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APPENDIX A STATE-OF-TlIE-ART A.1 SURVEY OF CURRENT PRACTICE A comprehensive evaluation of the state-of-the-art in areas related to interchange design and traffic operations was conducted as part of this research. The focus of this Valuation was on issues underlying the design and operation of interchanges In urban or suburban areas. More specifically, the issues related to the signal-controlled ramp terminals and traffic flow along the cross street through the interchange. Consideration was also given to the relationship between the interchange terminals and any adjacent, closely-spaced signalized intersections. One aspect of the evaluation involved a survey of transportation engineers. The intent of this survey was to gain insight into the current practices and concerns of engineers who evaluate interchange traffic operations. The survey was conducted In two stages. The first stage consisted of a one-page questionnaire. This questionnaire was intended to obtain basic types of information such as: 1. Common interchange types (geometric configurations) 2. Common operational problems 3. Common interchange operations analysis techniques 4. Common measures of effectiveness used for evaluation 5. Willingness of the respondent to participate in the second-stage survey. 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 successfully used to evaluate interchange operations. The findings from these two surveys are described In the next section. A.. F~rst-Stage Survey Distribution. The f~rst-stage survey was sent during the first week of February, 1994. More than 2,400 surveys were sent out to engineers In the U.S. and abroad. The members of the following groups were specifically targeted: AASHTO Subcommittee on Traffic Engineering; AASHTO Subcommittee on Design; AASHTO Special Committee on Transportation Systems Operation; ITE Urban Traffic Engineers Council; and ITE Consultants Council. A

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Individuals in these groups include engineers responsible for planning, design, and operations of transportation facilities In the United States. In addition, several hundred surveys were sent to selected members of the Institute of Transportation Engineers OTE). After a thorough review of each returned questionnaire, a finalized total of 350 first-stage questionnaires were deemed completely responsive and valid. This group represents a 15-percent response rate, which is within the 10 to 20 percent rate expected prior to the survey. Overall, there were 146 responses from the public sector, Including 68 from state Dons, 63 from cities in 16 states, and 15 from counties In ~ states. Seventeen responses were received from outside of the United States (i.e., Canada - Il. Germany - 2, South Africa - 41. Responses were also received from IS7 consultants in 23 states. The geographical distribution of the responses is summarized in Table Apt. Results. The f~rst-stage questionnaire consisted of six questions, primarily requesting but not limited to multiple-choice replies. The results for Questions I, 3, 4, 5, and 6 are provided in Table A-2. The response format for Question 2 is somewhat different from the other questions and will be discussed separately. Question ~ inquired about the frequency of interchange operations analysis. An analysis of the survey responses shown in Table A-2 indicates that cities/counties and consultants evaluate interchanges about "3 to 6 times per year. " In contrast, most state DOTs evaluate interchanges "less Man 3 times per year." However, a relatively large percentage of state DOTs indicate that they evaluate interchanges as frequently as "once per week." Question 3 asked the respondents to rank the Operational problems listed in terms of their frequency of occurrence at interchanges that the respondent is personally aware of through their work experiences. As indicated In Table A-2, "~nadequatecapacity" was given the highest ranldng signifying it as the most frequently occurring problem. This problem was followed by "queue spillback" and then "weaving" in terms of Heir frequency of occurrence. Operational problems other than the three listed were described by twenty-two respondents. A common theme In these problems was a lack of effective signal coordination between the ramp terminals (or between the ramp terminal and adjacent signalized intersections. Question 4 inquired about He types of analysis methods used to evaluate Interchange traffic operations. In general, software methods were more frequently used than manual methods. The most commonly used software method is the Highway Capacity Software (HCS). PASSER IT and TRANSYT-7F were also found to be frequently used. Question 5 inquired about the most useful measure of effectiveness (MOE) for evaluating interchange traffic operations, particularly at ramp terminals. The most commonly selected MOE was delay, followed by spillback frequency, and volume-to~apacity ratio. The "other" category was infrequently used. Those that did use it indicated Hat speed or travel time measured along the cross street through the interchange would be most helpful. A - 2

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Table A-1. Geographical distribution of responses to first-stage questionnaire. Number of Responses Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware noridla Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri State Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York Norm Carolina Nor h Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Vermont . . I Vlrg~a |~ash~gu)n | West Virginia | Wisconsin 1 Wyoming Number of Responses A - 3

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Table A-2. Summary ~ I Numbe - (Percent) of Responses Response | City &County i State DOT I Question 1. How often do you analyze some aspect of traffic operations at signalized intersections? [~ Once per Week l 11 (14%) | 18 (26%) l 0~ it- Ma at, 13 (17%) 14 (21%) . ~ w ~ Am. per Ye~r 28 (36%) 11 (16%) . [~;I:~Wu 24 (31%) 24 (35%) !~1~5~e 2 (3%) 1 (1%) 1 Question 3. Please rank the operational problem that you have encountered on the cross street at the most frequently used "Existing" interc Lange type. (1- no problem; ~ - serious problem) | Average Rank Inadequate Capacity 3.7 3.7 W~: ~ 2.2 2.3 t1~ Kid 1~:k 3.5 3.5 uestion 4. What analysis techniques do you use to evaluate traffic operations at the interchange ramp terminals? (mark all that apply) l Numbt (Percent) of Responses' Highway Capacity Manual 25 (32%) 20 (29%) Over Manual Methods 9 (12%) 9 (13%) Highway Capacity Software 38 (49%) 48 (71%) TRANSYT-7F 37 (47%) 30 (44%) PASSER II 35 (45%) 31 (46%) PASSER III 22 (28%) 20 (29%) JI:A~81M 8 (10%) 15 (22%) Other Software Methods 10 (13%) 9 (13%) Question 5. What measure of effectiveness would be the most useful in evaluating traffic operations at the ramp terminals? (Including ~:1b ADAM 1 ~30 (38%) 33 (49%) Queue Spillback Frequency 34 (44%) 39 (57%) Delay per Vehicle 52 (67%) 44 (65%) Thru Movement Bandwidth 30 (38%) 21 (31 %) Saw ~r `/:h~l: 17 (22%) 10 (15%) ~5 (6O ~1 (1%) Question 6. Would you be milling to respond to a more detailed questionnaire concerning the details of interchange ramp Junct_ ~ _~ Yes 1 36 (46%) 1 38 (56%) . . No 1 34 (44%) 1 28 (41 %) No Response 1 8 (10~) l 2 (3%) Consultant 32 (17%) 50 (27%) 70 (37%) 35 (19%) O (0%) 3~8 2.6 3.7 77 (41%) 11 tS~) 161 (86%) 57 (30%) 35 (19%) 35 (19%) 80 (43%) 99 (53%) 115 (61%) 34 (18%) - 29 (16%) 10 (5%) 105 (56%) 70 (37%) 12 (6%) Notes: 1 - Percentages for Questions 4 and 5 do not sum to 100% due to the "mark all that apply" nature of the questions. A - 4

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Question 6 inquired about the willingness of the respondent to participate in the Second- Stage Survey. All total, 179 U.S. respondents indicated that they would be willing to participate. This represents about 51 percent of the 350 U.S. responses received. Question 2 was used to identify the interchange configurations Mat were most commonly being evaluated by engineers. The frequency of evaluation was further categorized by "existing interchanges, ~ "interchanges In design, " and "interchanges in planning. " This categorization was helpful In identifying current trends In Interchange design. Variations of the question were prepared for engineers employed in the public or private sectors. Engineers employed in the public sector were asked to assess the percentage of each type of signalized interchange in their jurisdiction that are "existing," "in design," or "in planning." Engineers employed in the private sector were asked to assess the percentage of interchanges that Hey typically evaluate as part of their consulting activities. The response to Question 2 is illustrated In Table A-3. As the data in this table suggest, the most commonly evaluated Interchange configuration is He Compressed Diamond. However, all of He interchange forms were selected with sufficient frequency as to suggest Hat none should be excluded from consideration in the development of melons to evaluate Interchange operations. CD TD TDw/F PC Other Responses Table A-3. Distribution of interchange type by agency and stage of project development. ,. ., Interchange Existing Interchanges Typlel City or County . 30% State DOT 59% 13% 8% . 0% . 0% . 52 Design or Construction Consultant City or Colmty _ State DOT _ _ ~ 45% 38% _ 13% 17% 5% 9% l ~ 21%0 30% _ . 6% 6% 32 76 COIlSllltaIlt City or County 37% 9% 27% 9% 8% Planning State Consultan DOT 52% 40% 4% ~ 16% 10% 6% 24% 32% 0% 6% . 11 1 21 1 104 Notes: 1 - InterchangeType Descriptions: CD - Compressed&amond (ramps 120 tO 240 m); TD - Tight diamond (ramps less Man 120 m); TDw/F - Tight diamond win frontage roads; PC - Partial cloverleaf of several variations. Discussion of Results. The first-stage survey results show that practicing engineers are concerned win the effective operation of interchanges. Questions 1, 2, and 3 were asked to determine how much and what is being done on interchange design and Aerations. Based on the replies given for Question 3, engineers frequently encounter operational problems at interchanges in urban areas. However, it appears that neither the reasons for the problems (e.g., lack of capacity, queue spilIback, weaving, etc.) are well understood nor are He solutions (e.g., ~nterchange-specific analysts techniques) readily available. These Innitations hinder an engineers ability to analyze interchange traffic operations. A - 5

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As a means of examining the operational problems at interchanges in more detail, the second-stage questionnaire was developed and distributed to the interested f~rst-stage respondent. The results from the second-stage questionnaire can be found in the next section. Question 2 verified that the diamond interchange (either compressed or tight urban) was the most common existing, designed, and planned interchange. This fact is likely due to the reduced right-of-way costs associated with interchanges of the diamond familY. relative to those of He partial cloverleaf family. Ha, of, Question 4 was asked to determine which traffic models are being used by practicing engineers to evaluate interchange operations. The most common type of analysis used by the respondents is computer software models and, most often, He Highway Capacity Software (HCS). This may be due to its widespread acceptance, consistency with the Highway Capacity Manual, or the relative ease with which it can be used. As the current HCS is relegated to worksheet-based procedures that are sufficiently simple that they can be used in a manual fashion, it tends to be limited in its ability to evaluate traffic flc~v problems in interchange areas. As a result, several computer-baseds~mulation models were often cited by the respondents. Specifically, TRANSYT-7F was cited by nearly half of all the respondents. This 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-M was also cited by 40 to 50 percent of the respondents as being a usefill tool to analyze arterial traffic flow through interchange ramp terminals. This large response may be due to the fact that PASSER-II optimizes signal timing based on progression analysis. In order to better understand the strengths and weaknesses of these models, as perceived by the users, the second-stage questionnaire requested that the respondents expand upon their reasons for selecting a specific analysis tool. The results of the second-stage survey can be found In a later section. Question 5 asked the respondents to identify an MOE that they felt would be useful in evaluating traffic operations at an interchange. In order to better explain traffic operations at an interchange, MOEs must be selected that are comprehensible and practical. Thus, it is important that the MOEs selected to evaluate an interchange be those that are easy to observe and to comprehend (not something abstract In nature). Delay per vehicle was the MOE most often selected by respondents. This finding is probably due in part to the fact that the HCM uses delay to describe the level of service provided to motorists at intersections. It would appear to be a logical extension on the part of the respondents as a diamond interchange has the appearance of two arterial intersections rather than two closely-spaced ramp terminals whose individual operatic is highly dependent on the signal operation of the other ramp terminal. After delay, queue spillback frequency was the next most frequently cited MOE by the respondents. This is consistent with the findings regarding operation problems, as requested in Question 3. Queue spillback is recognized by many engineers as a significant problem at urban interchanges. It is likely that the length of the queues formed between the ramp terminals and the frequency that they spillback into the upstream ramp terminal (or closely-spaced adjacent A - 6

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signalized intersection) could be used as a primary indicator of the quality of flow within the interchange area. Question 6 showed a willingness to respond to the second-stage questionnaire. The large positive response received in this regard is believed to represent the engineering commun~ty's overall level of interest in the topic of this research. A.~.2 Second-Stage Survey The findings from the f~rst-stage survey provided important information regarding the extent of operational problems at urban interchanges and the general thoughts of the practicing engineering community regarding techniques for evaluation of these problems. These findings were used to develop the format and content of the second-stage survey. This survey sought specific details of operational problems occurring at specific types of interchanges. The second- stage survey also inquired about the strengths and weaknesses of specific analysis techniques. Distribution. The second-stage survey was sent during the last week of March 1994. This survey was sent to 179 individuals who indicated a willingness to respond to it from the first survey. A total of 31 completed surveys were returned representing a 17 percent response rate, a rate that was somewhat lower than anticipated. The findings from the second-stage survey were generally consistent with those from the f~rst-stage survey. Therefore, it was concluded that the information obtained from Me second-sta~ survey would tee more representative then the small sample size would otherwise suggest. Possible reasons for the small sample size could include a combination of the following: (~) the survey may have been conducted during a busy time of the year for Me respondents, (2) respondents may have believed that the time required to complete the survey was excessive, and (3) the return date may not have allowed Me respondent enough time to adequately respond. Of the 3 1 surveys returned, 29 were determined to be valid responses In the context that they addressed the interchange types and issues described in the survey. Valid responses were returned from 10 state DOTs, ~ cities In 6 states, 9 consultants In ~ states, and 2 cities in Chnada. Overall, 21 states are represented among the 29 valid returned surveys. The response rate was about 29 percent for the DOTs, 25 percent for the cities, 0 percent ibr the counties, 9 percent for Me consultants, and IS percent for international replies. Results. The findings from the second-stage survey are described in the following paragraphs. These findings are presented in the following format: the individual question is repeated (in italics); then, the response to each question is summarized; finally, some observations and insights are provided to put Me findings in the proper context. In general, each respondent was asked to identify one interchange of the diamond or partial cloverleaf family and answer the survey questions as they relate to this interchange. The interchange that they selected was to have attribute s that were consistent with the objectives of this research and that were otherwise not unusual or geometrically constrained. Specifically, the A - 7

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selected interchange was to be located in an urban or suburban setting, have signalized ramp terminals, and a distance between ramp terminals of 275 meters or less. The respondents were encouraged to complete additional survey forms for a second or third interchange, if tune permitted. ]. Please sketch the interchange. The types of interchanges sketched (and described In subsequent questions) ranged from the partial cloverleaf to the single-point urban interchange. In three instances, the respondent submitted a second survey describing a different interchange. As a result, descriptions of 32 interchanges were received; however, one interchange was described twice by two different respondents. As a result, only 31 unique interchanges are described in the summary statistics. These Interchanges are distributed among the seven interchange types listed below. 1. Tight Urban Diamond (less than 120 m between ramps): 2. Tight Urban Diamond with frontage roads: 3. Compressed Diamond (120 to 240 m between ramps): 4. Conventional Diamond (more than 240 m between ramps): 5. Single Point Urban Diamond: 6. Partial Cloverleaf (Type A): 7. Partial Cloverleaf (Type AB): 10 2 11 2 2 3 1 Vent is the distance between the two ramp terminals (as measured along the cross street from stop line to stop line) ? Average: 150 meters, Minimum: 60 meters, Standard Deviation: 90 meters Maximum: 410 meters These distances are not representative of all interchanges because the survey specifically requested information on interchanges whose ramp-to-ramp separation distance was less than 275 meters. However, they are representative of urban interchanges that tend to experience traffic operational problems because of short ramp separation distances 3. Wheat is the distance between the ramp terminal and the nearest downstream signalized intersection (as measured along the cross street from stop line to stop lined ? Average: IS0 meters, Minimum: 50 meters, Standard Deviation: 90 meters Maximum: 440 meters As with Question 2, these distances should not be taken as typical of all interchange locations; just those interchanges in urban areas with relatively close ramp spacings. The respondent was informed (in the survey) that one objective of the project was to address the operational impact of closely-spaced intersections. As a result' the respondents, tended to include A - 8

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interchanges with closely-spaced intersections. These closely-spaced intersections often lead to problems such as queue spiliback between ramp terminals and left-turn bay overflow. 4. Coul~you provide a block diagram illustrating the phase sequence for one signal cycle? Twenty-four respondents provided phase sequence information. The open nature of this question led to a wide range of response formats. As a result, it was difficult to generalize the types of phasing based on the descriptions provided by the respondents. The problems with interpretation were grouped into three categories. First, very few of the respondents used Me block diagram format requested; many provided signal timing information fran plan sets or from manufacturer-specif~c controller printouts that could not be translated with any real certainty. Second, it was apparent that many respondents were only guessing at the phase sequence based on their observation rather than obtaining the actual sequence from the appropriate authority. Finally, many respondents described We phase sequence for each ramp terminal but did not convey the manner in which they were coordinated. After reviewing the phase sequences provided, the following generalizations were made. First, only 2 of the 25 diamond interchanges appear to be using me four-phase-with-overIap phasing. It was expected that this type of phasing would be more prevalent due to its ability to deal with high-volume left-turns and narrow ramp separation distances. Second, it appeared that most of the interchanges with two controllers used three-phase operation at each ramp terminal with, presumably, some type of signal offset tuning used to coordinate the two major street through movements at the ramp terminals. 5. Wheat type of signal control is used to implement the phasing dlescnbed in Question 4? About 59 percent of the respondents indicated that two controllers were used at the interchange (one controller for each ramp terminals. Another 31 percent of the respondents indicated that one controller was used for both terminals; the remaining 10 percent did not know the controller type. As diamond interchanges were the most common interchange type cited In Question I, it is somewhat surprising that so many sites had two controllers at the interchange. One common controller for both diamond interchange ramp terminals is generally best able to maintain the type of two-way traffic progression necessary to eliminate queues on the street segment Internal to the ramp terminals. The trend of using two controllers (with presumably signal offset timing) may possibly contribute to the queue spillback that many of the Interchanges exhibit because of the lower level of coordination it affords to the left-turn movements. 6. What control mode does the controller provide ? About 75 percent of the respor~ents indicated that semiactuated control was used at their interchange. Thirteen percent indicated that pretuned control was used and 9 percent indicated that fi~ly-actuated control was used. Comparison of the responses among Questions 5 and 6 indicate that Mere is no correlation between the number of controllers and the type of control mode. A - 9

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7. Is the interchange controllerts) coordinated with the cross street signal system? As semi-actuated control implies coordination, it is logical that coordination was found at the same percentage of interchanges as those having semi-actuated control. In fact, this was Me case, 75 percent of the Interchanges described had semi-actuated control. The high percentage of coordinated interchanges suggests that, while efforts should be made elsewhere in Improving Interchange traffic operations, impacts on coordination should not be forgotten. 8. Describe the traffic flow problem which tends to be most disruptive to smooth traffic flow. Although this question asked about the most disruptive problem, most respondents chose to describe more than one problem. In general, they selected one or more of We traffic flow problems that were described in the survey. These problems are restated below along with the percentage of responses Mat identified a particular problem as berg Me most disruptive. 41% a. Capaciy restriction due to queue spillback between ramp terminals. 34% b. Capacity restriction due to queue spillback from a ramp terminal into the upstream signalized intersection. 31 % c. Capacity restriction due to cross street left-turn bay queue overflow into the through lanes. 25% d. Unbalanced lane volumes on the cross street approaches to the romp terminals due to h~gh-volllme downstream turn movement. 25 % e. Flow turbulence between a ramp terminal and an adjacent signalized intersection due tohigh-volume lane changing (i.e., right-turn at terminal followed by left-turn at intersection, or vice versa). 22% I. Capacity restriction due to queue spillback from a signalized intersection into the upstream ramp te~lllinal. 22% g. Capacitor restriction due to queue spillback from the off-ramp signal into the freeway main lanes. 19% h. Poor signal coordination between the two ramp terminals due to complex signal phasing, variability in hourly turning movement volumes, or minimal interior queue storage space. 16% i. Capacitor restriction due to queue spilIback from a ramp meter into the upstream ramp terminal. 6% j. Poor or nonexistent signal coordination between Me ramp terminals and adjacent intersections due to jurisdictional policies (i.e., Cider control of the intersection and State control of the interchange). 0% k. Poor or nonexistent signal coordination between the ramp terminal and ramp meter. Based on the percentages listed above, it appears that "queue spiliback between ramp terminals" is the most frequently found problem at interchanges in narrow-rights-of-way. When combined with "left-turn bay overflow, " it would appear that traffic flow problems et interchanges are most frequently found between the ramp terminals, where the volume of left-turns is highest. A- 10

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One response from a consultant in Portland, Oregon reported a lack of capacity between the terminals of a compressed diamond interchange. This interchange has ore controller for both terminals and operates In a three-phase sequence. The respondent indicated that the restricted capacity "results in a queue spilIback into the adjacent cross street signalized intersection. " This spilIback, In turn, "results in little or no capacity for local circulation" at the adjacent intersection. Another response from a consultant in New York identified problems associated with turning movements. The respondent reported that the tight urban diamond exhibited left-turn bay queue overflow at one of the ramp terminals and severe turbulence associated with high-volume weaving on the cross street between the ramp and adjacent signalized Intersection. The maneuver that caused most of this turbulence was the off-ramp right-turn movement becoming a left-turn movement at the downstream intersection. Further examination of the responses to this question revealed that all of the reported flow problems related to queue spilIback between the ramp terminals were associated with tight or compressed diamond interchanges. Single point diamond interchanges, conventional (wide) diamond Interchanges, and partial cloverleaf interchanges were not associated with queue spillback-related flow problems. The single point diamonds do not experience queue spiliback because Hey combine the two ramp terminals into one intersection. TO conventional and partial cloverleaf interchanges do not experience spillback because of the relatively large distances separating Be two ramp terminals. 9. What treatments have you applied! (or would apply) to alleviate the traffic flow problem described in Question S? A wide range of treatments were described by the respondents. There were no definitive trends although it appeared that geometric changes were commonly seen as the only available treatment. Typical geometric treatments included adding a second left-turn lane or an additional through lane to the cross street. In some instances, the respondent recognized the difficulty of adding lanes to (i.e., wideIiing) an existing bridge. One of the more Interesting signal timing treatments was the use of signal phasing at the adjacent Intersection to separate the traffic movements accessing the on-ramp so as to prevent the congestion associated with a high-volume of weaving vehicles. Many respondents indicated that improved or updated signal timing and coordination helped mitigate some traffic problems. 10. If you were asked to evaluate and quantify the problem described in Question 8, what Abyss technique (or techniques) would you presently use ? The analysis techniques cited by most (60 percent) of the respondents can be described as those developed for isolated signalized intersections. These techniques were used for the analysis of the individual ramp terminals and adjacent intersection. Of those techniques identified, that described in Chapter 9 of the 1985 Highway Capacity Manual (HCM) was cited as being most frequently used. PASSER IT was identified by 33 percent of the respondents as being helpful in coordinating the two ramp terminals and the adjacent signalized intersection. Other, less frequently noted techniques included the use of the NETSIM and TRANSYT-7F computer models. . A- 11

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length of ~ a + 44d~b Jr tie = Cdf (A-45) Subject to each phase, m, satisfying its minimum green requirements ltm > min In As long as the two signals operate independently, cycle times can be different to accommodate variable traffic demands, green splits can be provided without constraints to better satisfy those demands, and capacities are at a maximum. Capacity principles described in Chapter 9 - Signalized Intersections of the HCM would apply, as follows. For a representative intersection and cycle, Cj, the sum of critical phases is Via ~ Sib + Tic = Ci (A-46) which is equivalent to (g l Via (g [)ib (g Chic Ci (A47) Letting [3 equal the sum of the three lost times per phase, the total effective green time per cycle is gia gib gic Ci [3 And since the v/c ratio for a phase or related lane group "m" is given by X. = (A-48) ~ VC 1 im 1` Sg) m (A-49) Solving for We effective green, am' and substituting into Equation A-48 for the available effective green time, yields a more general expression of vanables (, sx~J ia t~ sx! fib ~ SX) ic (A-50) Dividing by the cycle results in the fundamental capacity equation for intersections of A -42

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j Sat ia ~ SX) ib ( SX) ic C, (A-51) Letting Y = As be the flow ratio of demand flow to saturation flow, then ~ X ! ia ~ X) ib ~ X] ic ci (A-52) Defining a new term, the pie ratio for a critical phase m, to be Him at,, xNJ It, sXl/1 (A-53) zm Im which is the proportion of the available green time needed (used) to serve the demand volume for a given geometry and degree of saturation, then for each intersection, i, the pie ratio must equal the proportion of the cycle time available for moving traffic rr`-~ Ci - L, ~ Hi = ~ brim = 3 = ~ _ 3 (A-54) m=} ci i For planning and design purposes, the fundamental capacity equation (A-5 1) may be solved for critical service volumes for given average/design assumptions. First, a signal timing strategy is usually assumed that provides equal v/c ratios for all critical phases such that X. = X. = X. = X. = X. a zb IC am I ~ ib ~~ ic ~~ im (A-55) following the welI-known Webster strategy which also tends to minimize intersection delay. Thus, for equal degrees of saturations for all critical movements m, X im = X `, Equation A-5 ~ becomes X~ ~ s\J ia X~ ~ s\J ib X it 5~11 ic Ci (A-56) A - 43

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so that for the three critical phases at intersection i, the total intersection flow ratio is m=3 m=3 L Y = Yim v = Xi 1 - - m=1 m=1 (sJ im ~c,J (A-57) For planning arid design purposes, it is also convenient to work with locally adjusted average saturation flow values, and per lane volumes, to estimate the resulting flow ratios; y _ (v) ~ S J or on a per lane basis = 1 (~i' - J zm SO Rj (by) ~ NJ im (A-58) y 1 ( v ~Via (A-S9) such that the equivalent critical lane results are Vila } Vilb + ilc = X ~ 1 - 3: Sila Silb silo ~ci ) (A-60) Assuming that S'la = Silb = Silk and that v`/b and vile have been adjusted slightly to equivalent through volumes (TV,, CV'~c) to keep the flow ratios the same, then the sum of the "equivalent through vehicle" critical lane service volumes for a given Xj would be m =3 CV. = ~ CV. = s. X. al zlm zla z m =1 L3 1 -- C. \ 1 The average allowable service flow per critical phase, Pa, would be f P il 3 Sila Xi ~ 3 C A - 44 l (A-61) (A-62)

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where ~ is the average lost time per critical phase. The equivalent through vehicle can represent passenger cars only, or the average fleet mix for the locale by adjusting S'`a acccordingly. Assuming that s,,,, = ~ 800 vphgp} for the local traffic mix, X, = ~ .0 for capacity flow, ~ = 4.0 sec/phase, and C = 100 see; then the total critical lane capacity flow, Cry, for intersection i from Equation A-61 would be CVji = IS00 X 1.0 ~1.0 - ~ )~ = 1584vphpl (A-63) and the resulting average critical lane capacity per phase from Equation A-62 is Pil = 1 8 00 x 1 .0 ( 0 3 3 3 - -1 = 52 8 Vphpl (A-64) 100) Other critical lane service volumes can be calculated for the degree of saturation selected. In addition, an operational analysis could be conducted to determine the overall degree of saturation (X,) on the intersection produced by the critical volume loading present. Coordinated Intersections. Traffic signals at most interchanges are coordinated to improve overall traffic operations because the intersections are closely spaced and traffic volumes are often high. Under these conditions, coordination generally improves operational reliability and reduces internal queueing, queue spilIback into upstream intersections, and the threat of operational gridlock. At lower traffic volumes, cross arterial progression can also be provided in most cases to reduce queueing. The overall quality of operations depends on the features of the signal system deployed, the progression provided, arid other factors. Coordinated signal operation implies Cat the two intersections no longer can operate independently. The first coordination constraint applied usually is that the two cycles, Cu and Ca5 must be the same length at a particular point in time. This cycle constraint is true whether Me interchange is controlled by one controller unit or by two. Thus (A-65) Delays and queueing incurred on the two external approaches to the lower-volume intersection will increase due to operations at a suboptimal (higher) cycle, assuming that the interchange would operate at the cycle of the higher-volume intersection. Signal coordination within the interchange can almost eliminate outbound delays, but arterial coordination is required to mitigate arterial approach delays incurred on the inbound Phase a.

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Cycle timing is cr~ticalto interchange operations for many complex arid interrelated reasons. Capacity analysis should recognize this central control parameter. The first consideration in establishing cycle time is to determine whether interchange control is coordinated with the cross street arterial or not. If yes, then cycle times wall be fixed for various coordination time periods. The interchange' slocal control may be coordinated pretimed or coordinated(semi) actuated, but the system cycle length is the same in either case. The second consideration in establishing cycle time, given that cross arterial coordination is not effected, is whether the interchange' scontroller~s~is pretimed or coordinated (semi) actuated. Local interchange coordination is presumed. Pretimed systems are fixed to prescribed durations regardless of current traffic demands and local capacity provided. Presumably forecasted traffic demands and estimated roadway capacity were considered in the initial selection of cycle times, but conditions may have changed. For locally coordinated actuated control, field measurements are highly recommended over unproven analytical models or engineering judgement. Actuated control is reactive to queues and tends to be unstable in congested operational environments and, therefore, may generate extremely long cycles and undesirable green splits based only on maximum green settings, which may further exacerbate the congestion. Another critical operational feature affecting interchange traffic operations is whether the green splits at the two intersections depend on one another. If two separate controllers are used (or independent rings are provided using one controller), then capacity estimates are best given by Equation A-S I. If phasing is dependent (e.g. only one controller is used with dependent phases), then more complex demand analysis is required consistent with the type of interchange and phasing used. Operations at "four-phase" diamonds is a classic example, but others abound. Coordinated Diamond Interchanges. A popular diamond interchange signal timing strategy is "four-phase with two overlaps." In addition to having many of the above timing features (e.g., same cycle, a fixed sequence, and a fixed offset), this strategy also provides quality platoon progression for the arterial traffic in both directions of flow through the interchange by either special controller design, or by judicious signal timing. By either method, the following signal timing relationship must occur 66J for four-phase with two overlaps signalization to result Gua GUb + Gda ~ Glib = Ci + ~ (A-66) where it is presumed that Go and Go, are the thru and ramp phases, respectively, and 4) is the total interchange "overlap" for both directions of flow through the interchange (5~. This operational requirement provides great progression for the arterial traffic passing through the interchange. However, the sum of the four external phases serving traffic input to the interchange is fixed for a constant cycle and does not have full flexibility to optimally adjust to all possible traffic patterns that might arise at the interchange. In addition, this constraint (Equation A-66) further implies that the sum of the two internal left turns within the interchange is also fixed 669 at . . . A -46

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GUC ~ Gdc = Ci ~(A-67) because the sum ofthe conflicting phases must equal two cycles (Equations A-66 and A-671. This fact may be a significant constraint on the optimal solution depending on the cycle time, minimum green times required, and traffic pattern being serviced 664. The computer signal timing program PASSER Ill, developed at Texas Transportation Institute, contains these strategies for developing optimal signal timing for all fonns of two-level signalized diamond interchanges. PASSER ITI also contains delay/difference-in-relative offset aIgonthms, somewhat like TRANSYT 7F, to evaluate traffic performance for given signal timings fly. A.2.10 Interchange Capacity Shoddies Most operational studies reported in the literature have been conducted on signalized tight urban diamond interchanges (TUDI), probably because of operational problems due to the closely spaced ramp terminal signals. These signal spacings in many urban areas are often on the order of 70-] 00 meters. Capelle and Pinnell wrote In We early ~ 960's f7) that: "After studying the problem of evaluating the capacity of diamond interchanges, it was determined~at it would be necessary to consider the two signalized intersections as a single unit. This is due primanlyto the requirements of signalization which should perform two basic functions. These functions are as follows: (a) all highway volume conflicting movements at both intersections must be separated, and (b) storing of vehicles between the two intersections must be kept to a minimum due to limited distance between them." The above study was conducted at diamonds that were "locking up" using three-phase operation. Capelle and Pinnell (7J then tested a new phasing plan that has since become known as "four-phase with two overlaps" to improve operations. They proposed a method for calculating interchange capacity for this strategy which they termed the critical lane capacity, CVc as being CV = (C + 4 + 4D + 8) 3600 (A-68) where C represents the cycle length, D the starting delay, and H the saturation headway. The starting delay used for their calculations was the time required for the first two vehicles in a lane to enter the intersection. The critical lane capacity, CVc, represents the maximum sum of the four critical lane approach volumes from the four external approaches to the interchange. Capelle and Pinnell (79 computed critical lane capacity using H= 2.] seconds/vehicle and D = 5.8 sec. A 2.] seconds saturation headway is equivalent to a saturation flow of 1,714 vphgpl in the HCM. In a recent HCQSC Literature review, Lee (~9 updated the Capelle/PinnellMethodto include recent interchange studies in the Phoenix area using Hook's data (99. The equivalent Hook's value for starting delay and average saturation headway. weighted bY the volumes of the movements were , , . . ~ , A - 47

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7.1 and 1.89 seconds, respectively. Capelle and Pinnell assumed that the starting delay was incurred by the first two vehicles, while Hook assumed the third vehicle in queue. Following some additional modifications, Lee developed the equivalent sum of critical lane volumes shown in column 3 of Table A-15. Column 4 was derived by TT] from work on NCHRP 3-40 (109 described below. TABLE A-15. Critical Lane Capacity of Diamond Interchanges by CapeNe/Pinnell, Lee, and NCHRP 3-40 Cycle ~OriginalCritical ~Updated Critical Length Lane Capacity Lane Capacity(2) 40 1,611 1,821 50 1 1,635 1 1,838 60 1,650 1,849 70 I 1,660 T 1,857 80 1,668 1,863 100 1 1,674 T 1,872 180 1,692 1,886 . f~' Based on 1961 values for starting d. .ay, D, of 5.8 seconds and average headway, H. c 2.1 seconds (7). (2) Based on current values of D = 5.2 seconds and H = 1.9 seconds, (8). IT ! (3) Based on studies published in References 9,10,11,12, and 13. NCHRP 3-40 Cntical Lane Capacity(3) 1,980 - 1,984 1,987 1,989 1,990 1,992 1,996 About the time Lee was performing his analysis, Messer and Bonneson were publishing a more updated version ofthese formulations in NCHRP 345 (109 based on the Phoenix data (9,11) plus additional data collected in Florida and Texas by Bonneson (12,13,149. The basic "saturation flow" model followed the earlier work by Messer in 1975/76 (15) described in the previous section. The critical movement model for interchange capacityis, however, basically a reciprocal formulation ofthe headway model presentedby Capelle and Pinnellin 1961, but with slightly different saturation flow and start-up delay calibration factors. Messer, et al, showed in NCHRP 3-40 (10) that He sum of the four critical external inputs to a diamond interchange operating with four-phase with two external overlap signal timing has a critical lane capacity of CV = CV + CV + CV + CV Ic ua ub da db A-48 ila I C C ~ . (A-69)

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where: CV,c sum of interchange critical input volumes, vphpl; adjusted saturation flow for all critical input phases, vphgpl; (= 3600/H above) total interchange overlap, see; number of critical input phases, n = 4; average phase lost time, see; and cycle length, sec. The total interchange overlap is a function of the center-to-center spacing between the ramps, arterial grade, and quality of cross street coordination. An equation for estimating ~ for nominal conditions of no grade nor coordination is given ~ the PASSER Ill users manual as 4) = 2 [0.sO ~ 40.137L ] (A-70) for art intersection spacing of ~ meters subject to a maximum speed of 50 km/in (30 mph). Higher maximum speeds and lower overlaps may be appropriate urlder well coordinated cross street operations. Messer's updated interchange/intersectioncapacity model (109 can be applied to other types oftwo-leve! signalized interchanges operating in a coordinated system/common cycle mode. The model estimates the sum of critical lane volumes, CVc' that can be input into the interchange from the four external approaches according to the following equation Chic = sofa [1 ~ ~/C n(Zs [e)/C] (A-71) where sea equals the mean saturation flow rate for all critical phases, (s = 3,600/H above), ~ is the total phase overlap in the interchange, h, is the number of critical phases, Is is the platoon startup lost time (about 2.0 seconds) per phase, and le is the end lost time associated with ending the phase as related to the width of the interchange and the duration of We signal change intervals (the yellow warning and (all?) red clearance intervals). The average phase capacity, P., can be estimated by dividing by the number of critical input phases, n, on the external approaches to yield Pa = s~atl/n + ~/nC ~ (Is ~ Ic)/c] (A-72) Equations developed in the earlier research projects to estimate the above parameters are given in the following section. A -49

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The capacity of an interchange depends on several operational parameters, as Equation A-71 illustrated. Signalized interchanges are character~zedby the number of critical phases that may exist (usually 2 for 4-quad parclos, 3 for 2-quad parclos arid many diamonds, or 4 for many TUDIs), by the total phase overlap 4) that may be present (usually 0.0 except for four-phase overlap systems), arid by the total amours of clearance time used to safely terminate phases. Operational Parameters. TTI used the above referenced reports (12, 13, 14J to develop several useful relationships to study interchange capacity presented in NCHRP 345 (109. Saturation flow for protected left tutus at interchanges was estimated from: Sin = 3,600/~1.50 + 1 1l/r0,245) (A-73) where so' is the saturation flow per larle for left turns, pcphgpI, and r is the average left turn radius ofthe tuning maneuver, ft. A so, value of 2,000 pcphep] is predicted at a turning radius of 200 feet ~ . . ~ ~ ``l ~ ~ ~ ~A ~ ~ (60 m). This was the maximum value of saturation flow recommended,which was also the assumed value for through movements under ideal conditions (] 09. The application of Equation A-73 to signalized interchanges could easily follow HCM procedures where an adjustment factor for left turns, based on the radius of turn, is applied to the saturation flow for "ideal conditions" of 2,000 pcphgp] for interchanges. A protected left turn factor,fp as derived from Equation A-73, would then be (109 fit = 1 .0/~0.83 3 + 0.6 1 7/r 0.245' (A-74) Quantifying the effects of trucks and other heavy vehicles on saturation flow at traffic sign~s is another matter. The passenger car equivalency (PCE) used in the ~ 985 HCM was ~ .5 for through traffic only, but Molina (169 showed that the PCE for typical through moving urban truck traffic averages about 2.7, web a range from I.7 for small trucks to 3.7 for five-axIe trucks. The 1994 HCM provided an small increase in the average PCE of heavy vehicles at signalized intersections to 2.0. Heavy truck volumes turning left from off-ramps under tight geometric conditions could have an even larger impact on interchange capacity. Estimation of phase clearance lost times for interchanges is somewhat complicated by the diverse intemal clearance paths taken by vehicles traveling through the interchanges and the different forms of interchanges. Poppe (~]J estimated the clearance lost time, for a SPU} as related to the signal change interval, CT, of the phase as 1 = 0.95CI - 2.3 c (A-75) with an it-square of 0.97, suggesting an "end use" of the initial portion of the yellow interval of 2.3 seconds. These results compared well with Bonneson's Flonda data (129 and with those collected within this study and reported in Appendix C. A - 50

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REFERENCES Munj al, P.K. "An Analysis of Diamond Interchanges." Transportation Research Record 349, Transportation Research Board, Washington, D.C. (1971) pp. 47-64. Highway Capacity Manual." Special Report 209, Third Edition, Transportation Research Board, Washington, D.C. (1994~. Fambro, D. B., Messer C.~., and Andersen, D.A. "Estimation of Unprotected Left-Turn Capacity at SignalizedIntersections." Transportation Research Record 644, Transportation Research Board, Washington, D.C. (1977), pp.1 13-1 19. 4. 6. 8. 10. 11. Fambro, D.B., Roupha~l, N.M., Sloup, P.R., Daniel, J.R., Li, J., Anwar, M., and Engelbrecht, R.J. "Highway Capacity Revisions for Chapters 9 and 1 1 ." Federal Highway Administration, FHWA-RD-96-088, Washington, D.C. (1996~. Messer, C.J., Fambro, D.B., and Richards, S.H. "Optimization of Pretimed Signalized Diamond Interchanges." Transportation Research Record 644, Transportation Research Board, Washington, D.C. (1977) pp. 78-84. Messer, C.~., Whitson, R.H., and Carvell, I.D. "A Real-Time Frontage Road Progression Analysis and Control Strategy." Transportation Research Record 503, Transportation Research Board,Washington,D.C.~1974) pp.l-12. Capelle, D.G. and Pinnell, C. "Capacity Study of Signalized Diamond Interchanges." Highway Research Board Bulletin 291, Highway Research Board, Washington, D.C. (1961~. Lee, J.C. "Review of Diamond Interchange Analysis Techniques: Past and Present." Synthesis Paper for Co~runittee A3A10. Transportation Research Board, Washington, D.C. (1992). Hook, D.~. and Upchurch, I. "Companson of Operational Parameters for Conventional Diamond Interchanges and Single-Point Diamond Interchanges," Transportation Research Record 1356, Transportation Research Board, Washington, D.C. (19921. Messer, Cal., Bonneson, J.A., Anderson, S.D., and McFarland, W.F. "Single-Point Urban Interchange Design and Operational Analysis." NCHRP 345, Transportation Research Board, Washington, D.C. (1991~. Poppe, M.~., Radwan, A.E., and Matthias, I.S. "Some Traffic Parameters for the Evaluation of the Single-Point Diamond Interchange." Transportation Research Record 1303, Washington, D.C. (1991~. A - 51

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Bonneson, I.A. "A Study of Headway and Lost Time at Single-Point Urban Intercharlges.'' Transportation Research Record 1365, Transportation Research Board, Washington, D.C. (1992~. Bonneson, J.A. "Factors Affecting Bridge Size and Clearance Time of the Single-Point Urban Interchange." Journal of Transportation Engineering, Vol. ~ ~ 9, No. I, American Society of Civil Engineers, New York (] 993~. 14. Bonneson, J. A., "Operational Efficiency of the Single-Po~nt Urban Interchange." ITE Journal, VoT 62, No. 6. Institute of Transportation Engineers, Washington, D.C. (! 9921. 15. Messer, CJ., and D.J. Berry. "Effects of Design Alternatives on Quality of Service at Signalized Diamond Interchanges." Transportation Research Recorc! 538, Transportation Research Board, Washington, D.C. (19751. 16. Molina, C.A. "Passenger Car Equivalents of Trucks at Signalized Intersections." ITE Journal, Vol 54, No. 9. Institute of Transportation Engineers, Washington, D.C. (1988). A - 52