance to downstream queue). It includes the discharge characteristics of more than ~. ~. ~ 5 1,000 queued vehicles. ~ hese vetches were observed at twelve sites for 33 traffic movements in 63 instrurnentedlanes. All ofthe sites had extensive traffic queues during some or all ofthe s~x-hour study period and at least eight sites had some degree of queue spillback. There were more than 3~800 signal cycles observed during the study periods. _ . _ ~ ~ . . ~ ' ~ ' ~ 1 1 ~ The saturat~ontlow rate, start-up lost fume, and clearance lOSt time are summar~zea~n ~ ante ~ for the two junction and movement types studied. As the columns in this table indicate, the saturation flow rate and start-up lost time date were segregated into "with" arid "without" spillback categories. The "with" spillback category relates to the vehicles observed during signal phases that experienced queue spillback from the downstream intersection. The data included in this category represent only those vehicles able to discharge before the onset of spillback. Vehicles that discharge prior to spillback were found to have low saturation flow rates, they had little incentive to discharge at higher rates because they were essentially discharging into the back of the downstream queue. The saturation flow rate for each traffic lane studied was computed as the reciprocal of the minimum discharge headway measured for that lane. This latter quantity was computed as the average of all headway s observed for the fifth and higher queue positions in each traffic lane studied. This technique for computing the saturation flow rate is consistent with the procedure described in the 1994 HCM (3, Chapter 9). 2- 19
Table 6. Capacity database summary statistics Without Spillback With Spillback3 Junction Movement Type Typei No. Sat. Start-Up No. Sat. Cycles Flow Lost Cycles Flow Rater Time Rater (pcphgpl) (see) (pcphgpl) 1 Interchange Left-Turn 1 ,564 1,957 2.80 ~ Through ~2,O57 ~1,925 ~2.65 ~52 ~1,659 ntersection ~ LeR-Tu~n ~15 ~1,967 ~4.40 ~6 ~1,622 Through ~ 1,474 ~1,915 ~2.46 ~108 ~1,667 Average or Total: 1 5,110 I 1,935 1 3.08 1 166 1 1,651 , . Start-Up Lost Time (see) Clearance Lost Time (see) 2.77 1.69 2.60 3.04 2.55 1.87 3.11 1 2.20 2.77 Notes: 1 - Left-turn movements from bow We off-ramp and the arterial. Through movements along We arterial. 2 - Based on the average headway of We fifth Trough last queued passenger car. 3 - Based on the average headway of the fifth Trough last queued passenger car able to discharge prior to queue spillback from the downstream intersection. "--" no data available. In general, the saturation flow rate is very similar among the interchanges and intersections studied. An examination of the saturation flow rates categorized by interchange type (e.g., compressed diamond, parclo B. etc.) indicated that there were no significant differences in flow rate among types. On the other hand, the data in Table 6 indicate that the left-turn movements may be discharging more efficiently than the through movements at the study sites, however, the difference is relatively small. As with Me saturation flow rates, the start-up lost times in Table 6 varied among the "with" and "without" spillback categories. In general, start-up lost time in the "without" spillback category tends to be higher as a consequence of the extra time lost by the discharging traffic queue as it accelerates to the higher speeds associated with the higher saturation flow rates. Typical values of start-up lost time for the "without" category range from 2.46 to 2.80 seconds (excluding the data in the "intersection/left-tu~n"category) whereas values for the "with" category range from ~ .69 to ~ .87 seconds. The difference between these two ranges suggests that the more normal, "without" spillback condition is associated with about I.0 seconds more start-up lost time than the "with" spillback condition. Table 6 also summarizes the lost time at the end of the phase for the junction and movement types studied. The clearance lost time reported in this table was computed as being equal to the yellow-plus-red-clearar~ceinterval less the initial portion of the yellow interval used by the average driver (i.e., green extension). In general, it was found that drivers entered the intersection after the yellow was presented in about 27 percent of the phases studied; although, the frequency of this behavior varied widely among the study sites. The average amount of green extension was found to be relatively constant at 2.5 seconds across the twelve study sites during Decongested conditions. 2 - 20
The data in Table 6 indicate that the average clearance lost time is about 2.77 seconds. This value is within the range of I.2 to 2.8 seconds recognized by the ~ 994 HCM (3, Chapter 2), although it is very near the upper limit of this range. This trend is likely due to the longer change intervals used at some of the interchanges and intersections studied. Lane Utilization. Traffic events recorded on video tape during the capacity studies were used to create a database of traffic characteristics and performance measures for calibrating a lane utilization model. The data collected included the lane volume per cycle, number of approach traffic lanes, distribution of traffic volumes to downstream turns, and the type of interchange. The assembled lane utilization mode! database includes the entry and exit time and location for 8,198 vehicles observed at twelve sites for 32 traffic movements. Of these vehicles, about 65 percent represent through movements, the balance were leR-turn vehicles in multi-lane lane groups. The analysts ofthe lane utilization database focused on the computation of a lane utilization factor for each of the left-turn and through movement lane groups studied. This utilization factor was computed using the following equation: v' N U man (~) ~ V' t where: U= lane utilization factor for the lane group, v ace = maximum demand flow rate in any of N lanes, vpcpl; vi' = demand flow rate in lane i, i = I, 2, N. vpcpl; and N = number of lanes in the lane group. The lane utilization factors computed for the through movement lane groups at the twelve study sites are shown in Table 7. The factors recommended in the ~ 994 HEM 63, Chapter 99 for application at isolated intersections are also shown in this table. These recommended values are consistent with the computed values in that larger factors are associated with lane groups with a larger number of lanes. In contrast, the recommended values tend to be smaller than the computed values. This trend suggests that lane utilization in interchange areas tends to be more unbalanced than at isolated intersections. This result was anticipated because of the significant turning activity in interchange areas and the resultant need for drivers to preposition themselves in the left-most (or right-most) lane on the street segment prior to the segment from which the turn watt be made. Oueue Length. The data reduction procedure for the oueue tenth database required a ~ _ =, - 1.- ~ ' ~ ~ camera view of the front and back of the through movement traffic queue on an intersection approach. The front view was used to measure the distance-to-stop-line and starting-reaction time of the first queued driver. The back view was used to measure the same statistics for the last queued vehicle. All distance measurements were made at the start of the phase; all reaction time measurements were made relative to the start of the phase. Queues with trucks or motorcycles were not considered. Left-turn queues were not studied. 2 - 21
Table 7e Lane utilization database summary statistics .. Movement | Number ofLanesin the Lane Group l Type' ~2 Lanes | 3 Lanes | 4 Lanes l I Left-Turn 1.17 1.28 Through 1 .12 1 .26 1 .32 I. 994 HCM 1 1.05 1 1.10 1 1.10 , 5 Lanes 1.72 1 10 Notes: 1 - Lefc-turn movements from both the off-ramp and the arterial. Through movements along the arterial. 2 - Recommended value in the 1994 HCM (3, p. 9-13J for through movements. "--" no data available. The assembled queue length database contains queue length and reaction time measurements for 122 first-in-queuepassenger ears and i,053 last-in-queuepassenger ears. This date was obtained at eight of the twelve study sites. Studies were not conducted at four sites because of the lack of an adequate view of the traffic queue. The analysis of the queue length model database focused on both the computation of the average lane length occupied by a queued passenger car and the average queued driver starting reaction time. Each characteristic was quantified for the first vehicle in queue arid for the "second and subsequent" vehicles in queue. This approach was undertaken because it was evident that Me lane length and reaction time differed significantly among the two categories. Based on an analysis ofthe queue length data, the average lane length occupied by the first queue~passenger car was found to be 5.0 meters. This length includes four to five meters for Me actual vehicle and up to one meter between the average vehicle's front bumper and the stop line. The average lane length occupied by the second and subsequent queued vehicles was found to be 7.0 meters per passenger car. This length includes four to five meters for the actual vehicle length and art average inter-vehicle "buffer" distance of two to three meters. The average reaction time for the first-in-queue drivers was found to be 1.52 seconds. In contrast,the average reaction time for the subsequent queued drivers was found to be 1.06 seconds. The reaction time of the first driver was measured as the time from the start of green to observed initiation of motion. The reaction time of all subsequent drivers was measured as the time from the start of motion of the preceding vehicle to the observed start of motion of the subject vehicle. This trend was expected because the first driver has more of a "surprise" situation (i.e., the signal indication changing from red to green) than the subsequent queued drivers who can look ahead, see that the indication is green, arid anticipate their time of departure. As a result, the first drivers should require slightly more reaction time than the subsequent queued drivers. 2 -22
Weaving. Weaving data reduction required the use of both camera views to track vehicles through the weaving section. 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 We downstream signalized intersection. The two camera recordings were synchronized in time and played back simultaneously to obtain the travel time and stopping location of weaving and non-weaving vehicles. A sampling technique was used to select the tracked vehicles as the lengthy tracking time for each vehicle precluded the collection of a 100-percent sample. The weaving mode] database contains entry times for ~ 7,939 vehicles. Ofthese vehicles, 980 were tracked though the study segment. About one-half of the tracked vehicles (i.e., 421 of 980) were observed to complete a weaving maneuver. The analysis of the weaving mode! database focused on the volume and speed of the weaving and non-weaving traffic streams. These data were collected because it was hypothesized that the volume ofthe two conflicting traffic streams would affect their individual running speeds through the weaving section. It was theonzed that these speeds would decrease with increasing volume. The average volumes and speeds Trough the weaving section for the six StU6Y sites are listed in Table 8. . ~ Table X. Weaving database summary statistics Variable ~ Average Volume , 11 Total arsenal volume entering weaving section 1,409 vph Arterial lane volume entering weaving section 575 vphp! Weaving volume (off-ramp right to downstream left) 151 vph Speed Artenal vehicle spot speed at entry to weaving section 14.] mls Arterial vehicle running speed through weaving section ~ 0.6 m/s Arterial vehicle speed reduction due to weaving activity 3.4 mls Weaving vehicle running speed through weaving section 8.OWs As the volumes in Table ~ indicate, the six study sites had relatively high weaving volumes. On average, the weaving vehicles accounted for about one-half of the off-ramp right-turn volume at any one site. The arsenal lane volumes were also relatively high such that weaving opportunities were limited during a significant portion of the signal cycle. It should be noted that the off-ramp nght-turn movement at three of the sites was signalized (with right-turn on red allowed), the other three were yield-controlled. 2 -23
Two types of speed statistic were reported for the arsenal vehicles. One statistic is the spot speed of the arterial vehicles at a point just upstream of the off-ramp. The second statistic is the running speed ofthe saline arterial vehicles. This latter speed related the distance traveled through the weaving section to the corresponding travel time. The distance and time were measured from the point of entry to the weaving section to the downstream intersection stop line or to the first point of joining the stopped queue associated with the downstream signal, whichever was reached first. The difference between the arterial spot speed and the running speed is an indicator of a speed reduction in the weaving area due to weaving activity. The average speed reduction at the study sites was 3.4 m/s. This statistic is more useful than the spot or running speeds alone because it eliminates the effect of differing speed limits among the sites. A preliminary examination of this speed differenceindicatesa strong correlationbetweenit end the total arterialand weaving volumes. Increases in either volume level tended to increase the speed reduction. As shown in Table 8, the average weaving vehicle speed is 8.0 m/s. This speed tends to be lower then that ofthe arterial vehicles because the weaving vehicle enters the weaving section at a relatively slow speed due to the ramp control (i.e., signal or yield sign). Some preliminary analysis of this speed indicates that it decreases with increasing arterial large volume. 2.4 CAPACITY CHARACTERISTICS _ This section summarizes He models that can collectively be used to predict the capacity of traffic movements at signalizedinterchange ramp terminals and other closely-spaced intersections. Specifically, these models predict three important capacity characteristics,they are: saturation flow rate, start-up lost time, and clearance lost time. Details of the development and calibration of these models are provided in Appendix C. It should be noted that the traffic characteristics described in this section reflect passenger car performance only as all heavy vehicles were excluded from the database. The analysis of the traffic data collected at He twelve study sites followed a two-step process. First, analysis of variance (ANOVA)techniques were used to identify factors influencing the ~ff~c characteristic under examination, to control for differences in sample size, and to account for extraneous differences among otherwise similar sites. The ANOVA was implemented with the Statistical Analysis System's (SAS) (4) general linear model (GEM). All significance tests were conducted at a 95 percent confidence level (i.e., a = 0.05). Then, once the influential factors were identified from the ANOVA,both linear and non-linear regression techniques were used to calibrate the data (via these factors) to the proposed model. 2.4.! Saturation Flow Rate for Through Movements The saturation flow rate model for through movements was developed from a mode] of the minimum discharge headway of a stopped queue. Specifically, the saturation flow rate model was derived as the inverse of the minimum discharge headway model. Headways were explicitly 2 -24
modeled because they represent the most fundamental characteristic describing the efficiency of the discharge process. The minimum discharge headway is defined as the average headway of all headways observed for the fifth and higher queue positions; its reciprocal is saturation flow rate. This method of computing the saturation flow rate is consistent troth the procedure described in the 1994 HCM (3, Chapter 99. The following discussion describes the calibration of a minimum discharge headway mode} for through movements, its algebraic transformationinto a saturation flow rate model' and finally, a sensitivity analysis of the transformed model. Factors Affecting Discharge Headway. A review of the literature on the topic of through movement headways suggests that several site-specific factors exist that can have an effect on the discharge process. For example, Bonneson f69 examined data from a previous study of s~ngle-po~nt urban interchanges by Messer et al (2) and found that the number of vehicles served per cycle had an effect on the minimum discharge headway. Specifically, he found that the headways observed for each queue position were lower when there were more vehicles queued behind that position. He called this headway compression effect being due to "traffic pressure." In this context, traffic pressure is believed to result from the presence of aggressive drivers (e.g., commuters~that are anxious to minimize their traveltime in otherwise high-volume conditions. As these drivers are typically traveling dunug the morning and evening peak traffic periods, they are typically found to be concentrated in the large queues associated with these periods. It should be nosed that Stokes, Messer, and Stover (79 found a similar effect of traffic queues on headways; they tenned this effect "headway compression." Bonneson (6) recommended the following equation for predicting the minimum discharge . . ~ neacway or a single-point urban interchange Trough movement as a function of traffic pressure: H,k = 1.57 ~ 770 -0.0086v~' (2) us where: He = through movement minimum discharge headway, sec/veh; us = speed at saturation flow, m/s; and vl' = demand flow rate per lane (i.e., traffic pressure), vpcpl. The speed in Equation 2 represents the maximum speed drivers tend to reach as they discharge from a traffic queue. In theory, it represents the speed associated with a traffic stream flowing at its saturation flow rate. This speed was found to vary between 12 and ~ 5 m/s in the sites studied by Bonneson 66J. One reason offered for this variation was the proximity of some sites to adjacent intersections. Specifically, Bonneson noted that lower speeds were associated with those sites where the distance to the downstream intersection (and its associated queue) was relatively short. This suggests that discharge headways may be lower because of lower discharge speeds that result from He impending downstream stop faced by the discharging drivers. 2 - 25
The HCM (39 describes many additional factors that can affect discharge headway. These factors include: lane width, vehicle classification, local bus frequency, parking activity, approach grade, and area type. To avoid confounding the effect of these factors with those specifically being considered in this study (e.g., distance to back of queue), several steps were taken to avoid or remove Me aforementioned factors from the data collected for this project. Specifically, the study sites all had lane widths of about 3.6 meters, approach grades of less than +2.5 percent, no local busses, arid no parking activity. In addition, all heavy vehicles (i.e., vehicles with more than two axles) and all queued vehicles that followed heavy vehicles were removed from the data base. Mode! Calibration. The calibrated minimum discharge headway model for through movements is shown in Equation 3. ~ ~ 13 (I ~ is) + 2~ ~ Use (~ _ 0 00453 v`') ( ) where: H,h = through movement minimum discharge headway, sec/veh; D = effective distance to the back of downstream queue (or stop line if no queue) at the start of the subject (or upstream) phase, m; Is = indicator variable (~.0 if spillback occurs during phase, 0.0 otherwise), arid v,' = demand flow rate per lane (i.e., traffic pressure), vpcpl. The statistics in Table 9 indicate that the calibrated mode! explains only about four percent of the variabilityin the headway date. The remaining variability is primarily due to Me random (or ur~explainable) variability inherent in headway data. Some of Me variability is also due to differences among the traffic lanes and sites studied. Never~eless,the statistics in Table 9 indicate that there is a statistically significant relationship between minimum discharge headway, traffic pressure, and distance to the back of queue. The root mean square error and number of observations can be used to estimate the minimum standard deviation (or precision) of the predicted average mimmum discharge headway as +0.006 sec/veh. Table 9. Calibrated through movement minimum discharge headway mode! .. ,1 Model Statistics R2 Root Mean Square Error: Observations: 0.04 0.56 sec/veh 7,704 Value Hth v, D Range of Model Variables Variable Variable Name UnitsMinimum Through movement men. discharge headway sec/veh0.61 Demand flow rate per lane (traffic pressure) vpcpl5 Distance to back of downstream queue meters35 2 - 26 Maximum 6.8 . 37 315
As the coefficient values in Table 9 show, the magnitude of the effect of distance-to-queue is dependent on whether queue spillback occurred during the phase. Phases without spillback had a smaller regression coefficient indicating less sensitivity to distance. In general, the coefficients predict a larger minimum headway for those queues discharging prior to the occurrence of spillback than for those that discharge without spillback ever occurring. Spillback conditions are characterized by the backward progression of a downstream queue into the upstream intersection such that the subject (or upstream) intersection movement is effectively blocked from discharging dunug some or all of the signal phase. The "distance to queue" vanableD is defined as the distance to the back of the downstream queue at the start of the subject phase. It is measured from the subject movement stop line to the "effective"back of queue. The effective beck of queue represents the location of the back of queue if all vehicles on the downstream street segment (moving or stopped) at the start of the phase were joined into a stopped queue. If there are no moving vehicles at the start of the phase, then the effective and actual distance to queue are the same. If there are no vehicles on the downstream segment at the start of the phase, then the effective distance to queue would equal the distance to the through movement stop line at the downstream intersection. The calibrated mode} indicates that the minimum discharge headway decreases with increasing distance to downstream queue. -O Several additional effects were also evaluated during the model calibration process. Specifically,the effect of j unction type, phase duration, and downstream signal indication were also evaluated. This latter factor was considered because it was reasoned that drivers might discharge at a more efficient rate if the downstream signal indication was green (as opposed to red), particularlyif there was no downstream queue. Based on this additional analysis, it was concluded that these factors did not significantly affect discharge headway after the effects of distance to queue and traffic pressure were removed. Interpretation of Mode! Statistics. Three statistics are provided in Table 9 to indicate the quality of fit ofthe calibrated model. First, the "t-statistic"is provided for each independent variable to test the hypothesis that its regression coefficient equals to zero. When the t-statistic exceeds ~ .96, the hypothesis is rejected and it can be concluded that the corresponding variable has a significant effect on the dependent variable. In this situation, there is a 5 percent (or less) chance of this conclusion being in error. In all cases, a graphical examination of the relationship between the dependent and independent variables was used to confirm the significance of the effect. . . The second measure of quality of fit is the root mean square error. This statistic represents the standard deviation ofthe dependent variable. Presumably,the error represented by this statistic is from random sources; however, there could also be some variation due to systematic effects. Knowledge of typical values of the root mean square error for Me dependent variable can be a useful gage to assess whether additional systematic error exists in the data. For example, the standard deviation of vehicle headways is rarely reported In the Literature to be less than 0.45 sec. Therefore, as the root mean square error of 0.56 reported in Table 9 exceeds 0.45, it is possible that there is some additional systematic error in the data that additional mode] variables could explain. 2 - 27
The third measure of quality of fit is the R2 statistic. This statistic represents the portion of the variability explained by the model relative to the total variability in the data. As such, it can range in value from 0.0 to 1.0. In general, larger values of R2 indicate a good fit; however, the value (or range of values) used to denote a "good" fit is dependent on the amount of random variability in the data. For example,the only way that an R2 of 1.0 can tee achievedis when all ofthe variability in the data is due systematic sources (i.e., there is no random error) ants! the model properly includes an independent variable for each systematic effect. The equation for computing R2 was examined to determine the factors that would influence its magnitude (see Appendix C). This analysis indicated that three factors could have a significant influence on the R2 value: (1) the amount of variability in the data due to random sources, (2) the variability in the independentvariable,and (3) the magnitude ofthe regression coefficient associated with the independent variable. Based on this analysis, it was concluded that the largest R2 value possible for the headway data is about 0.38 (as opposed to the 0.8 and above that is traditionally expected). Of course, the regression model would have to include enough variables to account for all ofthe systematic variability in the data in order to obtain this value. It was also concluded that the relatively subtle effect of the independent variables considered in this analysis (as represented by the magnitude of their regression coefficients) limit the R: to about the value obtained (i.e., 0.04). Saturation Flow Rate Model. The calibrated through movement minimum discharge headway model was convertedinto an equivalent saturation flow rate model. The form ofthis model was patterned after that used in Chapter 9 of the HCM A). Specifically, the saturation flow rate for a particular location is estimated as the product of the ideal saturation flow rate and the various site- specific adjustment factors. In this context, the adjustment factors found in this research relate to the effect of distance to the downstream queue at the start of green, spillback occurrence, and traffic pressure. The basic form ofthe model is: 5! = So xfD xf~ where: s, = saturation flow rate per lane under prevailing conditions, vphgpl; so = saturation flow rate per lane under ideal conditions, pcphgpl; fD = adjustment factor for distance to downstream queue at green onset fV = adjustment factor for volume level (i.e., traffic pressure). The ideal saturation flow rate represents the saturation flow rate when not affected by any external environmental factors (i.e., grade), atypical vehicles (i.e., trucks), and constrained geometries (e.g., less than 3.6-meter lane widths, curved travel path). In this regard, the saturation flow rate would be equal to the ideal rate when all factor effects are optimum for efficient traffic flow and the corresponding adjustment factors are equal to 1.0. Based on this definition, it was determined that an infinite distance-to-queue under non-spillback conditions and a traffic pressure of 1 5.0 vpcpl were representative of ideal conditions for Trough movements. .. . .. ~ (4) ; and 2 - 28
Using the aforementioned definition of ideal conditions and associated parametric values, the resulting ideal saturation flow rate so was derived from Equation 3 as 1,990 pcphgpl. As the precision of this estimate (i.e., about +12 pcphgpl) was found to include 2,000 pcphgpI, this latter value is recommended as the ideal saturation flow rate for through movements. The definition of ideal conditions was also used to derive the following adjustment factors: JD 1 : no spillback 3 D 1 21.8 1 + D with spiNback (5) f = ~(6) where: D = effective distance to the back of downstream queue (or stop line if no queue) at the start of the subject (or upstream) phase, m; and v,' = demand flow rate per lane (i.e., traffic pressure), vpcpl. Sensitivity Analysis. The relationship between distance-to-queue, spilIback, traffic pressure, and saturation flow rate are shown in Figure 6. The trends shown indicate that saturation flow rate increases as the distance to the back of queue becomes longer. They also indicate Mat phases that incur spilIback have a lower saturation flow rate, for the same distance to queue, tears phases that do not incur spilIback. Finally, saturation flow rate is shown to increase with increasing traffic pressure. 2.4.2 Saturation Flow Rate for Lefi-Turn Movements The saturation flow rate mode} for left-turn movements was developed from a mode} of the min~murn discharge headway of left-turn vehicles. The following discussion describes the calibration of a minimum discharge headway model, its algebraic transformation into a saturation flow rate model, and finally, a sensitivity analysis of the transformed model. With one exception, the left-turn movements included in this study represent left-turns at interchange ramp terminals. The orate exception was a left-turn movement at an adjacent signalized intersection. Ofthe two types of left-turn movements at ramp tenninals (i.e., off-ramp and arterial), the majority of the data were collected for the off-ramp lefc-turr~ movement. Nevertheless, it is believed that We factors identified in this section are sufficiently general that they are applicable to off-ramp and arsenal lefc-turn movements at interchanges and to lefi-tu~n movements at adjacent intersections. 2 - 29
1900 1 700 1 500 1 300 1100 900 700 Saturation Flow Rate per Lane, vphgpl Without Spillback 1 :::::::::::-: Of ' ~`~ ~ With Spillback / - // - - - - - - -,b'. ~Traffic Pressure: / 3 vpcpl by 1 10vpcpl ., , 1 ' I 0 60 120 180 240 300 Distance to the Downstream Queue, m Figure 6. Elect of distance-to-queue, spiRback occurrence, ant! traffic pressure on through movement saturation flow rate. The left-turn movements studied rarely, if ever, experienced queue spilIback during the study periods due to the nature of the signal phase coordination between the two interchange ramp terminals. Hence, in contrast to the through movements studied, the variability in left-turn headways among sites cannot be explained by differences in the distance to the downstream queue. This restriction is a characteristic of the twelve sites studied; certainly, left-turn movements can be affected by downstream queuing conditions at other sites. In fact, it is likely that the effect will be very similar to that found for the through movements. Factors Affecting Discharge Headway. A review of the literature on the topic of left-turn headways suggests that several site-specific factors exist that can have an effect on the left-turn discharge process. For example, Kimber et al (89 measured saturation flows on curves with radii ranging from 6 to 35 meters and developed an equation for predicting saturation flow rate as a function of turn radius. An equivalent relationship, as it relates to minimum discharge headway, is: H', = 1.73 + where: H', = left-turn movement minimum discharge headway, sec/veh; and R = radius of curvature of the leD-turn travel path (at center of path), m. 2 - 30 (7)
In a previous stud of headwavs at intersections and single-point urban interchanges, Bonneson 66J, found an effect of radius on headway consistent with that found by Kimber Gil. The range of radii includedin this study was IS to 84 meters. Bonneson also found that the number of vehicles served per cycle had an effect on left-sum headway. This effect was referred to as "traffic pressure" in a preceding section. Bonneson recommended the following equation for predicting the minimum discharge headway of a left-tu~n movement as a function of radius and traffic pressure: H 1 58 + 0 830 _ 0 0121 ' R 0.245 where: v,' = demand flow rate per lane (i.e., traffic pressure), vpcpl. (8) As discussed in a previous section, the HCM 63J describes many additional factors that can affect discharge headway (e.g., lane width, vehicle classification, etc.~. To avoid confounding the effect ofthese factors with those specifically being considered in this study (e.g., turn radius), the study sites were selected to have as near ideal conditions as possible for all non-relevar~t factors. Mode} Calibration. The field data were used to calibrate the leR-turn movement minimum discharge headway model, as shown in Equation 9. Statistics describing the model's predictive performance and the range of each model variable are provided in Table ~ O. H., = 1.55~1 + -~ (1 - 0.00630v~')¢ + 0.86Btg) (9) with tg = (C)Ig + 0.27 (1 Ig) where: H., = lef~c-turn movement minimum discharge headway, sec/veh, R = radius of curvature of the left-tutn travel path (at center of path), m, v,' = demand flow rate per lane (i.e., traffic pressure), vpcpl; g = effective green time where platoon motion (flow) can occur, see, C= cycle length, see, tg = signalization variable (0.0 < tg < go); Ig = indicator variable (1.0 if g/C < gx, 0.0 otherwise), and gx = maximum g/C ratio (larger g/C ratios have no additional effect on headway). (10) As the statisticsin Table 10 indicate, He calibrated model explains only about five percent ofthe variability in the headway data. The remaining 95 percent of the variability is primarily due to the inherent randomness in headway data (as described in a preceding section dealing with the saturation flow rate model for through movements). Nevertheless,the statisticsin Table lO indicate 2 - 31
a statistically significant relationship between minimum discharge headway, radius, traffic pressure, and g/C ratio. The minimum precision of the average headway estimate is about +0.007 sec/veh. Table 10. Calibrated left-turn movement minimum discharge headway mode! . Model Statistics ~ Value R2 0.05 Root Mean Square Error: 0.44 Observations: 14, 1 53 Range of Mode} Variables Variable Variable Name Units Minimum . H', LeD-turn movement min. discharge headway sec/veh 0.83 , R Radius of curvature of travel paw meters 15 v`' Demand flow rate per lane Traffic pressure) vpcpl c/C Effective green to cycle length ratio na 0.06 . 98 26 Maximum 3.5 0.5s Saturation Flow Rate Model. The calibrated left-turn movement minimum discharge headway model was convertedinto an equivalent saturation flow rate model. The form ofthis model was patterned after that used in Chapter 9 of the HCM 632. Specifically, the saturation flow rate for a particular location is estimated as the product of the ideal saturation flow rate and the various site- specific adjustment factors. In this context, the adjustment factors found in this research relate to the effect oftraff~c pressure, signal timing, and turn radius. The basic fonn of the mode! is: 5i = 50 X fR x fV fglc where: so = saturation flow rate per lane trader prevailing conditions, vphgpl; so = saturation flow rate per lane under ideal conditions, pcphgpl; fR = adjustment factor for the radius of the travel path, if = adjustment factor for volume level (i.e., traffic pressure), and Age = adjustment factor for signal timing. The ideal saturation flow rate represents the saturation flow rate when not affected by any external envirorunental factors, atypical vehicles, and constrained geometncs. In this regard, the saturation flow rate would be equal to the ideal rate when all factor effects are optimum for efficient traffic flow arid the corresponding adjustment factors are equal to I.0. Based on this definition, it was determined that an infinite radius, a traffic pressure of 10.0 vpcpI, arid a g/C ratio greater than 0.27 were representative of ideal conditions for left-turn movements. Using the aforementioned definition of ideal conditions and associated parametric values, the resulting ideal saturation flow rate so was derived from Equation 9 as 2,010 pcphgpl. As the precision of this estimate (i.e., about +12 pcphgpl) includes 2,000 pcphgpI, this latter value is 2 - 32
recommended as the ideal saturation flow rate for a left-turn movements (although it is recognized that the radius of the travel path is assumed to be infinitely long). The definition of ideal conditions was also used to derive the following adjustment factors: 1 ~ ~ (12) R f = ~13i v 1.07 - 0.00672v~' ' 1 14 g/c 0.810 +0.703 ~( ) tg = j)Ig + 0.27 (1 - Ig) (15) where: R = radius of curvature of the left-turn travel path (at center of path), m, v'' = demand flow rate per lane (i.e., traffic pressure), vpcpl; g= elective green time where platoon motion (flow) can occur, see, C= cycle length, see, tg = Ig = signalization variable (0.0 < tg < 0.27), arid indicator variable (~.0 if g/C < 0.27 , 0.0 otherwise). Sensitivity Analysis. The calibrated model was used to examine the effect of radius, traffic pressure, and g/C ratio on the saturation flow rate of left-tu~n movements. This effect is shown in Figure 7 for the respective characteristics. The trend lines shown in this figure reflect left-t~n volumes of 3 arid 10 vpcpl and g/C ratios of 0.16 and 0.27. These ranges were selected to be inclusive of about 90 percept office observations in the database. In general, the model has a trend of increasing saturation flow rate with radius. The range of traffic volume (i.e., pressure) considered makes a difference of about ~ 00 pcphgpl in saturation flow rate. In contrast, the g/C ratio has almost twice the effect as traffic pressure (i.e., a change of about ~ 60 pcphgpl). Of course, g/C ratio has no effect when the ratio increases beyond 0.27 2 - 33
Saturation Flow Rate per Lane, vphgpl '~ , g/C = 0.16 - 1 800 1700 1 600 -it/ , ~ ) ,slOsC27~- Traffic Pressure: 3 vpcpl 1 0 vpcpl 0 15 30 45 60 75 90 105 Radius of Curvature, m Figure 7. Elector tra~cpressure, signal timin& and radius on leff-turn movement saturationflow rate. 2.4.3 Start-Up Lost Time for Through Movements The time "lost" at the start of a phase stems from the fact that the headways of the vehicles in the first few queue positions are larger than those of vehicles in the higher queue positions. The headways ofthese first few queued vehicles are large because ofthe acceleration/hey are undergoing as they cross the stop line. Once the vehicles in these positions near the "desired" discharge speed, their headway s converge to the minimum discharge headway. Thus, factors that influence this speed (e.g., distance to queue, radius, lane width, etc.) also affect minimum discharge headway and saturation flow rate. As a result, there is an inherent relationship between saturation flow rate and start-up lost time. This section describes the calibration of the start-up lost time model for through movements. As with the saturation flow rate model, a start-up lost time mode! is developed for the left-turn movement in a subsequent section. Mode! Calibration. An examination of the start-up lost time and saturation flow rate data indicated that Were was a strong linear relationship between the two variables. Based on this examination, a linear model form was calibrated using the field data. The calibrated mode] for through traffic is: Is = -4.64 + 0.00373 s, where: Is = start-up lost time for through traffic, see, and so - saturation flow rate per lane for through traffic urlder prevailing conditions, vphgpl. 2 - 34 (16)
Statistics describing the model's predictive performance and the range of each mode} variable are presented in Table ~ ~ . As the statistics in this table indicate, the calibrated model explains about 41 percent ofthe variability in the data which is indicative of a strong correlation between start-up lost time and saturation flow rate. Based on the root mean square error and number of observations, the minimum precision of the average start-up lost time estimate is about +0.02 sec. Table Il. Calibrated through movement start-up lost lime mode! . Model Statistics Value R2 0.41 Root Mean Square Error: | 1.07sec l . ; Observations: 1,927 , Range of Model Variables l _ ; Variable Variable Name Units Minimum 15 Start-up lost tune see -3.1 i. s, | Saturation flow rate perlane | vphgpl | 1,257 ~ 3,326 Maximum 8.0 Sensitivity Analysis. The calibrated mode! of start-up lost time was used to examine the sensitivity of through movement start-up lost time to saturation flow rate. This relationship is shown in Figure 8. As this figure indicates, the start-up lost times for saturation flow rates of 1,800 arid 1,900 vphgp! are about 2.0 and 2.5 seconds, respectively. These values are slightly larger than the I.0 to 2.0 seconds recommended in Chapter 2 of the HCM (3J. 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Start-up Lost Time, see Movement: I _'s -Through If Left-Turn ~ , ~. ~, 1 0.0 1400 1 1 ~1 1 600 1 800 2000 Saturation Flow Rate per Lane, vphgpl 2200 Figure 8. Expected through movement start-up lost time as afiunction of saturation flow rate. 2 - 35
2.4.4 Start-up Lost Time for Left-Turn Movements Model Calibration. An examination of the saturation flow rate and start-up lost time data for the left-turn movements studied indicated that a linear relationship existed between the two charactenstics, similar to that found for the through movements. Thus, a linear model form was also calibrated for the left-turn movement data. The calibrated model for left turns is: It = ~4 43 + 0.00362 s, (17) where: 5 = start-up lost time for left turn traffic, see; and s, = saturation flow rate per lane for left turns under prevailing conditions, vphgpl. Statistics describing the model's predictive performance end the range of each model variable are presented in Table ~ 2. As the statistics in this table indicate, the calibrated model explains about 34 percent ofthe variability in the headway data which is indicative of a good correlation between start-up lost time and saturation flow rate. The minimum precision of the average start-up lost time estimate is about +0.04 sec. Table 12. Calibrated lefts n movement start-up lost time mode! Model Statistics | Value R2 0.34 Root Mean Square Error: 1.14 see Observations: 714 Range of Model Variables . Variable Variable Name Units Minimum . 15 Start-up lost time see -1.5 . . . s, Saturation flow rate per lane pcphgpl 1,339 Maximum 7.8 2,770 Sensitivity Analysis. The calibrated model of start-up lost time was used to examine the sensitivity of left-t~ movement start-up lost tune to saturation flow rate. This relationship is also shown in Figure 8. As this figure indicates, the start-up lost times for saturation flow rates of 1,800 and 1,900 pcphgpl are about 2.0 arid 2.5 seconds, respectively. These values are slightly larger than the ~ .0 to 2.0 seconds recommended in Chapter 2 of the HCM (3J. Figure ~ facilitates comparison of the relationships between start-up lost time and saturation flow rate for left and through movements. The comparison indicates that there is very little difference between the two movements In this regard. Therefore, it appears reasonable to conclude that the effect of saturation flow rate on start-up lost time is independent of movement type. 2 - 36
2.4.5 Clearance Lost Time When the yellow indication is presented at the end of a phase, drivers close to the intersection generally continue on through the intersection because stopping would be impossible or, at least, very uncomfortable. Thus, these "clearings drivers tend to use the first few seconds of the yellow interval. The remaining portion of the yellow interval that is not used by the average clearing driver plus the red clearance interval is defined as the clearance lost time. Based on this definition, the following equation can be used to compute clearance lost time: ~ = y ~ R - gy ~e - --c where: le = clearance lost time, see; Y= yellow interval, see; RC = red clearance interval, see; and gy= effective green extension into the yellow interval, sec. It was hypothesized that extent of driver encroachment into the yellow interval could be affected by the cleanug vehicle's speed, With of the intersection, and delay if not clearing. Thus, model calibration focused on defining a relationship between green extension, speed, intersection width, and signal timing (as a surrogate for delay). Green extension was quantified as the average duration of the yellow interval used during phases where it was observed to be used to some degree. Phases where the yellow interval was not used were excluded from the analysis because the reason for this lack of use was not determinable from the data. In general, the yellow interval was used in about 27 percent of the phases, although this frequency varied widely among the twelve study sites. Model Calibration. After an exploratory analysis of variance, several influential factors were identified that had a significant effect on end use. These factors were related to the duration of green extension using the following linear model form: gy = 1.48 + 0.014 SL + 6.40 (X - 0.8811x where: X= (19) go= effective green extension into the yellow interval, see; SL = approach speed limit, km/h; volume-to-capacity ratio for the lane group, and ~x= indicator variable (~.0 if X> be, 0.0 otherwise). The analysis considered 1,044 signal phases with observed driver use of the yellow (and in some cases, red clearance) interval. These phases were observed at twelve interchange ramp terminals and at twelve intersection approaches. The green extension data used in this analysis represent observations made for both left-turn arid through movements. The left-turns at the interchanges were made from either the on-ramp or the arterial. Statistics describing the model's predictive performance and the range of each mode! variable are presented in Table 13. 2 - 37
Table 13. Calibrated green extension mode] Model Statistics Value R2 0.1 1 Root Mean Square Error: 1.33 seconds Observations: 1044 Range of Model Variables Variable Variable NameUnits Minimum gY ~see 0.02 _ SL Approach speed limit km/in 56 Xi Volume-to-capacity ratio in lane i na 0.08 Maximum 7.3 72 1.3 The R2 statistic in Table ~ 3 indicates that the calibrated model accounts for eleven percent of the variability in the green extension data. The remaining variability is likely due to random sources; although, some of it may be due to differences among the study sites (that was not explained by speed limit and volume-to-capacityratio). Nevertheless, it is believed that the calibrated mode! provides a relatively good fit to the data and that it can be used to predict the average green extension with reasonable precision (i.e., a minimum of ~ 0.04 sec.~. Sensitivity Analysis. The calibrated model was used to examine the effect of speed limit and volume-to-capacity ratio on clearance lost time. Prior to conducting this examination, it was necessary to define the duration of the yellow and red clearance intervals. Recognizing that the yellow interval duration is often dependent on the approach speed and that there are a wide range of methods teeing used to determine yellowintervalduration,it was decided to set the yellowinterval equal to 0.062 times Me approach speed (i.e., Y = 0. 062 * speeds limit (/ - hid. This approach yields values generally consistent with other me~ods or policies. The red clearance interval was established es 1.0 second. Using these values, the clearance lost time was computed for a range of speed limits and volume-to-capacity ratios. The results of this examination are shown in Figure 9. As Figure 9 illustrates, clearance lost time increases With approach speed limit and decreases with increasing volume-to-capacity ratio. In general, it ranges from 1.0 to 3.0 seconds for Apical speed limits arid uncongested conditions. This range compares with the I.2 to 2.8-second range for clearance lost time suggestedin Chapter2 ofthe HCM (39. Clearance lost time increases with speed because of a corresponding increase in the yellow interval; however, it should be noted that this effect is offset to some degree by the increase in green extension associated with higher speeds. 2 - 38
4.0 1 .0 0.0 Clearance Lost Time, sec x-ratio = 1.05 _ 1 1 48 56 64 72 80 Approach Speed Limit, km/in Figure 9. Elect of approach speed limit on clearance lost time. 2.4.6 Lane Utilization The quality of service provided by a signalized intersection is highly dependent on the volume-to-capacity ratio of the intersection and its associated signal phases. One consideration in determining demand volume for the phase is the distribution of traffic among the lanes it serves. More specifically, these would be the lanes available to a "large group," as defined in Chapter 9 of the HCM (3). Obviously' if the traffic for a given lane group is concentrated in only one of Me several available lanes, then the phase duration would need to be long enough to serve traffic in this one lane. Alternatively, if the phase duration is not increased, then the capacity of the lane group is effectively reduced by the degree of underutilization of its lower volume lanes. This section describes the calibration arid examination of a mode] for predicting the lane utilization factor. This factor is traditionally used in a capacity analysis to adjust the lane group volume such that the resulting, adjusted volume reflects the traffic demand in the lane with the highest demand. Equation ~ was used to compute the lane utilization factor for each signal cycle at each site and lane group studied. Mode] Development. The lane utilization model developed in this research is based on a quantitative descnption of the two problems previously described: (~) drivers not distributing themselves as evenly as possible, and (2) drivers propositioning for a downstream turn. The first problem is more fundamental in nature and deals specifically with the random nature of vehicle 2 - 39
u = [1 +0.423( )+0.433N 2v arrivals per cycle and the extent that drivers collectively can and will distribute themselves among available traffic lanes. Unbalanced lane use stemming from this problem would be found in any multi-lane lane group on an intersection approach. The second problem is of a site-specific nature as it relates to the effects of downstream turn movements on a driver's lane choice at the upstream intersection. This problem would not necessarily be found in all multi-lane lane groups. A theoretic model Mat describes both of the aforementioned lane use problems was developed for this research and calibrated with field data (see Appendix C). This model is applicable to interchanges, adjacent intersections, and over intersections where propositioning may occur. The form of this model is: ~, ] (1 -I ) + [1 05 (Vd' ~ Ydr )~] where: U= lane utilization factor for the lane group; v;' = demand flow rate in lane i, i = 1, 2, N. vpcpl; . (20) vie, = flow rate in the lane group Mat will be turning left at the downstream intersection, vpc, a. V'dr = HOW rate in tne lane group that Will oe rurmng right al me aowns~eam 1mersecuon, vpc, N= number of lanes in We lane group, lanes; Ip = indicator variable (1.0 if Matc(v'dl, V'dr)/v ' > 1/N, 0.0 otherwise), and Ma~c(v 'dBASE 'do) = larger of v a, and v ,dr Statistics describingthe model'spredictiveperformanceand the range of each model variable are provided in Table 14. As the statistics provided in this table indicate, the calibrated model provides a reasonably good fit to the data. The minimum precision of the average lane utilization factor estimate is about +0.0l, based on the root mean square error and the number of observations. The ~2 Of 0. ~ ~ is lower than values traditionally expected, however, it must be remembered that there is considerable random variability in the lane utilization factor. This variability stems from the fact that two random variables (i.e., v 'A and v ~ are being used in the computation of the lane utilization factor. Thus, the variability in this factor represents the combined variability of the two underlying random variables. Sensitivity Analysis. Figure ~ O illustrates the relationship between lane utilization, lane group flow rate, and number-of-lanes, as predicted by the calibrated lane utilization model. In general, the large utilization factor increases with number of lanes and decreases with increasing volume. It should be noted that the predicted lane utilization factors exceed the values recommended by the HCM (39 (i.e., ~ .05 at two through lanes, ~ . ~ O at three through lanes). Also shown in Figure ~ O are the lane utilization factors predicted by a model developed by Fambro et al (9' fop. This model is coined the "TT! Model" in reference to the authors' affiliation. It was calibrated to ten traffic movements at nine signalized intersections. In general, the TT} Mode] 2 - 40
Table 14. Calibrated lane utilization mode! Model Statistics Value R2. . 0.18 Root Mean Square Error: 0. Range of Model Variables 1 1 Variable Variable Definition U V m`D: l N V' V'` v Units Minimum Maximum Lane utilization factor , Maxanum lane flow rate ~ any lane Number of lanes in He lane Coup - No. of vehicles tu~ning left downs~earr~ 1 No. of vehicles horning right downstream na 1.0 1.56 vpcpl 5.8 na 2 _ vpc o 40.3 4 23.3 vpc o 16. Demand flow rate for the lane Coup vpc ~2.4 69.7 predictions compare favorably with those of the calibrated large utilization model; however, the agreement is best at Me higher flow rates. I-his agreement is partly due to the fact that both data bases had the majority of their observations in this higher range of flow rates. This agreement suggests Mat the calibrated lane utilization model may be applicable to all signalized intersections. 1.8 1.6 1.4 Lane Utilization Factor \\ \ it\ ~Proposed Model ~ TTI Model _ 3 Lanes 1.0 ! 1 1 ; ' 0 5 10 15 20 25 Demand Flow Rate for the Lane Group, vpc 30 35 40 Figure JO. Elect offlow rate and number of lanes on the lane utilization factor. 2 -41
2.5 TRAFFIC CONTROL, SPILLBACK AND PERFORMANCE The research problem statement of NCHRP 3-47 identified queue spilIback as being the primary traffic operational"problem"that confronts1Taffic engineers trying to improve traffic flow at high-volume signalized interchanges. Moreover, the national survey of traffic engineers conducted in the initial stages of this research also confirmed that queue spilIback and related capacity issues were believed to be majoroperationalproblems observed et signalizedinterchanges. This research program has produced some new arid important operational findings regarding spilIback that might help to better explain the operational dynamics occurring during oversaturation conditions. An important finding is that traffic response to control inputs during undersaturation conditions is basically the reverse sensitivity to what occurs during oversaturation conditions. Traffic control plans that are designed to provide priority arterial flow dunng undersaturation may not provide the same relative priority and expected performance during oversaturation. A series of microscopic traffic simulation studies are presented which illustrate the response sensitivities of traffic signal systems observed for throughtput (arterial volume) and for traffic delay experienced on internal links along the arterial and on external approach movements feeding Me arterial. 2.5.1 Experimental Testbed The TRAF-NETSIM simulation mode! (59 was employed to study closely spaced intersections often found at signalized interchanges. NETSIM was chosen because of its capability to simulate congested traffic conditions, including spillback, and its supporting graphics for visualiz~n~the ex~enmental process. The four-intersection studY teethed is depicted in Figure ~ I. Of a representative diamond interchange are noted as being intersectionsj and k in Figure ~ ~ . The outer two signalized intersections along the crossing arterial are noted as being intersections i and Z. . __ ~ ~ ~ ~, ~ . The signalized ramp terminals L/ · · 7 1 Z 7 R l - ~\~ 7~ / ~ , , , , , , Figure 11. Experimental testbedfor signalized interchange with crossing arterial. 2 - 42
Experimentation with the traffic performance on individual linksj-k, such as between the two signals of the interchange, demonstrate how the traffic performance varies with control inputs. Two traffic measures examined were (l ) arterial throughput (the smaller of the traf F~c demand or service capacity), and (2) traffic delay experienced using the link (due to the traffic signal). Only research issues were examined and demonstrated. Such topics as showing how capacity and delay vary with cycle time were accepted as known technology (39 and were not studied herein. See Appendix A for further details on existing procedures and recent research on the subject (~l,). An arterial street is a connected chain of links such that link ij is connected to linkj-k, etc. For traffic flow In the i-j-k direction, traffic signal j is defined as the downstream node of link ij and the upstream node of linkj-k. Thus, precedence and dependency relationships exist between links and may be operative at any time conditions warrant. Determining when conditions are critical is a necessary part of any traffic analysis methodology. 2.5.2 Equation of Continuity The well-known equation of continuity serves as the fundamental theory of traffic flow on all types of traffic links, including impeded and congested operations. The equation of continuity, also known as the input-output model, is n(L't) = nO ~ `£vm' - '£Cmt n(L,f) ~ nmaX where: n(L,t) = number of vehicles operating on the link of length L at time t, vehicles, ~0 = number of vehicles operating on the link at the start of period, vehicles, am = total arrival flow into head of link destined to movement m, vph; cm = output flow < capacity of link serving movement m, vph, Id = stopline queue storage density of 143 vpkmpI, or a storage spacing of 7.0 m/vein (23 flc/veh); and maximum number of vehicles that can store on link, vehicles, (21) The equation of continuity can be used to examine the boundanes of flow and dependencies for a wide range of operations, including undersaturated and oversaturated conditions. 2.5.3 Undersaturated Conditions Undersaturated traffic conditions are those wherein the traffic demand on an approach to a signal phase is less than the operational capacity of the signal phase that serves it. All other lane groups that may interact with this traffic movement must also be undersaturated. Principal factors which affect whether a phase is undersaturated include: I. the arrival traffic demand, 2. the nominal phase capacity serving the demand; and 3. any impediments to saturation flow of the subject phase due to spillback. 2 -43
Undersaturation is normally thought of as being a deterministic condition where the existing traffic demand is less than the nominal phase capacity (3J. Moreover, undersaturated conditions may also be thought of as not having any flow dependency problems. However, this research has shown that closely spaced signalized intersections, whose traffic signals are poorly timed, can have both demand starvation on the link and still cause flow blockages on the next upstream link due to queue spilIback, even dunng nominally undersaturated conditions. Demand starvation results in wasted green at the downstream signal. The flow blockages due to queue spiliback can then cause oversaturationto occur. Results of simulation exper~mentsw~} be presented that demonstrate these findings. Three examples wall be used to illustrate the range of traffic situations that might be encountered in the field and the resulting operational responses that might be observed as existing signal timings are evaluated arid possible timing changes envisioned. Arterial Dominance. This traffic pattern is ~ 00% arsenal through traffic. Queue spilIback, blockage, and other impediments to flow can occur on short links that have poorly timed traffic signals, even dunug undersaturated conditions along the arterial. A water transportation example illustrates the worst-case signal timing situation. Consider traffic operations along the Panama . Canal. There, one objective is to minimize the water flow along the links of the canal (arterial) per passage of a ship (signal cycle). This minimum flow is accomplishedby using very short links and never having both upstream and downstream gates (greens) open simultaneously. Thus, using the equation of continuity, the maximum flow,fc (L,~ (in Asps), that can occur on a link, of length (meters), where no simultaneous input-output flows occur dunng maximum storage conditions is: N k L L fC(L,C) = ," , ~7C C C -- ~a fir (22, The minimum (cntical) unstreamor downstream green, gc, required to fill or dissipate, respectively, the critical flow without simultaneous signal coordination is: k L L o _ _ , ~ 5 ~_ - ~ 3.5 s Phases longer than fir run the risk of not being "effectively" green unless simultar~eous (23) input-output c, ~ ~ _ _ flows occur during critical storage conditions. Equation 22 can also be solved for Cc, given Mat fc(~'C) = v, the arrival volume, to determine the critical cycle, Cc, that might produce upstream blockage armor downstream green starvation of the output phase. The resulting equation is k L C_ q - v 2 -44 (24)
These concepts are illustrated in the follow~ngNETSIM traffic simulations. Two connected lOO-meter links id and j-k are assumed to have only arterial through traffic ~ = 1400 vph on two lanes which are served by signal phases having a cycle of 120 seconds, effective green times g = 49 seconds, and s = 1900 vphpI, providing green ratios of g/C = 0.41 and a nominal phase capacity c = 1558 vph, which produce a nominal v/c ratio of 0.9 at each signal. Equations 22-24 predict a critical flow of 428 vphpI, a critical green of about 27 seconds, and a critical cycle of 73 seconds for each ~ OO-meter link. The short links are susceptible both to having upstream input blockage due to queue spilIback and also to simultaneously (within the same cycle, but later in the cycle) experiencing demand starvation. These operational problems are possible even though all signals are nominally undersaturated when no spilIback/blockage occurs. Continuing with the NETSIM study, the signal offset for link id was fixed at JO seconds to provide good arterial progression and minimal delay, and it was not varied. The offset for Tire; j-k was vaned over the entire 120-second cycle. The results from several studies of arterial throughput and delay follow. Figure 12 shows that throughput flow problems are occulting on the short downstream link j-k pnmanly due to "demand starvation." For offsets of 40 seconds or more, the throughput volume drops 39%, from a nominal two-lane flow of about 1400 vph to a flow rate of about 850 vph. This reduction in flow has Me outward appearance of being caused by a drop in phase capacity due to either having a reduced effective green or saturation flow. Of course, no downstream impediment actually exists and any control strategy designed on this false premise would be misguided. .. 1 _ 1600 1400 1 ^_ 1 ~ -~ ~ ^ 1200 ~' I ~ I ~ = I I o . s Ed 1 000 800 . 600 . 400 200 t o 1 0 10 20 30 40 50 60 70 80 90 100 1 10 120 Offset (see) _: '~* ~I I ~' ~. 1 1 1 Figure 12. Throughput variation on downstream link with change in offset for undersaturated conditions and arterial dominance. 2 -45
-' T ~ I ~ I ; 0 10 20 30 40 50 60 70 i' As noted in Figure 1 3, traffic delays occulting at the signal on the downstream link varied with offset in Me traditional sense. Low delays due to good progression result for offsets from 1 0-30 seconds; whereas, large delays arid queue spillbackoccu~Ted due to bad progression for offsets over 50 seconds. Figure 1 3 has the form of a traditional delay/difference-in-relative-offset plot, as used in PASSER Ill and TRANSYT-7F, that would be expected for longer links arid undersaturated conditions. No blockages are occurring to the output of the last downstream intersection k. _' 100 90 1 80 70 1 60 1 50 40 30~ 201` ,. 10 o `*` 1 - r 80 90 100 110 120 Offset (see) Figure 13. Delay variation on downstream link with change in o~setfor undersaturatedconditions and arterial dominance. Figures 14 and ~ 5 show We effect of queue spilIback on the upstream link id, itself having a fixed offset of ~ O seconds. as the signal offset of the downstream link irk is vaned over the cycles , .. . . .. .. . . ~ , . . I. ~ ~ , . as cescrlnec above. upstream throughput ROWS are seen to mop in figure 14 in me same mater as for the downstream signal, but Me reason for the upstream input response would now be more correctly described as being due to queue spiliback blocking the output of the green signal and not due to demand starvation as before. In Figure 15 signal delay on link id increases rapidly to maximum observable values for Me short link for downstream offsets exceeding 50 seconds. These maximum link delays occur for Me same operating conditions as do the reductions in capacity caused by queue spilIback in Figure 14. The link has Redoubtably become oversaturated for these inefficient traffic signal offset). 2 -46
600 400 _' ~ 1 ~1200 _ 1 ~ ~1000_ ~~ ~1 c. 800 ED O 600 ~1 1 ~ 400 200 off' '~* ~'' , I i 1 - o 1 0 20 30 40so 60 70 Offset (see) 80 90 100 1 10 120 Figure 14. Throughput variation on upstream link with offset variation on downstream link for undersaturated conditions and arterial dominance. 100 sot ~80 + 2 70_ . Cal i ~ 1 ~ ~ ;- ,, v 1 ~ I ~ ._ 60 1 50 _ 40 _ 30 1 20 _ 101 / O ~ ~t~ in ~ 0 10 20 30 40 f f ~\ , I I \ , 1 , I 50 60 70 80 90 100 110 120 Offset (see) Figure 15. Delay variation on upstream link with offset variation on downstream link for undersaturated conditions and arterial dominance. 2 -47
These results demonstrate/hat good/bad signaltimingofthe next downstream closely-spaced signal can seriously impact the connecting upstream link, even during undersaturated conditions. Moreover, traffic operations on the causal link would likewise suffer when signal timings are poor and blockages occur, but strangely not as much as would have occurred if the link had been longer because there is no place to store longer queues. None of these studies show the difficulties that cross street traffic may have in gaining access to and using the major arterial facility because all fink traffic is composed of arterial through traffic. Later studies unit illustrate this problem area. Arterial Predominance. This traffic pattern has 80 percept arterialtraffic,whichis thought to be typical of nominal arterial streets outside of interchanges and- away from shopping malls, over heavy traffic generators, and circulation systems like in downtown areas. Simulation results of arsenal throughput are not illustrated,but they show a slight aIld expected moderation in the effects Of demand starvation because of Me ability to feed some traffic into Me empty arterial during these conditions. As shown in Figure 13, traffic delay experienced upon anival at a traffic signal is known to vary with arrival pattern 639. The more traffic that arrives on a fixed green per cycle, the less the average delay per vehicle. On the other hand, the higher the proportion of traffic that arrives on red, the higher the delay. During undersaturated conditions, these proportions can vary and so can the resulting delay, as Figure 16 demonstrates based on the NETSIM simulations. Figure ~ 6 shows that link delay during undersaturation is very sensitive to signal offset for closely spaced intersections where almost no platoon dispersion has occurred from We upstream signal. A Filly dispersed platoon would become random flow so that delay would show no sensitivity to changes in signal onset. A link would have to be very long to provide the time to filly disperse a platoon that is composed of mostly arterial Trough traffic. r 80 2 6 it =1OOm USA ~ 300 m t I _ _ I I l 0 1 0 20 30 40 50 60 70 80 90 1 go Offset (see) Figure 16. Descry variation on link with o~setfor nominal arterial conditions. 2 - 48
Balanced Pattern. Assume that the input flows to the links ij and j-k are now all nearly balanced,rather then coming from just one input (like the arterial dominance case above). In these experiments using NETSIM, the through, left-on, and right-on movements to the head of the link were 50, 25 and 25% ofthe total downstream link volume, which were served by green ratios of 36, 26 and 26 %, of a ~ 00-second cycle, respectively. Figure ~ 7 presents the NETSIM simulation results for the observed throughput on link ij for links of 100, 200 and 300 meters Tong when the connected links ij andj-k are both undersaturatedat v/c ratios of 0.~. The throughput (of 1200 vph) changed only slightly as the signal offset Bit (the time between the start of arterial Trough greens id) vanes over the cycle dunug these undersaturated conditions for any of the firm distances studied. Some queue spilIback effects are noted for the 100 meter link for a small range of offsets. r ! _ , , ~ C) U. I ! O 1400 1200 __; _~_ 1 000 T | I 800 + l 600 1 400 200 n 0 10 20 30 40 50 60 70 80 90 100 Offset (see) Figure ~ 7. Throughput variation on link with offset change for balanced flow patterns. ~ 200 meter ~ 300 meter , | ~ 100 meters I ! 1 i Traffic delays incurred when arrival flows are nearly balanced and undersaturated show aimostno sensitivity for predictable change~to signaloffset,as demonstratedin Figure 18. Thislack of response sensitivity is totally different from that depicted in Figures 13 and 16 for arterial dominated traffic pattems. While the arrival flows are not random, they are nearly uniformly distributed. Selection ofprogression adjustment factors for delay estimationin HCM-level analyses should reflect this finding. No benefit ofprogression should tee assumed or expected for any signal timing plar1 developed when upstream flows are nearly constant throughout the cycle. Signal control strategies can only improve link operations by providing a larger green ratio (g/C). 2 -49
- loo 90 Sot T 260 ~H;~ 0 10 20 30 40 50 60 70 80 90 100 11 Offset (see) Figure 18. Variation in link delay with offset for undersaturated conditions and balanced flow patterns. One benefit of balanced input flows is that simultaneous displays of input-output greens and resulting flows occur, and occur more frequently when storage is critical. This feature increases the minimum flow that can occur on short links from that given by Equation 22 by the amount of flow that simultaneously occurs per cycle. This increase in flow may quickly reach the output limit set by the existing capacity of the downstream signal when multiple upstream turning lanes are present. 2.5.2 Oversaturated Conditions Dunng oversaturated conditions, when upstream traffic demand exceeds downstream signal capacity, queue spillback along the affected links will routinely fill during the signal cycle, and link flow becomes highly output dependent, rather than upstream demand dependent. As the following NETSIM simulation experiments show, variations in flow and delay do occur during oversaturation conditions depending on the length ofthe link, upstrearntraff~c pasterns, and signal offset. However, it may be surprising which upstream movements are impacted the most. As with undersaturated conditions, three traffic patterns will be examined by simulation. Arterial Dominance. The initial study of oversaturation assumes that all ofthe input traffic to the tvvo-link arterial teethed (i-j-k) has all arterial through traffic with an input traffic demand of 1.5 times the downstream signal capacity. Signal timings provide a cycle of 100 seconds and the arsenal green splits are 54°/O and 36% of the cycle. Figure 19 presents var~ationsis flow generated by NETSIM for a 100-m length when all of the link traffic is through traffic. As shown earlier, this traffic case is most susceptible to "demand starvation" as the noticeable drop in throughput indicates over a range of link signal offsets. The queue spillback during oversaturation would be blocking the upstream signal, and arrival flows to the link can input a value greater than the downstream signal capacity in this case. 2 - so
- 1 400 I ~ 1200, , & 1- 1 i ' & i ~ O 1 5 - E~ 1 000 800 600 - \~_~-~* *~'' 400 200 O ~! 0 1 0 20 30 40 50 60 70 80 90 1 00 1 ~1 Offset (see) 1 1 1 i i l Figure 19. Variation in throughput with offsetfor oversaturatedconditions and arterial dominance. Arterial Predominance. Some oversaturation studies were also conducted where the through traffic was 80% of the tote] arterial volume. Green splits were adjusted accordingly to provide the experimentally desired v/c ratio of 1.5. This traffic pattern is envisioned to reflect the "typical" or nominal urban signalized arterial traffic pattern of ~ 0% left turns, 80% through traffic, and ~ 0% right turns at an intersection. In this case, the primary study objectives were twofold: (~) to demonstrate that total link delay dunug oversaturation is insensitive to signal offset for typical arteriais, and (2) that the link delay is sensitive to We length of the link, as watt be subsequently modeled and shown. Not shown is the fact, however, that the overall travel speed on Me oversaturated link is insensitive to link length. Me signal delays on link id were investigated for lengths of ~ 00, 200 and 300 meters. As Figure 20 illustrates for the three lengths, arid predominantly (80%) arterial traffic, the average measurable (and experienced) delay on the link increases with length (because the queues can be longer), but the actual travel speed of vehicles varies little. Moreover, the delay expenenced on the link dunng oversaturation vaned little with offset over the entire cycle. The following delay mode} for oversaturation conditions takes advantage of the observed insensitivity of link delay with offset. Measured link delays for oversaturated conditions were shown to vary pnmarily with the length of the link and the throughput rate (effective capacity) of the downstream signal. The maximum delay per vehicle experienced while traveling on a link is primarily related to the average Ravel speed on the link according to the following delay model, which is developed in Appendix D. Delays may be less that this vague during oversaturated conditions if demand starvation also occurs in addition to queue spilIback. 2- 51
Ha. 140 1 ~ 120 ~ _ ~_~ + 100 meter ~ '°°t ! ~80 T 60 ~ ~ ~ - . ~ *__ do t 20 1 o ! i , I 200 meter - ~ 300 meter 1 ! 0 10 20 30 40 so 60 70 80 90 100 Offset (see) Figure 20. Tragic delay on link with variation in offset for oversat?vrated conditions and preclominantly arterial traffic pattern. As derived in Appendix D, the minimum average travel speed on the filly loaded link during oversaturation is given by u u = s (25) 1 (1 ~ p) where: u' = minimum link gavel speed during saturation, km/hr; us = speed at saturation flow, km/hr, r,g = effective red (r) and green (g) of the downstream phase, see, and ,9 = (~qr)/(isg) ~ 2.79 r/gof~e downstream phase. The average maximum link delay can be calculated as the difference between the overall link travel time and the baseline running time at the approach running speed Ha. The maximum link delay for a link of length L would be L L ~= _ _ l u u I a (26) Should the link also experience demand starvation, the "effective" link length experiencing delay should be reduced to reflect Me percentage of the cycle demand starvation occurs. 2 - 52
Balanced Pattern. Assume that the input flows to the links ij and j-k are now all nearly balanced, rather than coming from just one input (like arterial dominance above). In these experiments using NETSIM, the through, left-on, and nght-on movements to the head of the link were 50, 25 and 25% ofthe total downstreamlink volume, which were served by green ratios of 36, 26 and 26 %, of a ~ OO-second cycle, respectively, to yield the targeted oversaturation v/c ratio of ~ .5. Figure 21 presents NETSIM simulations ofobserved~roughputon linkj-k for links of 100, 200 and 300 meters long when Me linkj-k is oversaturatedat a v/c ratio of ~ .5. The total throughput on lirikj-k is seen to change very little with signal offset because the individual upstream movements can keep the downstream link filled sufficiently during its green to maintain saturation output flows. That is, during the time the downstream signal is green, the equation of continuity provides that: n(L,g) = no + tam g ~ `£Sm g O < n(L,g) < no where: (2~ n(L, g3 = number of vehicles operating on the link of length ~ at end of green, vehicles; number of vehicles operating on Me link at start of green vehicles; total arrival flow into link during green destined to movement m, vph; output saturation flow of movement m, subject to Sm g < capacity of link serving output movement m, vphg; and maximum number of vehicles that can store on link, vehicles, kqL with a typical storage density of 143 vpkmpI, or a storage spacing of 7.0 m/vein (23 D/veh). 1400 ~, 1200 ~ s 1000 1 ~1 1 i s 1 1 ° I ~ 600 400 800 _ l 200 O , i : : 0 10 20 30 40 50 60 70 80 90 100 l Offset (see) l~lOOmeterli I - I ~ 200 meter Figure 21. Throughput variation on link with change in offset for oversaturation and balanced trap qc pattern. 2 - 53
As long as Me arrival flow to the link plus the queue storage at start of downstream green exceeds the downstream phase capacity, the throughput on the link watt not change with offset, `9,j. However, the link's signal of Eset if, does control which upstream feeding movements benefit from the available, albeit insufficient, link capacity and which movements get little or no service. Figures 22-24 deInons~ate this finding for link spacings of 100, 200 and 300 meters. Note that the total input volumes for the Tree spacings equal the throughputs shown in Figure 21. r 1 l 400 1 I 1200 i_ I ~1000 1 ~_ 1 I , 1 'I E 800 1 1 ~1 _ ! O 1 ~ i 3 C _ 600 1 400 200 1l, + Tryout I l ~ Right LeD x Total _ _ _ 0 10 20 30 40 50 60 70 80 90 100 Offset (see) Figure 22. Input volume variation with change in o~setfor ~ 00 meter link, oversaturated condition and balanced traffic pattern. 400 1400 , ~1200X X XX - 31( ~ ~ 1000 ~ ~ Through ~800 A_ Right ;;, 600 _ ~ Led ' ~400_ ~ X Tom i ~ - 200 ~ ~_ 0 10 20 30 40 50 60 70 80 90 100 Offset (see) ~ 1 J Figure 23. Input volume variation with change in of[setfor 200 meter link, oversaturated condition arzc! balanced traffic pattern. 2 - 54
r 1400 1200 ~ _ 1000 800 600 l - -N 400 .. 200 ~ Cal ~ . i A '11 ~ Through = Rlght ! ! 0 10 20 30 40 50 60 70 80 90 100 Offset (see) Figure 24. Input volume variation with change in o~setfor 300 meter link oversaturated condition and balanced tragic pattern. Balanced haffic patterns produced arrival delay results on the link shown in Figure 25 that are similar to Figure 20. Figure 20 confirmed Equation 26 in that the maximum delay that can be experienced on a link is primarily a function of the length of the link, and it is not sensitive to excessive arrival volumes. Figure 25 shows that the link delay is basically insensitive to offset dunug oversaturation for most traffic patterns. Maximum delay is, however, a function of the link length and the effective capacity (green ratio) of the downstream signal. Thus, average travel speed is a good measure of level of service along an arterial, as used in Ch. 1 1--Signalized Arterials of the HCM (3J, but total travel time (or delay) is a better measure of disutility, or cost. The resulting traffic delays expenencedon the three input movements to the link reflect the limited capacity available and allocated to each one by changing the downstream signal offset. Traffic delays observed on the exterior input movements to the upstream intersection follow a consistent but reciprocalpatternto observed flows in that when capacity goes down delay goes up, as Figure 26 depicts for a ~ 00 meter link. Upstream input movement delays are seen to be highly affected by the selection of downstream signal offset. Similar highly sensitive delay patterns, adjusted for travel time differences, were observed in studies for 200 m and 300 m lengths having the same relatively balanced upstream input flows. Should it be desired to favor one movement over the others, then new models are needed to predict what the desired control offset should be. A powerful new computer algorithm, called the PDX Model, has been developed which provides promise of being able to assess the probable outcome of queue spillback and demand starvation on throughput and delay over all traffic patterns and volume conditions, including oversaturation. This model is described in Chapter Three arid Appendix D. 2 - 55
60~+ ~ it, :;~ ! 30~ 20: 10 _ 0 , I ~I ' : ! ' ! I ~ Dominant | ~ Predominant ~ ~ Balanced l 0 10 20 30 40 50 60 70 80 90 100 Offset (see) Figure 25. Link delay experiencedfor three traffic patterns for 1 00-meter link and oversaturated conditions. 100 ~ 90 1 1 C) I _ c:, I ~ 80 _ 70 1 60 _ 50 _ 40 1 30 _ 20 10 O I ! ~ ~ ~ ) I ~ Through ~ Right I It I Total 0 10 20 30 40 so 60 70 80 90 100 l Offset (see) Figure 26. Traffic delay experienced on upstream input movements as downstream offset changes for oversaturated conditions and balanced traffic pattern. 2 - 56
2.6 ARTERIAL WEAVING SPEED This section describes two models that can be used to evaluate the performance of selected traffic movements in weaving sections on arterial cross streets in interchange areas. This perfonnance is evaluated in terms of the speeds of both the weaving and non-weaving movements. The weaving maneuver that is considered is the off-ramp nght-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 is generally found to have the largest volume and to be the most disruptive to arterial traffic flow. Henceforth, the weaving problem described in this section 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 ~aaffi~c signals, as compared to the more extensively studied weaving that occurs on unintenupted flow facilities (such as freeways). 2.6.! 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 on-ramp and a closely-spaced signalized intersection. During each field study, flow rates, travel times, travel distance, and stopped delays were measured for seven different travel paths through the weaving section (e.g., upstream entry as a through movement and downstream exit as a right-turn, etc.~. Three different types of traffic control (i.e., signal, yield, and uncontrolled) are represented in the database for the off-ramp right-turn movement. Additional details of the data collection effort are provided In Appendix B. 2.6.2 Calibrated Models Model calibration 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 mode] predicts the weaving maneuver speed and the other mode! predicts the arterial maneuver speed. The dependent var~ableconsideredin both ofthese models is the maneuver speed. Maneuver speed is defined as an average running speed and represents the ratio of travel distance to travel time within the study section. The distance (and time) are measured from He 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 time) vanes from vehicle to vehicle. It also varies among the two maneuver types (i.e., arterial arid weaving) as the weaving maneuver often has to accelerate from a stopped (or sIowed) condition whereas the arterialmaneuver generally enters the weaving section et speed. The calibrated weaving maneuver speed mode] is: Um w = 3.741 U0408 e (-~l 045 -PU) VW/3600) (28) 2- 57
where: Um W = average maneuver speed for weaving vehicles, m/s, Ua = average arterial speed entering the weaving section, m/s, Pu = probability of a weaving vehicle being unblocked (i.e., able to change lanes freely), and Vw = average weaving flow rate, vph. This modeIrelates the weaving maneuver speed to the average speed of arterialvehicles 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 the "desired" speed of arterial drivers for the given arterial volume conditions when there is no weaving activity. The calibrated arterial maneuver speed mode} is: U = 1.986 U0 7~7 e (-0 634 Vo/3600) m,a a where: U`, a = average maneuver speed for arterial through vehicles, mls. Ua = average arterial speed entering the weaving section, m/s, and V,, = average arterial flow rate entering the weaving section, vph. (29) This mode! relates the arterial maneuver speed to the average speed of arterial vehicles as Hey enter the weaving section. The arterial maneuver speed decreases with increasing arterial flow rate. This latter flow rate is strongly correlated writhe weaving flow rate and, hence, indirectly accounts for the level of weaving activity. One of the independent variables used in the weaving maneuver speed mode] is the "probability of a weaving vehicle being unblocked'' Put This variable relates to He portion of time that the end ofthe off-ramp (i.e., the beginning ofthe weaving section) is not blocked by the passing of the arsenal traffic stream. The blocked condition is represented by the Connation of platoons in the arterial traffic stream (induced by signalization or random bunching). The quantity Pu can be computed as: Pu = ~Va ~(1 -] ~ + ~1 _ a NIL 2 0 ~ where: Pu = probability of a weaving vehicle being unblocked, s, = saturation flow rate per lane under prevailing conditions (a I,800), vphpl; N. = number of arterial through lanes in the subject direction, lanes; IL = indicator variable (~.0 if D,'2 w ~ 90 (N' - l), 0.0 otherwise); Dm w = average maneuver distance for weaving vehicles (= [a - [q a), m; and [q w = average length of queue joined by weaving vehicles, m. 2 - 58
Table ~ 5 lists several statistics that indicate the quaTity-of-fit for each maneuver speed model. As these statistics suggest, the weaving maneuver speed mode} accounts for 16 percent of the variability in the maneuver speed data. Likewise, the arterial maneuver speed mode} accounts for 22 percent of the variability in the data. In all cases, Me independent vanables included in the model were found 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 ofobservations,yields a minimum precision of+0.10 and +0.16 m/s for estimates of the average weaving and arterial maneuver speeds, respectively. Table 15. Maneuver speed mode! statistics | Maneuver Speed Model | Observations T R2 | Root Mean Square Error T Precision I Weaving 1 421 T 0 16 1 2.02 m/s T ~O.lOm/s ! Artenal T 324 1 0.22 T 2.94 m/s T +0~16m/s 1 Table 16 shows We range of values in the weaving database for the independent arid dependent variables included in Me maneuver speed models. The vanables are listed according to the applicable model. The values in this table indicate the range over which each mode] is considered valid. In general, the models were calibrated with sites having two or Tree arsenal through lanes (in the subject direction), closely spaced intersections, and a wide range of arterial flow rates. Table 16. Range of independent and dependent variables . . | Model Variable Variable Name Units Minimum2 Maximum2 Both' ~ N. Arterialthrough lanes n the subject direction T -- ~2 ~3 Average arterial entry peed ~m/s ~8~9| 21.8 | ~Ya Avg. arterial flow rate ntering the weaving section: vph 1 640 | 1,924 1 Weaving | Pu Probability of a weavii g vehicle being unblocked | -- | 0.27 | 0.82 || Kw ~ Average weaving flow rate vph 88 270 ~um w Weaving maneuver spa ed ~m/s ~ 2.8 ~18.7 | Arterial um, a Arterial maneuver speed m/s 1.9 23.4 _ Notes: 1 - Variables used by bow the weaving and arterial maneuver speed models. 2 - All average values are based on a 1 5-minute intervals. 2 - 59
2.6.3 Sensitivity Analysis Figure 27 illustrates the effect of arterial flow rate on weaving and arsenal maneuver speed. This figure shows the behavior of both models when all other 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 the 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 27 show that both models predict an exponentially decreasing maneuver speed wad increasing arterial flow rate. This trend is somewhat consistent with the traditional speed-flow relationship for uninterrupted traffic streams in uncongested conditions. This figure also shows Mat the arterial maneuver speed is always higher than the weaving maneuver speed for the same flow rate. This trend is reasonable since the arterial vehicles enter the weaving section at speed while the weaving vehicles often must accelerate from a stopped (or sIowed) condition when departing the off-ramp. The trend toward convergence of the two models at higher flow rates is also reasonable as the weaving maneuver speed should approach the arterial maneuver speed as the capacity of the weaving section is neared. Maneuver Speed, m/s 10 8 6 4 o . 12 ~ ~~ ~61 M/ea~jn9 ~ - _ _ _ us = 13.4 m/s Nt -2 IL= 0 2 VW = 170 VPh , I , i I I O 500 1000 1500 2000 2500 3000 3500 Average Arterial Flow Rate, vph Figure 27. Effect of arterialflow rate on weaving and arterial maneuver speeds. 2 -60
2.7 RAMP VVEAVING CAPACITY MODEL The section of the cross arterial roadway between an interchange ramp terminal and a closely-spaced downstream intersection generally experiences operational problems, reduced capacity, and deteriorated Levels of Service (LOS) when the ramp-to-intersection weaving is heavy and difficult to perform. The more difficult traffic maneuver to perform usually is the off-ramp right turn trying to cross and then turn left at the next downstream intersection. When the downstream intersection is signalized, additional queuing in the left turn lane shortens the elective weaving length, resulting in increased operational problems. An additional operational constraint is the physical capacity of the ramp-arterial crossing maneuver. This maneuver usually operates like a freeway merge operation dunng rush-hour conditions because even free right-turn maneuvers are usually performed from a stopped position in queue. The Highway Capacity Manual (3) does not address arterial weaving. This section will present a method for estimating arterial crossing capacity based on NETSIM traffic simulation studies. Bow random and progressed flow conditions along the arsenal can be evaluated. Models to predict operating speeds in arsenal weaving sections are presented in Appendix E. 2.7.1 Study Methodology The expenmentaltestbed shown in Figure 28 was coded In TRAF-NETSIM to simulate Me study conditions. An arterial free speed of 60 km/in was assumed. The distance between the ramp terminal and the downstreamintersection was 200 meters. The ramp traffic, on yield control, made a right turn onto the arterial and then made a left turn at the downstream intersection. The arterial traffic went through the downstream intersection without making any turns. The strategy was to heavily Toad the cross weave with abundar~t demand, i.e., maintain a standing off-ramp queue so that the maximum ramp crossing volume could be observed for different operating conditions. l 111 l Diamond Interchanged Figure 28. Arterial testbedfor ramp-to-arterial weaving analysis. 2 - 61 1 1 1 1 1 1 1 1 ~ t .] Area of Study 1 1 1 1 ~1 1 1 1 1 1 1 1 1 ~1 ~ ~ '
Preliminary testing revealed that the weaving capacity from the ramp terminal follows the pattern of a negative exponential function with increasing arsenal volume. Thus, negative exponential regression analysis was performed to mode! the weaving capacity. The basic form of the exponential regression equation for the predicting ramp capacity is shown below. OR ~-e~PQ. where: OR Q. a T 1 C He ramp crossing/weaving volume (vph); arterial through volume (vph)' coefficient ofthe model = Tc / 3600; coefficient of the model = Hs / 3600, critical gap of ramp weave, see, and minimum follow-up headway, sec. The coefficients of the exponential equation, a and ,B, for random flow were determined on the basis ofthe simulations for various arsenal through volume conditions. The coefficients a and ,B were computed by inputting the simulated arsenal and the ramp crossing volumes into SAS, a statistical software analysis package (49, and perfonning the desired regression analysis. For the random flow conditions, the arterial traffic was vaned from 100 vph to 2000 Ash. Weaving across one, two, and three arterial lanes was studied for the volume conditions noted. Also, the effect of the change in decile gap acceptance distribution in NETSIM was studied. For progressed flow conditions, the arterial traffic was vaned from a v/c of 0.2 (500 vph) to a v/c of 0.8 (2000 vph) for a three lane arterial. A cycle length of 100 seconds and a clearance interval offour seconds per phase were also assumed. Various PF ranging from 0.l to ~ .8 were also simulated by varying Me percent vehicles arriving on green (PINGS at the upstream intersection. 2.7.2 Study Results The next section consists ofthe results obtained in the various cases involving random flow conditions along the arterial. Also, the computed coefficients for determining the ramp crossing volumes for different arterial flow conditions are presented. Changes in the gap acceptance distnbution were observed to affect the ramp crossing vol~ne. The second section presents the calibration coefficients for the proposed negative exponential equation for computing the ramp crossing volume for different arterial through volumes. The third section covers the results of simulations involving several volume conditions and different progression factors. The effect of progression on the ramp crossing volume is discussedin detail in this section. The development of the final mode} fonn and the methodology used to predict the ramp capacitor across the arterial weaving section for various progression factors are presented In Chapter 3 and Appendix E. 2 - 62
Random Flow. Initial ramp capacity studies were conducted with NETSIM assuming that the cross arterial had no progression end random flow. Moreover, preliminary testing ofthe mode! assessed the sensitivity of capacity to the default gap acceptance function provided in the model. The ~ 994 HCM states that the critical gap for a right turn from a Yield sign onto a major street could be taken as 5.5 seconds (3~. TRAF-NETSIM assumes a decile distribution wherein the default median value is taken as 6.4 seconds. In order to simulate the HCM recommended distribution, Card Type 145 in TRAF-NETSIM was coded to produce a decile distribution having a median value of 5.5 seconds. Hence the data file with the new decile distribution and an upstream link length of 365 meters was simulated for random flow. The effect of changing the decile gap distribution for three lanes can be seen _ . . ~. . . . . . in Figure 29 Due to the lower (better) gap acceptance cnter~a, more ramp vehicles can make a right turn onto the arterial. Though the trend is similar' the ramp crossing volume for the HCM decile distribution is slightly higher thar1 the TRAF-NETSIM default decile distribution. Follow ing a review of the gap acceptance study results shown in Figure 29, it was arbitranly decided to continue using the NETSIM default distribution in subsequent mode} building. 1 1800 1 1 1600- % 1400 - "a £L 1200 _ i ~ 1 ~1000 ~ 800 I 1. | - - - - - Using default NETSIM median gap value I Using HCM median gap value 600 400 200 100 500 1000 Arterial Volume (vph) Figure 29. Elect of NETSIMdecile gap distribution for three-lane arterial. ~ 500 2000 The effect of the number of lanes on ramp crossing volumes is illustrated in Figure 30. The drop in the ramp crossing volume is sharper u ith an increase in the number of vehicles on the one- lane arterial because all the vehicles have to use the single lane so the number of acceptable gaps available is reduced. For the two and the three lane cases, the same number of vehicles are distributed over two or three lanes, as the case may be, and there is a lesser effect on the ramp crossing vehicles. The net increase in the vehicles per hour per lane for the one lane arterial case is largest and hence its ramp capacity is affected the most. 2 - 63
as E ! ~ _ O as . . 1 ~ Boo 1600 ~L ~. 1-lane ~2-lane 3-lane 1 ~ 400 _ 1200 1 , 000 'I Boo 1 600 1 Too 1 200 + O ! 100 500 1000 1500 2000 , _ _ = 500 1000 1500 Arte ria I Vo lu m e (vph ) Figure 30. Elect of number of lanes on maximum ramp volume. Observations ofthe simulation results of Figure 30 suggest~at an exponentialmode} would reasonably fit the interchange ramp capacity results generated by NETSIM. The values of ramp capacity were obtained by simulation of the desired conditions and the coefficients of the model were determined using SAS, a statistical analysis software package f49. Figure 3 1 shows how well We model fits the traffic simulation program values. The points indicate the average of ten simulation runs while Me lines indicate Me trend using the calibrated exponential model. 200 - 1' 1800 1600: ~ S/m 2/ane 1400 i. ~I ~ Sim. 3-/ane 1200 5` '\ &\ ~- Reg. 1-/ane 1 000 _ \ . . W Q 600 . ~ ` ` __ _ ^ 400 ~-- ~ - -_. ~ 100 500 1 000 1500 2000 ~ .__ ___ .___ .___ ____ Arterial Volume (vphJ 1l Figure 3 1. Comparisons of ramp capacityfor simulation and exponential regression mode! results. 2 - 64
Applying the exponential regression analysis in SAS, the average of the observed volume data for each case was used to estimate the Known coefficients cat and ,8 in the exponential equation. a multiplied by 3600,denotedas Tc, is the average critical gap time of the corresponding lane configuration, while ~ multiplied by 3600' denoted as Hi, is the minimum headway of the e e · r_4 ' , ~ ~ _ my_ e artery weaving section. ~ ~ i, , ~ la '~e 11 s lows t :le coen~c~ents ax and ~ of the exponential model computed for one, two and three lane arterials. The coefficients in the proposed exponential equation are accurate estimations of the TRAF-NETSIM simulated operations in terms of standard errors and their variances. Table ~ ~ illustrates the coefficients of the mode! on a per lane basis. For the per large analysis, the results of the one, two and three lane cases were pooled and regressed. It cart be observed that the values of TC arid Hs are close to that of the one lane case. Table 17. Coefficients of the exponential regression mode' I,anes ~ -lane 2-lane 3-lane Coefficients a ~ ~a ~a ~ _ Exponential 0.00195 0.000657 0.001 I S 0.000574 0.00088 0.000565 R2 Value 0.9977 0.9995 0.9989 Conversion of ~Tc ~Tc ~ Its ~Tc ~ E Coefficients Values (sec.) 7.02 2.36 4.26 2.06 3.17 2.03 Table IS. Coefficients of the exponential regression mode! on a per lane basis Coefficients Exponential R2 Value Conversion of Values Coefficients (sec.) a ~ 0.002091 ~ 0.9970 ~ Tc ~ 7.52 ~ 0.000583 Hs 2.10 Progressed Flow. The NETSIM simulations were used to determine ramp crossing volumes for progressed arterial flow. Different progression factors were analyzed, ranging from PFs of 0.1 to Its. A PF value of I.0 is essentially uncoordinated, uniformly distributed flow. Progression factors from unity reflect the degree of platooning ofthe dominant flow. Volume-to-capacity ratios of 0.2, 0.4, 0.6, 0.7 and 0.8 on the upstream feeding movements were studied for a three-lane arterial. operating in two chases to create two platoons flowing downstream ~ _' In order to simulate various PF, vehicles were emitted from the upstream intersection ~ such that one platoon aIrives , ~ . . _ on red and the other platoon arrives on green. At the merge point, the notion of red and green only characterizes the degree of platooning in the arterial flow, as there is no signal at the merge point. 2 - 65
Figure 32 summarizes the experimental results. Polynomial regression equations for these plots were determined using SAS. Dunug low volume conditions on the arterial, little change occurred in ramp crossing capacity for different PFs. As the volume on the arterial increased, the ramp crossing volume decreased significantly due to fewer acceptable gaps for the weaving maneuver. For higher volumes, the change in the ramp crossing volumes for venous PFs becomes more significant. A PFof ~ .0 is considered random flow and the ramp crossing volume is the least for a PFof I.0 when compared to other PFs between O.1 to 1.~. The flow graph takes the shape of a parabola which has its minimum at a PF of 1 .0. Figure 32 clearly indicates the trend of ramp crossing volumes for v/c ratios of 0.2, 0.4, 0.6, 0.7 and 0.S, respectively. Me difference in ramp crossing volume for a PFof O.] to that of a PFof I.0 Increases with an increase in arsenal volume. In other words, We difference between the ramp crossing volumes for a PF of 0. ~ to that of a PF of ~ .0 increases with an increase in the v/c ratios on the arterial. Since the green ratio (green t~me/cycle length) is the same along both the approaches of the arsenal, Me PEG for a PF less than I.0 corresponds to the PER for a PF greater than ~ .0 and vice-versa. Plots of ramp crossing volumes for PF less than I.0 are a mirror image of plots for PF greater than ~ .0 about the axis of PF of ~ .0. 1200 1 ~ ~ 1100 > 1 ~ 1000 ._ tan en O0 900 ! ~ `~: 800 .~For\dc=04 ~For~c=0.6 ~For~c=0.7 ~For~c=0.8~ v m- ,^~%,, a., ~_7 ~m Ha_ _7x ~3< X ~ INK 700 1 ~, . , , , 1 o.o 0.2 0.4 0.6 0.8 1.0 1.2 1. ~1.6 1.8 1l PF I Figure 32. Elect of PF on ramp crossing volume for various v/c. Adjustment Factors for Progression. In order to further simplify the simulation results, the regression equations from the graphs for various v/c ratios were used to determine individual values of ramp crossing volume. A PFof I.0, also considered es random flow, was used as the basis for development ofthe adjustment factors. The factors for over PF were computed by determining the ratio of the value at PF of ~ .0 to that of another PF. Because the coves were parabolic and the values on one side of the curve were mirror images of the over, adjustment factors for PF from 0. 2 - 66
to 1.0 were computed. Figure 33 presents adjustment factors for various PFrarging from 0.1 to 1.0 for volume-to-capacity (v/c) ratios of 0.4, 0.6, 0.7 and 0.~. 1.25 1. 1= JO 1.05 L. ~ 1.00 1.10 0.95 1 20 - 1 r I -~-v/c= 0.4 ___. vlc= 0.6 _____v /c = 0.7 vlc=0.8 1. i_ 0.90 , , , I 0.1 0.3 o.s 0.7 0.9 PF Figure 33. Capacity adjustment factors for various progression factors. ·1 l ll Table 19 shows the actual (average) capacity adjustment factors simulated for various progression factors ranging from 0.1 to 1.0. Table 20 provides related capacity adjustment factors obtained using the exponential equation (Equation 31) shown below as developed from Table 19 average results using SAS. Note that average arterial lane volumes V are used in Equation 3 1 to provide a more convenient data input format. fPF = 1 + °,0l5*eLo-oo44*v-3os*pFl where: ~_ JPF PF ramp weaving capacity adjustment factor; progression factor, and V = arsenal volume per hour per lane (vphpl). (32) From a comparison ofTables 19 and 20, it can be seen that the above exponential equation follows a close fit of the actual average adjustment factors. The sum of squares error (SSE) was determined to be 0.00217. 2 - 67
2.7.3 Determination of Ramp Capacity during Random Flow The ramp capacity during random flow, denoted by OR can be determined by inputting the total arterial volume in Equation 3 1. The computed coefficients a, ,8 shown in Table 1 7 have been computed on the basis of number of lanes in the arterial section and can be used in the exponential equation. The results of one, two and three lane arterials were pooled and regressed to compute the common coefficients for single and multilane arterials. Depending on the decree of accuracy required oy tne user, me a~rerent coe~nc~ents could ne used for predicting ramp capacity. Table 19. Actual adjustment factors for PF of 0.1 to 1.0 Progression Factors, PF v/c 0~4 0~6 0~7 0~8 0~1 1 046 1098 1150 1205 0~2 1 0~3 1 0~4 1 0~5 1 0~6 1 0~7 1 0~8 1 036 T 1~028 11.020 11~014 11 009 T 1 005 11 002 077 T 1 059 11 043 11~030 11 009 T 1 011 11~005 1.118 T 1 090 11.066 11046 11 019 T 1 017 1 1 007 1.162 T 1 124 11.091 11063 11 030 T 1 023 1 1.010 0~9 1 1~0 1 001 1.001 1 002 1.000 1.000 1.000 1.003 1 eOOO Table 20. Computed adjustment factors for PF of 0.1 to 1.0 Progression Factors, PF v/c 0~4 0~6 0~7 0~8 0~1 1 048 1.100 .142 1208 0~2 1 0~3 1 0~4 1 0~5 1 0~6 1 0~7 1 0~8 1 035 1 026 1 019 1 014 1~010 1 008 1 006 1 074 1 054 1 040 1029 1 021 1 016 1 012 . 1~105 1 077 1 057 1042 1.031 1 023 1 017 . 1153 1 113 1 083 1061 1 045 1 033 1 025 0~9 1 1~0 1 004 1 009 1 012 1 018 1 003 1 006 1 009 1 013 2~7~4 Adjustment for Sneakers Comparison ofthe simulation results between random flow and progressed flow at a PF of 1.0 revealed that the ramp crossing volume for a PF of 1.0 was higher. The difference between the ramp crossing volumes between random and progressed flow increased with an increase in arsenal volumes. This difference in ramp crossing volumes was attributed to the sneakers crossing during the two phase change intervals i.e., sneakers (S,9. In over words, the ramp vehicles completed the weaving maneuver by making use of the large gap available to the ramp vehicles during the two phase change intervals of four seconds each at the upstream intersection. The random flow conditions had a situation wherein the upstream intersection had 100 percent green on the arsenal movement and hence the effect of sneakers was not observed. On the average, approximately three vehicles were completing the weaving maneuver during each phase change interval. The effect of 2 - 68
sneakers was confirmed visually by observing the animation of the simulation for the required conditions in GTRAF. Thus, the ramp crossing capacity, adjusted for sneakers, would be QR Qua Sm where: Q R QR sm ramp capacity adjusted for sneakers (vph); ramp capacity for random flow (vph); and sneaker volume (vph). 2.7.5 Application ofAdjusiment Factors (33) In order to obtain the ramp capacity for different progression factors, the adjustment factors for progression,fpF, needs to be multiplied to the ramp capacity which has been adjusted for sneakers as follows: = where: QPF Q R fPF QPF QR fPF ramp capacity adjusted for progression (vph); ramp capacity for random flow (vph); and adjustment factor for progression. (34) The application methodology of this formulation of arterial weaving wall be presented in Chapter 3. Moreover, field studies of arterial weaving operations were conducted and are described in detail in Appendix E (129. Several empirical models of maneuver speeds and delays as related to local conditions are provided. These studies were extremely tedious and time consuming. Other initial NETSIM simulation studies of arteriaVramp weaving operations were conducted end reported (139. All of these studies showed the benefit of increased signal separation between the interchange and the next downstream signal together with the benefit of arterial signal coordination during undersaturated conditions. 2 - 69
