Texas Transportation Institute The Texas A&M University System College Station, Texas

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1 . Report No. FHWA/TX-04/ Governent Accession No. 3. Recipient's Catalog No. 4. Title and Subtitle A MODEL FOR EVALUATING INTEGRATION STRATEGIES FOR OPERATING DIAMOND INTERCHANGE AND RAMP METERING Technical Report Docuentation Page 5. Report Date Septeber Perforing Organization Code 7. Author(s) Zong Tian and Kevin Balke 9. Perforing Organization Nae and Address Texas Transportation Institute The Texas A&M University Syste College Station, Texas Sponsoring Agency Nae and Address Texas Departent of Transportation Research and Technology Ipleentation Office P. O. Box 5080 Austin, Texas Perforing Organization Report No. Report Work Unit No. (TRAIS). Contract or Grant No. Proect No Type of Report and Period Covered Research: Septeber 2002 August Sponsoring Agency Code 5. Suppleentary Notes Research perfored in cooperation with the Texas Departent of Transportation and the U.S. Departent of Transportation, Federal Highway Adinistration. Research Proect Title: A Model for Evaluating Integration Strategies for Operating Diaond Interchange and Rap Metering 6. Abstract Diaond interchanges and their associated raps are where the surface street arterial syste and the freeway syste interface. Historically, these two eleents of the syste have been operated with little or no coordination between the two. One danger of operating these two systes in isolation is that traffic fro the rap, particularly if it is etered, can spill back into the diaond interchange, causing it to becoe congested. The ai of this research was to develop integrated operational strategies for anaging the diaond interchange and rap etering operations for the purpose of iproving syste perforances. Modeling ethodologies were developed for analyzing an integrated diaond interchange rap etering syste (IDIRMS). A coputer odel naed DRIVE was developed, which is classified as a esoscopic siulation odel. The odel was validated against the VISSIM icroscopic siulation odel, and researchers found general agreeent between the two odels. Operational characteristics were also investigated using DRIVE to gain better understanding of the syste features. Integrated operational strategies were developed and evaluated under various traffic flow conditions. The analysis results indicate that with integrated operations through an adaptive signal control syste, the onset of freeway congestion and breakdown is effectively postponed. 7. Key Words Diaond Interchange, Rap Metering, Integration, DRIVE, Siulation 9. Security Classif.(of this report) Unclassified 20. Security Classif.(of this page) Unclassified 8. Distribution Stateent No restrictions. This docuent is available to the public through NTIS: National Technical Inforation Service 5285 Port Royal Road Springfield, Virginia No. of Pages Price For DOT F (8-72) Reproduction of copleted page authorized

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3 A MODEL FOR EVALUATING INTEGRATION STRATEGIES FOR OPERATING DIAMOND INTERCHANGE AND RAMP METERING by Zong Tian Associate Transportation Researcher Texas Transportation Institute and Kevin Balke, Ph.D., P.E. Research Engineer TransLink Research Center Director Texas Transportation Institute Report Proect Nuber Research Proect Title: A Model for Evaluating Integration Strategies for Operating Diaond Interchange and Rap Metering Sponsored by the Texas Departent of Transportation In Cooperation with the U.S. Departent of Transportation Federal Highway Adinistration Septeber 2003 TEXAS TRANSPORTATION INSTITUTE The Texas A&M University Syste College Station, Texas

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5 DISCLAIMER The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official view or policies of the Federal Highway Adinistration (FHWA) or the Texas Departent of Transportation (TxDOT). This report does not constitute a standard, specification, or regulation. The engineer in charge was Kevin Balke, P.E. (Texas, #66529). v

6 ACKNOWLEDGMENTS This proect was conducted as part of the TransLink research progra and was perfored in corporation with the Texas Departent of Transportation and the Federal Highway Adinistration. The proect tea recognizes the following TransLink partners for their generous support of the TransLink research progra: U.S. Departent of Transportation, Federal Highway Adinistration; Texas Departent of Transportation; Metropolitan Transit Authority of Harris County; Texas Transportation Institute; and Rockwell International. The proect tea would also like to recognize the following individuals for their support of this specific proect: David Gibson, Federal Highway Adinistration; Mark Olson, Federal Highway Adinistration; Al Kosik, Traffic Operations Division, Texas Departent of Transportation; Richard Reeves, Traffic Operations Division, Texas Departent of Transportation; Sally Wegann, Houston District, Texas Departent of Transportation; Terry Sas, Dallas District, Texas Departent of Transportation; Wallace Ewell, Fort Worth District, Texas Departent of Transportation Pat Irwin, San Antonio District, Texas Departent of Transportation The authors would also like to recognize Dr. Carroll Messer, Dr. Nadee Chaudhary, and Mr. Roelof Engelbrecht for the technical contributions and insights to this proect. vi

7 TABLE OF CONTENTS Page List of Figures...viii List of Tables... ix CHAPTER : INTRODUCTION... Proble Stateent... 2 Obectives of the Research... 3 Scope of Research... 4 Organization of Report... 5 CHAPTER 2: SYSTEM MODELING METHODOLOGIES... 7 IDIRMS Nubering Schee... 7 Diaond Interchange... 0 Freeway and Rap Metering... 4 Rap Flow Profiles... 7 Rap Queue Spillback CHAPTER 3: DEVELOPMENT OF THE MODELING SOFTWARE CHAPTER 4: MODEL VALIDATION Site Description VISSIM Model Developent Model Calibration and Validation Results CHAPTER 5: ANALYSES ON SYSTEM OPERATIONAL CHARACTERISTICS... 4 Effects of Diaond Signal Phasing on Rap queues... 4 Effects of Diaond Cycle Length on Rap Queues Effects of Rap Metering Operations on Freeway Perforance...45 CHAPTER 6: INTEGRATION STRATEGIES Resource Manageent Philosophy The Syste Operating Obectives Integration Strategies... 5 Evaluation of Operational Strategies under Recurring Congestion... 6 A Fraework for Selecting Operational Strategies CHAPTER 7: SUMMARY AND CONCLUSIONS REFERENCES vii

8 LIST OF FIGURES Page Figure. Queue Spillback at a Diaond Interchange with Rap Metering... 2 Figure 2. Proposed Integrated Syste and Its Boundaries... 5 Figure 3. Syste Eleents and Nubering Schees Figure 4. Delays and Queues for the Case with an Initial Queue and a Residual Queue... 2 Figure 5. Rap Arrival Flow Profile with Basic Three-Phase... 8 Figure 6. Rap Arrival Flow Profile with TTI Four-Phase Figure 7. Rap Arrival Flow Profile without Arterial Right-Turn Control... 2 Figure 8. Rap Arrival Flow Profile with Arterial Right-Turn Control Figure 9. Feeding Moveent Service Sequences and Rap Flow Profiles Figure 0. DRIVE Modules and Functions Figure. DRIVE Workflow Chart Figure 2. Rap and Diaond Interchange Delays with Basic Three-Phase and Queue Flush (Average of 5 Runs) Figure 3. Freeway Mainline Delay with Queue Flush Figure 4. Rap and Diaond Interchang Delays with Basic Three-Phase without Queue Flush (Average of 5 Runs) Figure 5. Freeway Mainline Delay without Queue Flush Figure 6. Oversaturated Case with Queue Spillback: Basic Three-Phase Figure 7. Oversaturated Case with Queue Spillback: TTI Four-Phase Figure 8. Queue Length Coparison with Basic Three-Phase and TTI Four-Phase Figure 9. Traffic Deand Evolution with Queue Spillback - Basic Three-Phase Figure 20. Traffic Deand Evolution with Queue Spillback - TTI Four-Phase Figure 2. Effect of Cycle Length on Rap Queue Length Figure 22. Freeway Throughput with Responsive Metering Rate Figure 23. Freeway Throughput with Fixed Metering Rate and Queue Flush Figure 24. Freeway Throughput with Fixed Metering Rate and without Rap Queue Flush Figure 25. Additional Detector Layouts for the Proposed Adaptive Control Syste Figure 26. Hold Internal Phases with Basic Three-Phase Figure 27. Hold Arterial Phases with Basic Three-Phase Figure 28. Hold Frontage Road Phase with Basic Three-Phase and Conditional Service Figure 29. Hold Frontage Road Phase (φ8) to Control Left-Side Rap Entry with TTI Four- Phase Figure 30. Hold Arterial Phase (φ2) to Control Left-Side Rap Entry with TTI Four-Phase Figure 3. Incident within Interchange Figure 32. Incident Downstrea of Interchange Figure 33. Queue Flush Duration with/without Integration Low Deand Figure 34. Queue Flush Duration with/without Integration High Deand Figure 35. Delay Evolution on Freeway with/without Integration viii

9 LIST OF TABLES Page Table. Diaond Interchange Moveents and Freeway On-Rap Deands Table 2. Proportion of Traffic Feeding Freeway On-Raps... 0 Table 3. Deterination of Q M (t) Values Table 4. Input/Output Inforation for DRIVE Software ix

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11 CHAPTER : INTRODUCTION Freeway interchanges establish interconnections between freeway systes and surface street arterials and provide the backbone of transportation networks. One of the ost coonly used interchange types in Texas is the tight urban diaond interchange (TUDI), where two traffic signals are installed on the arterial street to control the interchanging traffic (,2). Diaond interchanges are often characterized by unique traffic flow patterns, especially high turning oveents and liited spacing between the signals that ake anaging their operations difficult. To coplicate atters, the aority of freeway rap eters installed in Texas are located in the vicinity of diaond interchanges. As a result, diaond interchange locations are often sources of operational bottlenecks for both surface street arterials and freeways. One operational issues existing today is that the diaond interchange and rap etering are priarily treated as independent eleents. Traffic engineers and planners typically do not consider the interactions between these two eleents, nor do they consider the potential benefits that can be derived fro coordinating their operations (3). The lack of syste integration or coordination between the diaond signals and the rap etering signal often creates aor operational concerns, aong which queue spillback fro the etered rap is the ost obvious one. This situation is illustrated in Figure. During typical rush hours, high traffic deands on the freeway often require restricted entry of traffic fro the etered rap, thus resulting in long queues on the rap. The fact that the traffic released fro the upstrea diaond signal arrives in platoons also exacerbates the queue spillback effect, where liited storage spacing on the rap cannot accoodate the short-ter surge of large platoons. Unless the signal controller at the upstrea diaond interchange has soe way to sense the queue buildup, traffic would continue to flow to the rap, until the queue spills back to the surface street (e.g., frontage road or the diaond signal location). Such a queue spillback would interfere with the surface street operation and ay create safety concerns. Suggested strategies to control queue spillback generally involve soe queue override policies to flush the rap queues by either increasing the etering rate or terinating etering operations (4). However, such an operation ay lead to a freeway breakdown; a phenoenon indicated by a sudden speed drop and perhaps a drop in the flow. A

12 breakdown of the freeway affects the efficiencies of the entire syste. The purpose of this proect is to begin the process of investigating whether providing integrated operations between a diaond interchange and a rap eter would reduce the deficiencies (i.e., to iniize queue spillback and queue flush at the rap eter) of the current independent operations by developing appropriate integrated operational strategies on diaond control and rap etering. Traffic Queues Surface Arterial Rap Meter Diaond Signal To Frontage Road To Freeway Frontage Road Freeway Figure. Queue Spillback at a Diaond Interchange with Rap Metering. PROBLEM STATEMENT Current operations at a diaond interchange and a rap eter lack syste coordination between the two coponents. The lack of syste coordination is reflected by the fact that little consideration is currently given to diaond operational strategies that iniize or eliinate rap queue spillback when rap etering is in operation. Existing diaond interchange 2

13 strategies focus on serving traffic deands fro external approaches, which are onitored by various traffic sensors. Appropriate signal phasing and tiing are then developed to best serve the traffic deands (5,6). However, existing diaond operations copletely ignore the constraints iposed by the downstrea rap eter. Excessive and non-controlled release of traffic fro the diaond often results in queue spillback at the rap eter. On the other hand, the effectiveness of the rap etering (both the algorith design and the operational strategy) also plays an iportant role in controlling queue spillback (7,8,9). Queue spillback resulting fro the lack of coordination between the rap eter and diaond interchange creates serious operational concerns on the diaond interchange and the surface street arterial. Although queue override policies currently being used at rap eters can eliinate queue spillback, frequent queue flush can lead to freeway breakdown and diinish the ain purpose of rap etering. Therefore, a need exists to address the diaond interchange, rap etering, and freeway coponents in an integrated and coordinated anner to eliinate the deficiencies of the current operations. Integrated operational strategies need to be developed to iniize queue spillback occurrences at the rap eter while aintaining optial syste throughput. OBJECTIVES OF THE RESEARCH The goals of this research are: (a) to develop a ethodology for analyzing the operations of an integrated diaond interchange/rap-etering syste (IDIRMS); and (b) to investigate strategies for operating diaond interchanges and rap-etering systes in an integrated fashion that would reduce the deficiencies of the current operations. Specific obectives of this research include the following: Develop analytical procedures for estiating various perforance easures (e.g., rap queue length and syste delays) for the integrated diaond interchange/rap-etering syste, given a set of syste variables and paraeters (e.g., rap-etering rates, traffic deand profile on both freeway and diaond interchange approaches, diaond signal tiing and geoetric inforation such as spacing between diaond and rap eter). The overall ethodology can be applied for syste operations analysis, developent and 3

14 evaluation of integrated operational strategies aied at iniizing queue spillback occurrences on the etered rap. Use VISSIM (0), a well-calibrated icroscopic siulation odel, to validate the analytical procedures by coparing the perforance easures produced fro both the analytical procedures and icroscopic siulation odel. Establish a fraework and identify viable integrated operational strategies for IDIRMS based on a set of established obectives and priorities. One exaple of an operational strategy is to anipulate the signal tiing at the diaond interchange so that queue spillback can be iniized. The integrated strategies should take into account the close interactions between the diaond interchange signals and the rap eter. Evaluate the fraework and deonstrate its applicability that would allow traffic engineers and decision akers to evaluate specific operational strategies and provide tradeoff assessents on each strategy. SCOPE OF RESEARCH This proect was intended to be the first steps into exploring the basic relationship and potential benefits that ight be derived fro operating a diaond interchange and the raps iediately adacent to that diaond interchange in a coordinated fashion. This research was focused on identifying the basic relationships and developing analytical tools that could be used in the future to assess operating diaond interchanges and rap eters as a syste. While the research proect did exaine strategies that could be used to achieve integrated operations, it was never intended to develop a syste architecture, control logic, data flows, algoriths, or technologies that could be used in an actual operation. For the purposes of this research proect, we defined the boundaries of the syste to be that shown in Figure 2. This is a type of diaond interchange with one-way frontage roads, typically seen in urban Texas highways. The proect also assues that U-turn lanes are provided for both directions. The syste includes a segent of freeway ainline, rap eters, and a signalized diaond interchange. 4

15 Frontage Road Freeway Rap Meter Syste Boundaries Diaond Interchange Frontage Road Rap Meter Syste Boundaries Figure 2. Proposed Integrated Syste and Its Boundaries ORGANIZATION OF REPORT This report includes a total of seven chapters, including this introductory chapter. In Chapter 2 of this report, the researchers provide atheatical descriptions on the odeling process of an integrated diaond interchange/rap-etering syste. Chapter 3 describes the developent of coputer software that ipleents the aor odeling processes described in Chapter 2. Chapter 4 provides odel validation results against both VISSIM icroscopic siulation and PASSER III software. Chapter 5 provides soe analyses on the syste operational characteristics using the software developed in this research. The purpose of these 5

16 analyses is to gain better understanding of the syste features to facilitate the developent of operational strategies. Chapter 6 docuents the developent of operational strategies to achieve integrated operations between rap etering and a diaond interchange. The operations are deonstrated through siulation and their effectiveness is evaluated. Chapter 7 provides a suary and aor conclusions of the research. 6

17 CHAPTER 2: SYSTEM MODELING METHODOLOGIES This chapter docuents the aor odeling ethodologies for the IDIRMS. The syste and its boundaries are defined. A nubering schee is proposed for the aor origin-destination flows as well as aor traffic oveent flows in the syste. The odeling processes for diaond interchange, freeway ainline, and rap etering operations are described in atheatical equations. Special odeling efforts are conducted on the traffic arrival flow profiles at the rap eters and on diaond interchange operations considering rap queue spillback. IDIRMS NUMBERING SCHEME Figure 3 shows the nubering schee for the aor traffic flows within IDIRMS. The figure at the top includes the nubered origins (O i ) and destinations (D ); turning traffic oveents at the diaond interchange; and freeway ainline and on-rap flows. These traffic flows provide necessary inforation on the traffic deand side for perforing analyses on syste perforances. The figure at the botto is the standard phasing schee used in PASSER III. Once the origin-destination (OD) atrix is available, all other traffic flows can be derived, including 4 turning oveents at the diaond interchange, two on-rap flows, and two ainline flows. Table and Table 2 suarize the relationships aong various traffic oveent flows and OD flows. The variables listed in the tables are defined below: o,d = index for origin and destination, o ~6, d ~6 r = index for on-rap and freeway, r ~2 v o,d = traffic flow deand fro origin o and destination d, vph V = traffic oveent at the diaond interchange, vph, ~4 τ ra = the portion of diversion to rap r during incident conditions τ rb = the portion of diversion to the downstrea interchange during incident conditions R r = traffic deand at rap r, vph P,r = proportion of oveent that feeds rap r 7

18 O D 2 O 5 D 6 F 2 R D O 4 O D R F D 5 D O 2 O 6 φ4 φ2 A φ φ5 B φ6 φ8 Figure 3. Syste Eleents and Nubering Schees. 8

19 Table. Diaond Interchange Moveents and Freeway On-Rap Deands. Diaond/Rap Location Moveent OD Source Frontage Road LT V = v,3 + v 5,3 TH V 2 = v,5 + v 5,5 + v 5, + (τ a + τ b )v, Diaond Interchange Arterial A-Direction Frontage Road 2 Arterial B-Direction RT V 3 = v,4 + v 5,4 U V 3 = v 5,6 + v 5,2 + v,6 LT V 4 = v 3,2 + v 3,6 TH V 5 = v 3,3 RT V 6 = v 3, + v 3,5 LT V 7 = v 6,4 + v 2,4 TH V 8 = v 6,6 + v 6,2 + v 2,6 + (τ 2a + τ 2b )v 2,2 RT V 9 = v 6,3 + v 2,3 U V 4 = v 6,5 + v 6, + v 2,5 LT V 0 = v 4, + v 4,5 TH V = v 4,4 RT V 2 = v 4,6 + v 4,2 Rap Rap - R = v 3, + v 4, + v 5, + v 6, + τ a v, Rap 2 - R 2 = v 3,2 + v 4,2 + v 5,2 + v 5, + v 6,2 + τ 2a v 2,2 Freeway Direction - F = v, Direction 2 - F 2 = v 2,2 9

20 Table 2. Proportion of Traffic Feeding Freeway On-Raps. Feeding Rap Moveent, Proportion, p,r R R 2 V2 V6 V0 V4 V8 V2 V4 V3 p p p p p p p p 2, 6, 0, 4, 8,2 2,2 4,2 3,2 = v = v 5, 3, = v = v = v + v v 4, 6, 6,2 = v = v 4,2 3,2 = v 3, + v v v 5,2 4, 5,5 3,5 + v v + v + v v 4,2 4,5 6, 6,5 6,6 + v 3,2 + v 4,6 3,6 v + v 5,2 5,6 v 5, + v + τ v,5 + v v 6,2 + v 2,5 2,6 + v a + ( τ 2a, a + τ v,6 + ( τ 2,2 2a + τ b + τ 2b )v, )v 2,2 One critical eleent for analyzing the IDIRMS is the estiation of the OD flows. OD flows can be either obtained fro an actual OD survey or estiated based on link and turning oveent counts at specific locations. OD estiation is a subect that has attracted significant research interests and efforts (,2,3) and is not addressed in this report. Readers can refer to these studies for further details. DIAMOND INTERCHANGE The ethodology of odeling diaond interchange operations consists of analysis over ultiple cycles, with consideration of stochastic traffic deands for each cycle. The ethodologies for calculating capacities, delays, and queues at the diaond interchange follow siilar ethodologies as used in PASSER III (4); however, special considerations are given in odeling the effect of rap queue spillback on diaond interchange operations. Calculations on delays and queues use the standard arrival-departure queue polygon ethod, which is essentially calculating the unifor control delay and the initial queue delay 0

21 (i.e., the first ter and the third ter of delay equations) as docuented in PASSER III and in the Highway Capacity Manual (5). The second-ter delay, the rando and over-saturation delay, is not necessary because the calculation is precisely for the duration of one cycle length, and randoness is accounted for in the stochastic flows generated each cycle. Figure 4 illustrates a general case where both an initial queue, N, and a residual queue, N, exist for a traffic oveent during cycle. Other sybols in the figure are defined below: A, A 2, A 3 = total area (also total delay in veh-sec) during a portion of the cycle V = arrival rate for oveent during cycle S = saturation flow rate for oveent, vph ' S = departure flow rate when ipeded by the rap queue, vph ' N = queue length at the start of green, veh " N = queue length at the tie when the rap queue spills back and ipedes the discharge of oveent, veh NR = the residual queue due to rap queue spillback, veh NC = the residual queue due to oveent itself reaching over-saturation, veh r = effective red tie for oveent in cycle, sec t u, = portion of the green interval when oveent can discharge freely without ipedance, sec C = cycle length, sec

22 Flow V A 2 N A 3 NC NR N S N A N S r r + t u, C Tie in Cycle Figure 4. Delays and Queues for the Case with an Initial Queue and a Residual Queue. NC can be deterined based on Equation (): ( V c ) NC = C + N () 3600 where c = the unipeded capacity of oveent calculated based on Equation (2) c C r = s (2) C NR in Figure 4 is a portion of the total residual queue that is contributed by the rap queue spillback. Discussions on the calculation of NR are provided later in this chapter. 2

23 3 The total shaded areas of the queue polygon represent the total delays experienced by the vehicles arriving in the current cycle and are calculated based on the following equations: 2 ) 3600 (2 2 ) ( ' r V r N r N N A + = + = (3) 2 ] 3600 ) ( 2 [2 2 ) (,,, " ' 2 u u u t V s t V r N t N N A + = + = (4) ) ]( 3600 ) ( [ ) )( (,,, " 3 u u u t r C V s t V r N N t r C N N A + + = + = (5) The average delay for oveent during cycle is: CV A A A V C A A A d = + + = (6) The queue length is represented by the vertical distance in the queue polygon in Figure 4. The axiu queue is likely to occur at the start of the green interval. Delays and queues for the internal oveents are odeled siilarly to PASSER III based on the delay-offset ethodology (6,7). However, the effect of rap queue spillback is specifically odeled in our odel (e.g., rap queue spillback to internal left-turn oveent), which has not been addressed in PASSER III. The ethodology consists of an analysis procedure on a second-by-second basis. The analysis takes into consideration the unique arrival/departure flow profiles, which are associated with the phasing and tiing of the diaond interchange signal.

24 FREEWAY AND RAMP METERING Modeling freeway and rap etering operations is also based on the cuulative arrival/departure queue polygon ethod, but the analysis is carried out on a second-by-second basis. The following equations provide atheatical descriptions on the odeling process. Equations (7) through (9) describe the freeway ainline flow arriving iediately upstrea of the on-rap at tie interval t. The initial randoly generated deand, F r (t), is capped by a factor γ ties the free-flow capacity, C Fr, reflecting the axiu flow rate that can get to the point iediately upstrea of the rap erge. F r (t ) is the average flow at tie step t during the rap etering interval, n. F r (t ) is used to deterine the rap etering rate in Equation (), so that the sae rap etering rate would result for a etering interval. F r ( t) = Min[ F r ( t) + F r γc ( t ), γc Fr Fr, ], F ( t) > C r Otherwise Fr γ (7) F ( t) = Max(0, F ( t ) + F ( t) F ( t) (8) r r r r F ( t) = r n i+ n r t i= int( ) n+ n F ( i) (9) A Rr t Rr ( i) ( t) = (0) 3600 i= M r ( t) = Min[ C F M M F ( t), M r r,in r,in r,ax,, ], t CFr ( η ) qfr[int( ) n] n 3600 F r ( t) + M r,in > CFr Otherwise () 4

25 q Rr Rr ( t) M r ( t) ( t) = Max[0, qrr ( t ) + ] (2) 3600 D Rr ( t) = A ( t) q ( t) (3) Rr Rr ORr ( t) = 3600[ DRr ( t) DRr ( t )] (4) C Fr F ( RND, CQr, σ Qr ),, 3600qFr ( t ) + F"( t) + ORr ( t) > ηc ( t) = F ( RND, CFr, σ Fr ), Otherwise Fr (5) η is the breakdown factor (.5 is assued in the odel) to reflect that freeway breakdown will occur once the bottleneck deand is.5 ties or higher than the average freeflow capacity, C Fr. Equation (5) deterines the freeway ainline capacity at tie t, which has the two-capacity nature with rando variations, as given by the rando variable generation function, F. A Fr t [ F ( i) + ORr ( i)] ( t) = (6) i= 3600 q Fr F r ( t) + ORr ( t) CFr ( t) ( t) = Max[0, qfr ( t ) + ] (7) 3600 D Fr ( t) = A ( t) q ( t) (8) Fr Fr 5

26 OFr ( t) = 3600[ DFr ( t) DFr ( t )] (9) TD Rr = T i= qrr ( i) 3600 (20) TD Fr = T i= qfr ( i) 3600 (2) Where F r (t) = randoly generated freeway ainline deand for direction r and tie interval t, vph F r (t) = capped freeway ainline arrival flow rate at the point of rap erge location, F r vph " ( t) = average ainline arrival flow rate during rap etering interval, vph F r (t) = ainline residual deand at tie interval t, vph R r (t)= traffic arrival rate at tie interval t at rap r, vph M r (t)= rap etering rate at tie interval t at rap r, vph A Rr (t) = cuulative nuber of arrivals at tie interval t and rap r, veh D Rr (t)= cuulative nuber of departures at tie interval t and rap r, veh O Rr (t) = throughput at tie interval t and rap r, vph A Fr (t) = cuulative nuber of arrivals at tie interval t and freeway direction r, veh D Fr (t) = cuulative nuber of departures at tie interval t and freeway direction r, veh O Fr (t) = ainline throughput at tie interval t and freeway direction r, vph C Fr (t) = freeway capacity at tie interval t and direction r, vph C Fr = free-flow capacity of ainline direction r, vph C Qr = queue-discharge capacity of ainline direction r, vph 6

27 σ Fr = standard deviation of free-flow capacity for direction r, veh σ Qr = standard deviation of queue-discharge capacity for direction r, veh M r,in = iniu etering rate for rap r, vph M r,ax = axiu etering rate for rap r, vph q Fr (t) = freeway ainline queue length at tie interval t and direction r, veh q Rr (t) = queue length at tie interval t and rap r, veh TD Fr = total freeway ainline delay for direction r, veh-hr TD Rr = total delay for rap r, veh-hr η = breakdown factor,.5 γ = flow cap factor,.2 RAMP FLOW PROFILES Modeling rap etering and freeway operations requires adequate description of the rap arrival flow profile, R r (t), which is uniquely deterined based on the diaond phasing and tiing. This section provides detailed descriptions on odeling the arrival flow profiles at the rap eter. The proect focuses on the two coonly used diaond phasing schees: basic three-phase and TTI four-phase (6). With the existence of an upstrea signalized diaond interchange, vehicles arrive at the rap eter with unique flow structures. Figure 5 and Figure 6 illustrate the arrival flow profiles at rap (R) with basic three-phase and TTI four-phase phasing schees, respectively. The profiles shown in both figures assue that the arterial right-turn oveent (M6) and the U-turn oveent (M4) are uncontrolled and would arrive at the rap randoly. It is also assued that platoons released fro the diaond interchange do not disperse while traveling to the rapetering location. 7

28 Rap Arrival Flow W g q,4-2 W 2 l 4 W 3 W 4 g q,-0 W 5 0 t t 2 t 3 t 4 t 5 Cycle Tie ф4 ф2 ф W = S 2 *p 2, + V 6 *p 6, + V 4 *p 4, t = g q,4 W 2 = V 2 *p 2, + V 6 *p 6, + V 4 *p 4, t 2 = ф 4 - l 4 = g 4 W 3 = V 6 *p 6, + V 4 *p 4, t 3 = t 2 + l 4 + ф 2 W 4 = S 0 *p 0, + V 6 *p 6, + V 4 *p 4, t 4 = t 3 + g q, W 5 = V 6 *p 6, + V 4 *p 4, t 5 = C Figure 5. Rap Arrival Flow Profile with Basic Three-Phase. 8

29 Rap Arrival Flow W g q,4-2 W 2 W 3 g q,6-0 W 4 W 5 0 t t 2 t 3 t 4 t 5 Cycle Tie ф4 ф2 ф6 ф8 Overlap Overlap W = S 2 *p 2, + V 6 *p 6, + V 4 *p 4, t = g q,4 W 2 = V 2 *p 2, + V 6 *p 6, + V 4 *p 4, t 2 = ф 4 W 3 = µ*p 0, + V 6 *p 6, + V 4 *p 4, t 3 = t 2 + g q,6 W 4 = V 0 *p 0, + V 6 *p 6, + V 4 *p 4, t 4 = t 2 + ф 6 W 5 = V 6 *p 6, + V 4 *p 4, t 5 = C ** V 2 is the average flow rate of the unsaturated green portion, including the lost tie interval Figure 6. Rap Arrival Flow Profile with TTI Four-Phase. The sybols shown in both figures are described below: W t = arrival flow rate during tie period t t- and t t, vph g q,φ - = queue discharge portion of the green interval for signal phase φ and oveent, sec l φ = lost tie for phase φ Equations (22) through (24) show the calculations on g q,φ - : g q, N 2 + V2r4, = S 2 V2 g 4, x x 2 2 < (22) 9

30 g q,0 gx = N = S 0 0 Q S + V C, 3600, q q 0 0 < Q Q 0 0 (23) where g q,6 0 = 3600 ( N S N ( V ) + ( V + V 0 + V ) 0 ) r g 6 6,, x x < (24) N = the residual queue fro the previous cycle for oveent, veh q 0 = the axiu nuber of vehicles that would occur for oveent 0 (residual plus arrival) during the current cycle, veh Q 0 x = internal queue storage space for oveent 0, veh = v/c ratio for oveent S 0+, x 0+ are for the external approach on the arterial related to M0 and M. The individual flows in the flow profiles should satisfy Equation (25): R r = C 5 t= W ( t t t t t ) (25) When the arterial right-turn oveent is not controlled by the signal, such as the case of a channelized right-turn oveent, both basic three-phase and TTI four-phase can be represented by five different flow regions in a profile (see Figure 5 and Figure 6). When the right-turn oveent is controlled by the signal, ore than five flow regions are necessary to represent the flow profiles. Figure 7 and Figure 8 illustrate soe rap arrival flow profiles for a duration of six cycles with stochastic traffic deands in each cycle. Figure 7 shows the case without arterial right-turn control, and Figure 8 shows the case with arterial right-turn control. 20

31 Flow Rate, vph phase Cycle = 00 sec No RT Control Cycle Tie, sec Flow Rate, vph Phase Cycle = 00 sec No RT Control Cycle Tie, sec Figure 7. Rap Arrival Flow Profile without Arterial Right-Turn Control. 2

32 Flow Rate, vph phase Cycle = 00 sec with RT Control Cycle Tie, sec Flow Rate, vph Phase Cycle = 00 sec with RT Control Cycle Tie, sec Figure 8. Rap Arrival Flow Profile with Arterial Right-Turn Control. RAMP QUEUE SPILLBACK When sufficient storage between the rap eter and the diaond signal exists to store the vehicle queues, the diaond interchange signal can discharge the vehicles according to the traffic flow profiles depicted in Figure 7 and Figure 8 without incurring any ipedance. However, when the storage space is filled with queued vehicles due to either liited spacing or siply over-saturation, the rap queues would ipede traffic flows discharged fro the diaond signals, resulting in reduced capacity and increased delay for the affected traffic oveents. Previous studies on odeling queue spillback at signalized intersections are 22

33 generally based on two approaches. One approach is to reduce the saturation flow rate (,8). For exaple, Messer and Bonneson () proposed using a siple factor to adust the saturation flow rate based on the queue length of the downstrea link. The other approach is to reduce the effective green tie (9), considering the queue block effect as equivalent to the loss of green tie. Both approaches would reach siilar conclusions. Because odeling of rap operations and rap queues occur on a second-by-second basis, it is possible to have detailed odeling on the ipact of spillback on diaond interchange operations. The following discussions describe the odeling ethodology, which uses the approach of adusting discharging flows. The basic principle to odel vehicle discharge with potential queue spillback is based on the fact that the vehicle discharging rate is governed by the iniu of three flows, as shown in Equation (26): Q ( t) Min[ Q ( t), Q ( t), Q ( t)] R = W M B (26) where Q R (t) = discharging flow rate fro diaond signal at tie step t, vph Q W (t) = unipeded deand flow at tie slice t, vph Q M (t) = the axiu possible discharging flow rate at tie step t, vph Q B (t) = discharging flow rate that would result in queue spillback at tie step t, vph All these flows represent the traffic that would arrive at the rap eter. Because not all the traffic discharged fro the diaond interchange would arrive at the rap eter, the actual discharging flow rate at the diaond signal is norally higher (e.g., traffic going to the frontage road) than what is shown in Equation (26); therefore, the flow rate should be adusted accordingly based on the proportion of each oveent that goes to the rap eter. Q W (t) is the deand flow when there is no queue spillback to the diaond signal, so that vehicles can discharge fro the signal unipeded according to traffic flow profiles described in Figure 5 through Figure 8. Q M (t) is the axiu possible flow rate that can be discharged fro the diaond signal and would arrive at the rap eter. Q M (t) is the equivalent portion of the rap 23

34 arrival flow when the diaond signal is discharging at the saturation flow rate during a particular phase. Q M (t) varies depending on the diaond phasing schee, and its values are deterined based on Table 3. Table 3. Deterination of Q M (t) Values. Phasing Code Phase Sequence Tie and Entering Flows Φ4 t -2, W - Rap Φ2 t -3, W -3 Basic Three- Φ t -5, W -4 Phase Φ8 t 2-2, W 2- Rap 2 Φ6 t 2-3, W 2-3 Φ5 t 2-5, W 2-4 Φ4 t -2, W - Rap Φ6 t -5 Φ2, W -3 TTI Four-Phase Φ8,2 t -5, W -5 Φ8 t 2-2, W 2- Rap 2 Φ2 t 2-5 Φ2, W 2-3 Φ4,6 t 2-5, W 2-5 Note: Refer to Figures 5 and 6 for referencing t -t and W -t values for Rap Using rap as an exaple, when basic three-phase is used, the phasing sequence at the left-side signal is φ4, φ2, and φ. W - is the flow rate at the rap eter that is equivalent to when M2 discharges at its saturation flow rate. This flow can last up to t -2, the end of green of φ4, as long as there is sufficient deand for M2. Siilarly, W -4 is the rap arrival flow rate that is equivalent to when M discharges at its saturation flow rate, and it can last up to the point at t -5, the end of the green of φ, as long as there is a sufficient deand. Q B (t) is the flow that would result in queue spillback to block the diaond signal, which can be deterined based on Equation (27): Q ( t) = 3600[ Q q ( t )] M ( t) B r Rr + r (27) where Q r = storage space of rap r between the rap etering signal and the diaond interchange signal, veh 24

35 With Q R (t) deterined based on Equation (26) and the rap deand flow profile such as shown in Figure 5 or Figure 6, any vehicles that cannot be discharged freely are considered as part of the residual queues for the current cycle, as denoted by NR earlier. The following describes the ethodology to estiate NR, using rap and with basic three-phase as an exaple. During the current cycle, the traffic deands feeding rap fro the four feeding oveents (M2, M6, M0, M4) are given by Equations (28) through (3): V2 = p2,v 2 (28) V0 = p0,v 0 (29) V6 = p6,v 6 (30) V4 = p4,v 4 (3) denoted as The phasing sequence at the diaond signal is φ4, φ2, φ. The residual rap queues N φ 4, N φ 2, N φ during each phase are recorded during the process of odeling rap operations. Please note that M6 and M4 are uncontrolled and arrive at the rap uniforly during the cycle. Therefore, contributed by two oveents: M6 and M4; and M6, and M4. The residual queue for M2, N φ 4 is contributed by three oveents: M2, M6, and M4; NR 2, is deterined by: N φ 2 is N φ is contributed by three oveents: M0, 25

36 26 p N V V V V NR 2, = φ (32) The residual queue for M0, NR 0 is deterined by: p N V V V V NR 0, = φ (33) The residual queue for M6, NR 6, is deterined by: p N V V V V p N V V V p N V V V V NR 6, , , = φ φ φ (34) The residual queue for M4, NR 4, is deterined by: p N V V V V p N V V V p N V V V V NR 4, , , = φ φ φ (35) The ethodology described above for estiating residual queues due to rap spillback has an underlying assuption that once the rap queue blocks the diaond signal, the entire feeding oveent will be blocked, including traffic heading for the frontage road. However, spillback has no ipact on those traffic oveents that do not feed the on-raps, such as the right-turn oveent on the frontage approach (M3), the arterial left-turn oveent (M), and the arterial through oveent (M4, M5). While at the present stage it is not known whether basic three-phase and TTI four-phase would result in significant differences in rap delays and queues, the two phasing schees do present different ipacts on diaond interchange operations under queue spillback conditions. The two phasing schees result in the feeding traffic oveents being serviced in different sequences, as illustrated in Figure 9 for rap. It can be seen that the frontage road oveent (M2) is serviced following the arterial left-turn oveent (M0) with basic three-phase, while

37 M2 is serviced prior to M0 with TTI four-phase. Because M2 and M0 are the aor rap feeding oveents with higher flow rates and platoons, M2 is ore likely to face queue spillback with basic three-phase than with TTI four-phase. This operational feature is further verified later when odel validation is discussed. 4-Phase Rap Flow, vph φ4 φ6, φ8, Tie in Cycle a) Basic Three-Phase 3-Phase Rap Flow, vph φ4 φ2 φ Tie in Cycle b) TTI Four-Phase Figure 9. Feeding Moveent Service Sequences and Rap Flow Profiles. 27

38

39 CHAPTER 3: DEVELOPMENT OF THE MODELING SOFTWARE A coputer software naed DRIVE (Diaond Interchange/Rap Metering Integration Via Evaluation) was developed, which eployed the odeling ethodologies docuented in Chapter 2. DRIVE can be used to perfor syste analysis and evaluation of operational strategies for IDIRMS. Figure 0 depicts the ain odules and functions of DRIVE. DRIVE is designed to perfor odeling and analysis for the IDIRMS, which includes a diaond interchange, freeway on-raps with rap etering, and freeway ainline operations. DRIVE is classified as a esoscopic siulation odel and was developed using VisualBasic in Excel. VisualBasic in Excel takes advantage of both VisualBasic s prograing features and Excel s spreadsheet functions. Excel also serves as the siple user interface for processing input and output inforation. Unlike deterinistic odels such as PASSER III, TRANSYT-7F, and HCM, DRIVE is designed to perfor analysis over ultiple cycles (currently designed for an analysis period of 00 cycles), considering stochastic traffic deand variations. Therefore, DRIVE presents significant enhanceents over deterinistic odels by providing ore realistic traffic deand odeling and taking into consideration the ipact of over-saturation on syste perforances. Table 4 suarizes the aor input and output inforation for DRIVE. The odeling workflow chart is shown in Figure. 29

40 Initialization Initialize paraeters and variables Freeway Flow Generate rando freeway ainline deand Diaond Flow Generate rando deands for diaond interchange traffic oveents Paraeter Calculations Calculate actual deand considering residual deands fro previous cycle Diaond Signal Tiing Calculate saturation flow rates and green splits DRIVE Flow Profile Generate on-rap arrival flow profile Rap Metering Rap etering operations, freeway and rap queues, delays, and residual queues and deands Diaond MOEs Moveent delays, queues, throughputs, and residual queues Output Perforance easures and statistics Figure 0. DRIVE Modules and Functions. 30

41 Table 4. Input/Output Inforation for DRIVE Software. Input/Output Input Inforation and Paraeters Traffic Deand Geoetry and Traffic Flow Paraeters OD atrix Diaond: Internal storage space, lane configuration, diaond spacing, arterial speed On-Rap/Frontage Road: Rap queue storage, queue block storage, rap etering rates, queue flush rate Freeway: Average free-flow capacity and its standard deviation, average queue-discharge capacity and its standard deviation, freeway breakdown factor Output Signal Tiing Other Diaond Interchange Rap Freeway Suary Profiles Cycle length, phasing type, phase lost tie, etering rate interval Right-turn control type, eter flush ode, signal operations ode, fixed or stochastic deand option, rando nuber seed Total delay, average delay, axiu queue, 95-percentile queue, average queue, residual queue Throughput, axiu queue, 95-percentile queue, average queue, total delay, average delay, nuber of queue flush, tie duration of queue flush, rap eter attainability, % tie rap queue spillback, % tie queue blockage to diaond signal Throughput, total delay For every tie step: Queue length on both freeway ainline and on-rap, rap etering rates, freeway ainline and onrap throughputs 3

42 Identify Traffic Flow Conditions and a Candidate Control Strategy for Evaluation Generate Freeway Flows (Both Directions) for Duration of 00 Cycles on -sec Basis Generate Non-freeway OD Flows for the Next Cycle Calculate Traffic Deands at Both the Diaond Interchange and the Metered Raps (Consider Residual Deands) Deterine Diaond Signal Tiing Generate Arrival Flow Profiles on Metered Raps Model Traffic Interactions between Rap Meters and Diaond Interchange Model Freeway Flow and Rap Arrivals on a -sec Basis Keep Track of Queues at the Raps, Internal and External Approaches of the Interchange Record Residual Deands, Junction Capacity, and Other Perforance Measures No 00 Cycles Yes Calculate Syste Perforance Measures Figure. DRIVE Workflow Chart. 32

43 CHAPTER 4: MODEL VALIDATION Validation on the DRIVE odel was conducted using VISSIM (0), a icroscopic traffic siulation odel. Traffic deands and geoetric data fro a real interchange location were used to code the VISSIM odel. Validation of DRIVE was priarily based on coparing the delays between DRIVE and VISSIM for the aor traffic flows in the syste. This chapter presents the odel validation process and results. SITE DESCRIPTION Traffic volues and network geoetry data were collected at the Mayfield Road/SH 360 interchange located in Arlington, Texas, along the SH 360 corridor. A rap-etering syste consisting of five diaond interchanges was in operation for the northbound direction during the a.. peak period between 6:00 a.. and 9:00 a.. The Mayfield/SH 360 diaond interchange signal was operating with basic three-phase, but was not in coordination with other signals in the Mayfield Road arterial. The rap etering was operating at a fixed rate of 900 vph, the axiu etering rate for a typical single-lane rap eter. Excessive queue detectors were installed to trigger rap eter queue flush, a policy adopted in Texas as well in any other states (4) for rap etering operations. Therefore, rap queues never spilled back to the diaond interchange in the field. The average rap deand was 860 vph during the peak hour. Due to traffic deand fluctuation and its stochastic nature, rap traffic deands exceeded the 900 vph etering capacity during certain cycles of the peak period, and queue flushes were occasionally observed in the field. The diaond interchange itself has sufficient capacity to handle the traffic deands at the interchange. VISSIM MODEL DEVELOPMENT The priary reason for using VISSIM traffic siulation for odel validation was to duplicate the conditions of rap queue spillback, which could not be obtained fro the field. The validation process involved first calibrating the VISSIM odel and DRIVE for under- 33

44 saturated conditions based on PASSER III, where queue spillback did not occur. The odel was then odified to reflect the conditions with rap queue spillback. Validation of DRIVE was carried out by coparing the delays between DRIVE and VISSIM. The VISSIM odel was established based on the traffic flow, geoetry, and signal tiing inforation collected in the field at the Mayfield/SH 360 interchange, but with the following odifications: Since no truck traffic inforation was available, all the vehicles were coded as passenger cars. For consistency purposes, fixed signal tiing was used for the diaond interchange with the green splits deterined based on the ethodology of equal volue-tocapacity ratio, which was originally developed by Webster (20) and used in PASSER III. Rap etering was coded for both directions for the purpose of obtaining additional data points for odel validation, even though the southbound direction does not currently have a rap eter installed. Once the VISSIM odel was established, a basic calibration process was conducted to achieve the following obectives: The traffic volues obtained fro siulation should be checked to ensure correct coding on the traffic deands. The axiu rap etering throughput should atch its designed etering capacity of 900 vph. It is worth entioning about the second point that in VISSIM, there is no special logic designed for rap etering. Drivers react to a rap eter in a siilar anner to a traffic signal. To achieve the desired etering rate, a solution is to code the rap eter using VISSIM s VAP function (2). One critical eleent is to have a deand detector coded at the etering signal, siilarly to the deand detector used in the field. The rap-etering signal would reain red unless there is a call at the deand detector, which is consistent with the current trafficresponsive operations in Texas. 34

45 MODEL CALIBRATION AND VALIDATION RESULTS Average delay was selected as the priary easure of effectiveness (MOE) for coparison between DRIVE and VISSIM. Queue length would have been another candidate MOE; however, the queue length in each odel is easured differently. VISSIM reports the backup queues in distance easured fro a specified location, while DRIVE reports the queues in ters of the nuber of vehicles. While the backup queue could be converted into the nuber of vehicles, the average occupancy space by a vehicle dynaically changes in VISSIM depending on the rap etering rate. On the other hand, backup queue includes the shockwave effect and would be in general at higher values than what is calculated in DRIVE. The average delay was selected as the priary MOE for coparison because delays in both odels are easured in a ore consistent anner. However, it should be noted that the arrival/departure ethod used in DRIVE does not include the delays associated with deceleration and acceleration. A iniu delay would always occur in VISSIM due to the existence of rap etering. To ake it consistent between the delays calculated in both odels, the iniu delay due to rap etering was estiated in VISSIM by giving a very low rap deand. This iniu delay, found to be about 7.0 seconds, was added in DRIVE to the delays based on the queue polygon ethod. Considered as part of the odel calibration process, the under-saturated conditions, i.e., no existence of rap queue spillback, were analyzed using PASSER III, VISSIM, and DRIVE. The two cases analyzed included: a) rap eter with queue flush, the current field operations; and b) rap eter without queue flush. Figure 2 and Figure 3 are the results when the queue flush option was used, which was consistent with the existing rap-etering policy. Figure 2 copares the delays for the traffic oveents at the diaond interchange and the on-raps, while Figure 3 copares the delays for freeway ainlines. All the results were based on the average of five runs for both VISSIM and DRIVE with identical siulation tie (00 cycles or 0,000 seconds for this case). For diaond interchange oveents, the results fro PASSER III are also shown. With the queue flush policy, the diaond interchange and the on-raps operate under capacity. As can be seen, both VISSIM and DRIVE produced delays that atched well with the results fro PASSER III. As expected, the variations fro each run are low for undersaturated situations. As for the freeway ainline, DRIVE produced significantly higher delays for the peak direction (northbound) with very high variations. The off-peak direction reains 35