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ABSTRACT

MOON, JAE PIL. Comparing Operation and Safety between a New Nano Interchange and Conventional System Interchange. (Under the direction of Dr. Joseph E. Hummer.)

The primary purpose of this research is to estimate the capability and applicability of new nano interchange designs as they compare to conventional four-level interchanges. Nano interchanges were conceived to provide drivers with high speed and short travel distances while requiring less right of way in dense urban areas where real estate is expensive. This research consists of two tasks: (1) operational evaluation and (2) safety evaluation.

The operational evaluation compares measures of effectiveness (MOEs) between nano interchanges and conventional interchanges for thirty volume scenarios comprised of varied data for through volumes, ramp volumes, and percentages of heavy vehicles. The estimations were conducted for an entire interchange and for key freeway segments. The MOEs for an entire interchange are travel time, speed, delay time, and ramp travel time; and the MOEs for key freeway segments are density, speed, and level of service.

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The operational evaluation for an entire interchange shows that conventional interchanges perform better than nano interchanges for the volume scenarios tested. The analyses of key freeway segments show that most of operational difficulties for the nano interchanges are in diverging influence areas located on upgrade segments. The analyses also indicate that several merging influence areas that are connected to ramps with steeper and longer upgrades also have lower performance levels.

The safety prediction model developed unique linear or non-linear relationships among traffic, geometric, and environmental factors. Left-hand ramps appear to have higher collision frequencies than right-hand ramps, and on-ramps have higher collision frequencies than off-ramps. In addition to estimating the safety effects, this study compares three modeling procedures. This research shows that the Hauer procedure sufficiently represents linear and non-linear relationships in terms of diverse functional forms by each explanatory variable, whereas a generalized log-linear model does not adequately develop linear relationships for some explanatory variables in terms of linear functional forms. However, the generalized log-linear model with interaction terms among independent variables fits to data as well as the Hauer procedure.

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Comparing Operation and Safety between

a New Nano Interchange and

Conventional System Interchange

by

Jae Pil Moon

A dissertation submitted to the Graduate Faculty of North Carolina State University

In partial fulfillment of the Requirements for the degree of

Doctor of Philosophy

Civil Engineering

Raleigh, North Carolina

2007

APPROVE BY:

___________________________________ Dr. Nagui M. Rouphail

___________________________________ Dr. John R. Stone

___________________________________ Dr. Billy M. Williams

___________________________________ Dr. Joseph E. Hummer

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BIOGRAPHY

Jae Pil Moon was born in the City of Dae Gu, Gyeongsangbuk-Do, South Korea on January 13, 1970. He earned a Bachelor of Science in February 1992 and a Master of Science in February 1998 in Civil Engineering at Dankook University in South Korea. His Master of Science Degree Program was transportation engineering. He joined the Ph.D Degree Program in Civil, Construction, and Environmental Engineering at North Carolina State University in August 2003. His Ph.D Degree Program was transportation system engineering, and he has exposed to diverse research in traffic operation and safety.

In the middle of his Master of Science Degree Program, he enlisted in the Korea Air Force Officers’ Training School in March 1993, and after four months of training, he was commissioned as second lieutenant in June of the same year. As an air force civil engineering officer, he supervised many construction projects at the air force base and was honorably discharged as first lieutenant in June 1996.

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ACKNOWLEDGEMENTS

First, I would like to express gratitude to my advisor, Dr. Joseph E. Hummer. If it were not for his knowledge guidance, support, and encouragement, this dissertation could not have been successfully completed. I am grateful for the opportunity for diverse research during my Ph.D program. I would like to thank my dissertation advisory committee members, Dr. Nagui M. Rouphail, Dr. John R. Stone, and Dr. Billy M. Williams, who provided many invaluable comments and suggestions and helped to improve the quality of the dissertation. I would also like to thank Ms. Meredith Harris who worked with me and shared me with interesting research on nano interchanges.

I would like to thank Kent Taylor and David Price of the Traffic Survey Unit of the North Carolina Department of Transportation, who provided me with valuable traffic volume data. I also wish to thank Tony Ku of the Traffic Safety Systems Management Unit of the North Carolina Department of Transportation, who gave me permission to use the NC Traffic Engineering Accident Analysis System to acquire collision data. I would like to thank the Southeastern Transportation Center for supporting me with a scholarship which supported my work on this dissertation. I would also like to thank Dr. Dong Nyong Kim, who was my Master of Science advisor in Dankook University, South Korea, for his encouragement throughout my Ph.D Degree Program. During my time as a student at NCSU, I enjoyed time with ITE student members and Korean students studying here. Thank you all for your encouragement and warm friendship. It is too manifold to describe.

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TABLE OF CONTENTS

LIST OF TABLES... vi

LIST OF FIGURES... viii

CHAPTER 1: INTRODUCTION... 1

1.1 Background... 1

1.2 Objectives... 5

1.3 Scope... 5

CHAPTER 2: LITERATURE REVIEW... 7

2.1 Interchange-Related Operation... 7

2.2 Interchange-Related Safety... 9

2.3 Other Issues... 18

CHAPTER 3: OPERATIONAL EVALUATION... 19

3.1 Freeway-to-Freeway Interchange Type... 19

3.1.1 Nano Interchange ... 22

3.1.2 Conventional Directional Four-level Interchange ... 25

3.2 Operational Analysis Experiment... 26

3.2.1 Methodology ... 26

3.2.2 Traffic Simulation Model ... 29

3.2.3 Volume Scenarios Tested ... 30

3.2.4 Measures of Effectiveness (MOEs) ... 34

3.2.5 Number of Replications ... 36

3.3 Sensitivity Analysis and Calibration Process for VISSIM... 37

3.3.1 Vertical Sensitivity Analysis... 37

3.3.2 Horizontal Sensitivity Analysis ... 39

3.3.3 Calibration Analysis... 42

3.4 Operation Analysis Results... 51

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CHAPTER 4: SAFETY EVALUATION... 63

4.1 Data Description... 64

4.1.1 Identifying Dependent and Independent Variables... 64

4.1.2 Data Collection ... 66

4.1.3 Collisions Characteristics... 69

4.2 Approach to the Development of a Safety Prediction Model... 73

4.3 Collision Prediction Models... 79

4.3.1 Modeling All Total Collisions ... 79

4.3.1.1 Collision Models for All Total Collision Types ... 79

4.3.1.2 Collision Models for Severe Collisions ... 100

4.3.2 Modeling for Merge- and Diverge-Related Collisions ... 103

4.3.2.1 Collision Models for Related Total Collisions ... 103

4.3.2.2 Collision Models for Related Severe Collisions... 107

4.4 Summary... 110

CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS... 115

5.1 Findings and Conclusions... 115

5.2 Recommendations for Future Research... 118

REFERENCE... 120

APPENDICES... 126

Appendix AOperation Evaluation... 127

A.1 Entire Interchange MOEs... 128

A.2 Freeway Segment MOEs... 135

Appendix B Safety Evaluation... 172

B.1 Generalized Log-Linear Model for Collisions of All Types... 173

B.2 Generalized Log-Linear Model for Severe Collisions... 177

B.3 Hauer Method Model for Severe Collisions... 185

B.4 Generalized Log-Linear Model for Related Total Collisions... 195

B.5 Hauer Method Model for Related Total Collisions... 204

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LIST OF TABLES

Table 1.1 Ramp Configuration of Nano Interchange [2]... 4 Table 2.1 Collision Rates in California (from Lundy) [15] ... 15 Table 3.1 Typical Cross Section Design Elements [2] ... 22 Table 3.2 Geometric Design Elements by Ramp Design Speeds for Reversed Nano

Interchange [2] ... 24 Table 3.3 Geometric Design Elements by Ramp Design Speeds for Conventional

Interchanges [2] ... 26 Table 3.4 Volume Scenarios ... 33 Table 3.5 Measures of Effectiveness for an Entire Interchange and Key Freeway Segments 35 Table 3.6 Capacities of Freeway Types [4] ... 43 Table 3.7 Comparing Percentage Differences* in MOEs between Nano and Conventional

Interchanges ... 54 Table 3.8 Multivariate Analysis of Variance... 55 Table 3.9 Multivariate Analysis of Variance between Nano and Conventional Interchanges

by Ramp Design Speeds ... 56 Table 3.10 Comparing Differences in MOEs for Individual Segments between Nano and

Conventional Interchanges (Heavy Vehicles = 20% and Ramp Volumes = 1,600 veh/h) ... 58 Table 3.11 Comparing Differences in MOEs for Individual Segments between Nano and

Conventional Interchanges (for Heavy Vehicles = 20 % and Ramp Volumes = 1,000 veh/h) ... 59 Table 3.12 Comparing Differences in MOEs for Individual Segments between Nano and

Conventional Interchanges (for Heavy Vehicles = 10 % and Ramp Volumes = 1,600 veh/h) ... 60 Table 3.13 Comparing Differences in MOEs for Individual Segments between Nano and

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Table 4.2 Candidate Ramp Sites... 67

Table 4.3 Characteristics of Collisions (2002 - 2004) ... 70

Table 4.4 Comparison of Collisions between Left-hand Ramps and Right-hand Ramps ... 73

Table 4.5 Comparison of Collisions between On-Ramps and Off-Ramps... 73

Table 4.6 Comparison of Collisions between Urban Areas and Rural Areas... 73

Table 4.7 Forward Stepwise Procedure and Parameters for Equation 4-11 ... 82

Table 4.8 Forward Stepwise Procedure and Parameters for Equation 4-12 ... 83

Table 4.9 A Comparison of the Gamma Function and Power Function of the Main AADT for Total Collisions of All Types... 89

Table 4.10 A Comparison of the Exponential Function and Power Function of the Ramp ADT for Total Collisions of All Types... 93

Table 4.11 Stepwise Sequence and Parameters of Equation 4-18 ... 98

Table 4.12 Forward Stepwise Procedure and Parameters for Equation 4-19 ... 100

Table 4.13 Forward Stepwise Procedure and Parameters for Equation 4-20 ... 101

Table 4.14 Stepwise Sequence and Parameters of Equation 4-21 ... 103

Table 4.15 Forward Stepwise Procedure and Parameters of Equation 4-22... 104

Table 4.16 Forward Stepwise Procedure and Parameters of Equation 4-23... 105

Table 4.17 Stepwise Sequence and Parameters for Equation 4-24... 107

Table 4.18 Forward Stepwise Procedure and Parameters for Equation 4-25 ... 108

Table 4.19 Forward Stepwise Procedure and Parameters for Equation 4-26 ... 109

Table 4.20 Stepwise Sequence and Parameters for Equation 4-27... 110

Table 4.21 A Comparison of Overall Goodness-of-Fit between Models for Total Collisions of All Types ... 112

Table 4.22 A Comparison of Overall Goodness-of-Fit between Models for Severe Collisions ... 112

Table 4.23 A Comparison of the Overall Goodness-of-Fit between Models for Related Total Collisions ... 113

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LIST OF FIGURES

Figure 1.1 Schematic of typical conventional, directional, four-level system interchange

design [2] ... 2

Figure 1.2 Schematic of typical new nano interchange design [2] ... 4

Figure 1.3 Schematic for scope of the study... 6

Figure 2.1 Average collisions frequencies for off-ramps [14]... 13

Figure 2.2 Average collisions frequencies for on-ramps [14] ... 14

Figure 2.3 Collision type distribution [7] ... 16

Figure 2.4 Collision location distribution [7] ... 16

Figure 3.1 Schematics of freeway-to-freeway interchanges of interest... 20

Figure 3.2 Ramp configurations ... 21

Figure 3.3 Configuration of the reversed nano interchange ... 23

Figure 3.4 Reverse curve segment heading into the reversed nano interchange ... 24

Figure 3.5 Configuration of conventional directional four-level interchange ... 25

Figure 3.6 Typical right-hand and left-hand off-ramps and on-ramps in the nano interchange model... 28

Figure 3.7 Typical composite grades in the nano interchange design ... 29

Figure 3.8 Distribution of ramp turning movements ... 32

Figure 3.9 Speed-distance curves for heavy trucks on upgrade in VISSIM... 38

Figure 3.10 Speed-distance curves for cars on upgrade in VISSIM... 39

Figure 3.11 Speed- distance curves for heavy trucks on selected horizontal curves and upgrades (radius = 340 ft) ... 40

Figure 3.12 Speed-distance curves for heavy trucks on selected horizontal curves and upgrades (radius = 640 ft) ... 41

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Figure 3.16 Speed-flow relationships for headway time (CC1 = 0.85) ... 46

Figure 3.17 Speed-flow relationships for headway time (CC1 = 0.90) ... 46

Figure 3.18 Speed-flow relationships for headway time (CC1 = 0.95) ... 47

Figure 3.19 Speed-flow relationships for each truck percentage... 48

Figure 3.20 Adjusted speed-flow relationships for each truck percentage... 48

Figure 3.21 Volume levels handled by a ramp speed of 35 mph by each CC1 parameter ... 49

Figure 3.22 Volume levels handled by a ramp speed of 45 mph by each CC1 parameter ... 50

Figure 3.23 Volume levels handled by a ramp speed of 55 mph by each CC1 parameter ... 50

Figure 3.24 Segmented Freeway Facilities for Interchanges of Interest ... 56

Figure 4.1 Data collection boundary conditions of off-ramps and on-ramps ... 65

Figure 4.2 Example of a police collision report... 68

Figure 4.3 Distribution of Total Collisions over 3 years ... 70

Figure 4.4 Distribution of Fatal and Injury collisions over 3 years ... 71

Figure 4.5 Distribution of merging- and diverging-related Total collisions over 3 years ... 71

Figure 4.6 Distribution of merging- or diverging-related Fatal and Injury collisions over 3 years ... 72

Figure 4.7 CURE plot of main AADT for Equation 4-11 ... 84

Figure 4.8 CURE plot of ramp ADT for Equation 4-11 ... 84

Figure 4.9 CURE plot of main AADT for Equation 4-12 ... 85

Figure 4.10 CURE plot of ramp ADT for Equation 4-12 ... 85

Figure 4.11 A comparison of observed and predicted numbers of collisions for Equation 4-11 ... 86

Figure 4.12 A comparison of observed and predicted numbers of collisions for Equation 4-12 ... 87

Figure 4.13 EIF of main AADT for Total collisions of all types ... 89

Figure 4.14 Density and cumulative functions of well-known functions [12, 33] ... 90

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Figure 4.17 EIF of ramp ADT for Total collisions of all types ... 92 Figure 4.18 CURE plots of the exponential Function of the ramp ADT for Total collisions of all types ... 93 Figure 4.19 CURE plots of the power function of the ramp ADT for Total collisions of all

types ... 94 Figure 4.20 R-ratios of the position parameter for Total collisions of all types... 95 Figure 4.21 R-ratios of the type parameter for Total collisions of all types... 95 Figure 4.22 R-ratios of difference between design speeds of freeways and ramps for Total

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CHAPTER 1: INTRODUCTION

1.1 Background

Freeways are controlled access facilities that provide high speed and capacity operations. Interchanges are essential components in freeway operations because they fully control freeway access and handle the movement of traffic between freeways. Since the first modern interchange in the United States (US) was constructed and opened in 1928, engineers have developed and used numerous designs to effectively and safely manage traffic movements at interchanges [1]. According to the function of the highways, interchanges can be categorized as either service or system. Service interchanges connect freeways to non-freeway highways

or streets, and system interchanges connect two freeways. The two types of interchanges serve two different purposes: while service interchanges focus mainly on access to local streets, the main function of system interchanges is to provide high speed and capacity transfers.

In many cases, interchanges are inferior in design quality compared to the associated freeways. Some interchange designs result in problems pertaining to drivers, traffic, and the environment as the average daily traffic (ADT) on the interchanges approaches capacity. Many service and system interchanges contribute to excessive air pollution, fuel consumption, and collisions, in part because of the likelihood of increased speed differentials between freeway mainlines and ramp junctions. In addition to these potential problems, system interchanges also consume large amounts of right of way (ROW), especially in dense urban areas where real estate is precious and expensive. Attempts to limit the amount of ROW have contributed to interchanges that are poorly designed.

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Unfortunately, existing conventional interchanges have never fully complied with all the traffic, physical, and safety requirements. Many service interchanges have been improved recently through innovative access control strategies near ramp terminals and new geometric designs such as single points. However, unlike service interchange design, system interchange design has not advanced much recently.

Figure 1.1 shows a typical conventional, directional, four-level interchange, which is the most widely accepted system interchange found in the United States. This conventional interchange uses direct or indirect ramps that do not deviate greatly from the intended directions.

Figure 1.1 Schematic of typical conventional, directional, four-level system interchange design [2]

4 1

3

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allows direct connections to be made because each freeway is in a double-deck configuration where one direction is at a higher elevation than the other. Figure 1.2 shows the new nano interchange concept [2]. Mainline 4 is on the highest level, with mainlines 3, 2, and 1 positioned accordingly from high to low, respectively. Table 1.1 also shows the ramp configuration of the nano interchange [2]; i.e., ramp 1Æ2 connects mainline 1 to mainline 2. The most noticeable geometric characteristic of the nano interchange is that it uses direct connections for all the left turn and the right turn movements, made possible by the double-deck configuration. The nano interchange was designed with the expectation that it would provide shorter travel distances, higher speeds, lower amounts of ROW, and higher levels of service compared to some other designs.

However, the nano interchange has some obvious problems, such as: (1) confounding driver expectations by having left exits and entrances, because most drivers expect to have right exits and entrances; and (2) incurring high construction costs. Although the nano interchange may not necessarily work in low-to-medium density urban environments, it may be suitable for construction in other locations around the world – such as New York, Mexico City, Seoul, Shanghai, or Tokyo – where the construction costs and right-of-way needs make economic sense.

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Figure 1.2 Schematic of typical new nano interchange design [2]

Table 1.1 Ramp Configuration of Nano Interchange [2]

Ramp From To or Descend (D) Ascend (A) Spans # Levels

1 Æ 2 Level 1 Level 2 A 1

1 Æ 3 Level 1 Level 3 A 2

2 Æ 1 Level 2 Level 1 D 1

2 Æ 4 Level 2 Level 4 A 2

3 Æ 1 Level 3 Level 1 D 2

3 Æ 4 Level 3 Level 4 A 1

4 Æ 2 Level 4 Level 2 D 2

4 Æ 3 Level 4 Level 3 D 1

4

2

3

1

3ٛ 4 1ٛ 2

3ٛ 1 4ٛ 2 4ٛ 3

2ٛ 1 2ٛ 4

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1.2 Objectives

The objective of this study is to evaluate the functional capabilities and applicability of the new nano interchange in comparison to a conventional system interchange, specifically in densely developed urban areas. The functional capability and applicability estimations serve to evaluate the possibility of introducing the nano interchange in the real world. To fully evaluate the capabilities and applicability of the new interchange, several aspects may be considered, such as operations, safety, environmental factors, construction and right-of-way costs, and so on. Of these aspects, this study focuses on operations and safety.

Before going too far in these efforts, the new interchange needed to be designed in detail to minimize the construction costs while satisfying AASHTO 2004 [3] design criteria. The new interchange was designed for three ramp speeds. In a parallel effort [2], a comparable conventional directional interchange was also designed. Both designs, new and conventional, were applicable to a compact urban area. In addition to the two design efforts, estimated construction costs and right-of-way needs for each interchange design were taken into consideration.

This study, then, focuses on ways in which the two subject interchanges, designed in a parallel effort, function in terms of operations and safety.

1.3 Scope

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attempt to redesign the nano interchange to solve any problems that may arise out of the operational and safety estimations determined by this study.

Figure 1.3 Schematic for scope of the study * Design Criteria

* Typical Section * Comparison Selection

- Conventional 4-level Interchange * Horizontal and Vertical Alignment * Right-of-Way Requirement * Construction Cost Estimate

Driver Expectations Adjacent Interchanges Task 1

Operational Analysis * Isolated Interchange

* Traffic Scenarios by VISSIM

Task 2 Safety Estimation * Estimating the Safety Effects between Left-hand and Right-hand Ramps Design Task

See Ref. [2]

Environment Analysis

Constructability Estimating the function and applicability

for the nano interchange

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CHAPTER 2: LITERATURE REVIEW

The purpose of the literature review is to identify design elements and traffic factors that influence the operation and safety of freeway-to-freeway interchanges. The pertinent literature is reviewed in three sections. The first section examines procedures and issues pertaining to interchange operations; the second section examines interchange-related safety; and the last section is for other issues.

2.1 Interchange-Related Operation

First, operations characteristics relative to left-hand ramps need to be reviewed because the nano interchange includes left-hand ramp entrances and exits. Two early studies that examined the operational characteristics of left-hand ramps on urban freeways were conducted at Northwestern University. The first study, conducted by Berry et al., evaluated the operation of left-hand exit ramps by surveying field data in Chicago. This study also reviewed pertinent literature on operational aspects of left-hand ramps [4]. Data (volume, speeds, density, exiting paths, and hazardous maneuvers) were collected through time-lapse photography on three left-hand ramps and one right-hand ramp. The analysis compared the collected data of the left-hand ramps and the right-hand ramps. The researchers also analyzed the operational effects of unfamiliar drivers on left-hand ramps by conducting interviews.

The results show that left-hand ramps generally do not have an adverse impact on lane distributions, speeds, and volumes. Also, the Berry study offered no indication that hazardous maneuvers are more prevalent at left-hand exits than at right-hand exits designed for high speeds. This study also recommends that adequate advance directional signs are needed to advise unfamiliar drivers of specific ramp types.

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the Chicago area. The results show that although speeds and volume distributions between merging and through vehicles are large at left-hand ramps compared to right-hand ramps, the left-hand ramps do not cause any prolonged disruption of flow in the adjacent freeway lanes [5].

Several studies used simulation models to examine freeway interchange alternatives. A study conducted by Hanks et al. in 1992 evaluates the operations and safety impacts of alternative freeway-to-freeway interchanges under a variety of traffic demands. These analyses are applicable to five different geometric considerations using INTRAS and FREFLO models: (1) a comparison of merge and diverge terminals designed within an interchange; (2) ramp spacing; (3) the operational effects of left-hand ramps, (4) the provision of route continuity and lane balance, and (5) horizontal and vertical alignments within an interchange. The results show that, of the three ramp configurations considered in this study, a parallel ramp design appears to provide the greatest benefit associated with operations and safety, followed by the exterior taper ramp design, and lastly, the interior taper ramp design. The results also indicate that the route continuity and lane balance design criteria are important, and that ramp spacing data are needed to provide adequate distances. The Hanks study recommends that although experience shows that left-hand ramps may be implemented successfully using a proper design, left-hand ramps should be avoided [6].

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SPUIs between 1,500 veh/h and 5,500 veh/h, and partial cloverleafs between 1,500 veh/h and 2,500 veh/h. Garber et al. also document that when weaving volumes approach 1,000 veh/h, full cloverleafs with collector–distributor (C-D) roads, semi-directional, or directional connections should be used. The Garber study does not address left-hand exit or entrance ramps [7].

A recent study by Thompson et al. at North Carolina State University analyzes the operational impacts of service interchanges using the CORSIM model. The study also compares construction and right-of-way costs specific to the interchange alternatives. Travel times and stops were examined as MOEs, using different random number seeds for each of the two replications under several volume scenarios. ANOVA tests were performed to quantify the interactions of interchange design factors and volume factors [8].

2.2 Interchange-Related Safety

This section reviews past safety studies associated with interchanges. Past studies have described relationships between collisions and interchange features, such as configurations, ramp types, and so on. Whereas most of the early studies focused on comparing collision rates between interchange features using statistical hypothesis tests, other studies have developed safety prediction models through general multilinear and log-linear modeling.

In general, past studies indicate that collisions occur mostly at ramp terminals and in speed-change lanes (acceleration and deceleration lanes) in interspeed-changes. Common factors associated with interchange collisions are:

• Ramp and freeway mainline annual average daily traffic (AADT);

• Area type (rural and urban);

• Ramp type (off and on);

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• Speed-change lane length and configuration.

However, a definitive relationship between collisions and ramp geometric design features has not been established because of limited sample sizes. Likewise, although past studies show that left-hand ramps have higher collision rates than right-hand ramps, the differences in safety effects between left and right ramps have not been well quantified because relatively few left ramps exist.

Collision Prediction Modeling

In the past, most safety prediction models have used simple multiple-linear regression analysis under the assumption that collision frequency follows a normal distribution. However, model designers have pointed out problems with regard to simple multilinear safety models. They have found that the patterns of collision frequency data appear to have highly skewed distributions, with a substantial proportion close to zero. So, other researchers have applied Poisson or negative binominal distributions to safety prediction models

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10 9 8 7 6 5 4

3 0.78* 0.02* 0.69* 0.37* 0.37* 2.59* 1.62*

* 45 . 0 13 . 0 2 78 . 0 1 27 . 7 1 X X X X X X X X

e

e

e

e

e

e

e

e

X

X

e

Y

=

− − − − (2-1)

7 8

9

10 4.42* 0.48* 0.26* * 85 . 2 23 . 0 2 87 . 0 1 67 . 9 2 X X X X e e e e X X e

Y = − − − , (2-2) where

Y1 = expected number of Total collisions in a 3-year period on an entire ramp with an

adjacent speed-change lane;

Y2 = expected number of Fatal and Injury collisions in a 3-year period on an entire

ramp with an adjacent speed-change lane; X1 = ramp AADT (veh/day);

X2 = freeway mainline AADT (veh/day);

X3 = 1 if the ramp is a diamond ramp, 0 otherwise;

X4 = 1 if the ramp is a parclo loop ramp, 0 otherwise;

X5 = 1 if the ramp is a free-flow loop ramp, 0 otherwise;

X6 = 1 if the ramp is an outer connection ramp, 0 otherwise;

X7 = 1 if the area type is rural, 0 otherwise;

X8 = 1 if ramp is an off-ramp, 0 otherwise;

X9 = speed-change lane length; and

X10 = ramp length.

Bauer and Harwood excluded left ramps from these efforts. (Left ramps are included in this research thesis.)

Recently, Hauer suggested a safety prediction modeling process along with good tools for finding the function of causal-effect relationships and goodness of fit [10, 11]. He states that a prediction model should have both multiplicative and additive terms, as follows:

)], portion additive ( ) portion ( ) prediction for length segment [( ) parameter scale ( + × ×

= multiplicative

Y (2-3) where ) ) road to related factors ( ) flow traffic ( (

portion= f ×g ×K

tive multiplica

+ +

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The multiplicative component represents the influence of factors over a subject road, whereas the additive component accounts for the safety effects of a point in any road. Building a prediction model is accomplished by adding one variable after another, sequentially. Each variable has a functional form suitable for the causal-effect relationship, which is identified using two tools (the integrate-differentiate (ID) method and R-ratios), as suggested by Hauer and Bamfo [12]. The cumulative residuals (CURE) method confirms whether a model built using diverse functional forms for explanatory variables is a satisfactory fit to the data.

Hauer [10] also uses a negative multinomial distribution, generalized from a negative binomial distribution, to develop a safety prediction model. The negative multinomial distribution can represent the temporal changes of variables measured repeatedly over long periods of time, compared to commonly used distributions, such as a Poisson and negative binomial. The probability of the negative multinomial distribution is:

ϕ ϕ ϕ ϕ ϕ ϕ + = = + Γ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∏ + Γ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∏ = a i n j i a ij n j in i i Y a a Y a a a p ij ) )( ( ! ) ( ) , , , ( 1 1 2

1 L , (2-4)

where ainj represents collisions for entity i over period 1 to nj; ϕ is a dispersion parameter;

and Yi is the mean of entity i. The parameters of the negative multinomial model are

estimated by maximizing the log-likelihood function using the following equations:

∀ = i i l l

L() ln( ) and (2-5)

[

( _

]

ln

[

( )

]

( )ln( )

) ln( ) ln( ) (

1 i i i i i i

n j ij ij i i

i a Y LN a a Y

l L J ϕ ϕ ϕ ϕ ϕ ϕ + Γ + − Γ − + + ⎦ ⎤ ⎢ ⎣ ⎡ + =

=

. (2-6)

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AADT

Several studies have shown that traffic volumes are the strongest variables in interchange collision prediction models. Khorashadi (1998), for example, who examined the systematic differences in collision rates among traffic, geometric, and environmental variables in California, points out that higher traffic volumes are associated with significantly higher collisions [14].

Area Type

Some studies have found that the density of the surrounding area is an important contributor to a collision model. Area types are usually categorized as urban or rural. It appears that urban areas have higher collision rates than rural areas. As Figures 2.1 and 2.2 show, average collision frequencies at ramps in urban areas are significantly higher than in rural areas. This study also indicates that for collision rates, the opposite is so, i.e., that average collision frequencies at ramps in rural areas is higher than those in urban areas [14]. The Bauer and Harwood study shows that interchanges in urban areas generally tend to have more collisions than rural areas [9].

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Figure 2.2Average collisions frequencies for on-ramps [14]

Ramp Type (On and Off)

Past studies have evaluated the relative effects of on- and off-ramp types on collisions. In early studies, there was some controversy on this issue. For example, Lundy concluded that off-ramps have higher collision rates than on-ramps [15], but Mullins et al. showed the opposite [16]. The most recent studies, i.e., those of Bauer and Hardwood and Khorashadi, have clarified this issue. The Khorashadi study states that collision rates for on-ramps are lower than those for off-ramps [14]. The Bauer and Hardwood study indicates that the relative collision effects for off-ramps are significantly higher than for on-ramps, and that off-ramps have more Fatal and Injury collisions than on-ramps [9].

Ramp Type (Left and Right)

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left-summarized pertinent literature associated with safety [17], and Hall indicate that left-hand ramps are more prone to collisions than right-hand ramps [18].

Table 2.1 Collision Rates in California (from Lundy) [15]

Ramp Type On Off On + Off

Left hand ramps 0.93 (ACC/MV) 2.19 (ACC/MV) 1.91 (ACC/MV) Average 0.59 (ACC/MV) 0.95 (ACC/MV) 0.79 (ACC/MV) ACC/MV = Accident / Million Vehicles.

Unfortunately, no recent studies have been conducted that quantify the relative effects of left-hand ramps on collisions compared to right-left-hand ramps. For example, Bauer and Hardwood did not study these effects because of limited sample sizes.

Ramp Configuration

Ramp configurations differ according to the function of the interchange. Most service interchanges have one or more diamond, parclo loop, free-flow loop, or outer connection ramps. System interchanges have mostly semi-direct connections and direct ramps, and free-flow loop ramps are becoming less common.

The unique geometric designs specific to each ramp configuration might be associated with different collision rates. For example, Lundy showed that relationships exist between collision rates and ramp configurations [15], and Hall found that C-D roads need to be implemented in cloverleaf interchanges under high traffic demands. In addition, Hall showed that inner loop ramps and outer connector ramps have a tendency toward high collision frequencies [18].

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through statistical analyses. As a whole, although no significant differences were evident between the effects in most cases, Garber et al. showed the collision types and locations that prevailed at each interchange, as Figures 2.3 and 2.4 illustrate. The Garber study also points out that small sample sizes might have affected the statistical results [7].

Figure 2.3 Collision type distribution [7]

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type (on and off) and ramp area (urban and rural). The results indicate that relationships do not exist between ramp configurations and collisions for most of the analysis units. Khorashadi also noted that among ramp types with relatively higher than average collisions, scissor ramps, rest area ramps, and slip ramps were the worst in terms of safety [14].

Speed-Change Lane length

Past studies have shown that for interchange collisions, a substantial proportion of the collisions occur in the merging and diverging areas. Lundy states that about 52% of the collisions he studied occur on on-ramps related to merging areas, and 44% of off-ramp collisions occur in diverging areas. He also states that the longer the acceleration lane or deceleration lane, the lower the collision rates [15]. Hall also shows that inadequate lengths of acceleration and deceleration lanes contribute to higher collision rates [18]. Bauer and Harwood show that many collisions that occur in merging and diverging areas relate to the length of speed-change lanes. However, they also note that models combining the entire ramp with speed-change lanes are a better to fit to the data than models for speed-change lanes alone [9].

Ramp Geometric Design Features

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2.3 Other Issues

In addition to interchange features, human factors (driver errors) certainly have an impact on collisions. Driver errors occur under a variety of conditions: expectation violations, situations that put too much or too little demand on drivers, and deficient and misplaced information displays or poor signage. Of these factors, driver expectation is the most important in driver performance and information processing [19]. Driver expectation is consistently formulated during driving and information processing, and accumulates over previous experiences. If driver expectation is violated when driving in a specific situation, drivers may commit errors resulting in collisions. For example, most drivers unfamiliar with interchanges with left-hand ramps would reasonably expect to exit using right-hand ramps; therefore, some drivers are likely to maneuver hazardously or miss the exit when presented with a left-hand ramp. The nano interchange might raise this concern.

AASHTO (2004) also states that because left-hand entrances and exits are contrary to driver expectation and break up the uniformity of interchange patterns, their use is not recommended. AASHTO also points out that in the case of implementing left-hand ramps, special attention should be given to signage and providing for adequate decision sight distance to alert drivers that an unusual situation is imminent.

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CHAPTER 3: OPERATIONAL EVALUATION

The purpose of this portion of the study is to evaluate ways that freeway-to-freeway interchanges perform operationally relative to each other under a variety of volume scenarios. The following five factors are considered in the operational analysis in this study:

z Freeway-to-freeway interchange type; z Mainline freeway volumes;

z Ramp volumes and directional distributions; z Ramp design speeds; and

z The percentage of heavy vehicles.

In addition to the above factors, adjacent interchanges that are close to the subject interchanges are likely to affect operations. Although exploring the operational impacts of interchange spacing on freeways would be worthwhile, such an undertaking is out of the scope of this effort because of the extensive possibilities and combinations – including various interchange spacings, volume distributions and levels, and ramp positions and ramp types. Therefore, this operational study considers only the subject interchanges in isolation.

Each factor considered in this experiment is discussed in detail in the following sections.

3.1 Freeway-to-Freeway Interchange Type

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(a) (b)

Figure 3.1Schematics of freeway-to-freeway interchanges of interest

Ramp configurations in the interchanges, shown in Figure 3.2, encompass only direct or semi-direct ramps appropriate for freeway–to-freeway interchanges. In other words, no loop ramps appear in any of the designs under consideration. This factor makes the interchanges of interest relatively small in area and applicable to dense urban areas. Because all the interchanges of interest are designed for practical application in a compact urban area where construction and right-of-way costs are important in addition to operations and safety, the criteria for ramp design should correspond to this context. Ramp design speeds have an important effect on traffic operations and safety in an interchange. AASHTO states that the range of appropriate ramp design speeds for a highway design speed of 70 mph is from 60 mph (upper value) to 35 mph (lower value). However, a ramp design speed of 60 mph might not be the most practical speed for a compact urban area. Harris categorized ramp design speeds and set these at lower, middle, and upper levels, which correspond to 35 mph, 45 mph, and 55 mph, respectively. Interchanges with a ramp design speed of 35 mph (the lower case) consume the smallest amounts of right of way (ROW), and interchanges with a ramp design speed of 55 mph (the upper case) are likely to have the best traffic operation and safety.

New Nano Interchange

3

2

1

4

Conventional Four-Level Directional Interchange 4

2

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(a) (b)

(c) (d)

(e)

Figure 3.2 Ramp configurations

Table 3.1 shows the common design criteria adopted for both types of interchanges. Acceleration and deceleration lanes for entrance and exit terminals are of the parallel type. Radii, grades, and speed-change lane lengths correspond to information in AASHTO for each ramp design speed. (Refer to [2] for more detailed information.)

Direct Connection

Semi-Direct Connection (1)

Semi-Direct Connection (2) Semi-Direct Connection (3)

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Table 3.1 Typical Cross Section Design Elements [2]

Design Element Mainline Ramp

Design Speed (mph) 70 35, 45, 55

Lane Width (ft) 12 16

Median Width (ft) 22 -

Left 10 10

Shoulder Width (ft)

Right 10 12

Through Lanes 3 1

Maximum Superelevation 6 % 6 %

3.1.1 Nano Interchange

Two versions of the nano interchange emerged from the design work, namely the parallel nano interchange and the reversed nano interchange. The common design features of both nano interchanges are:

z Direct left-turn and right-turn connections whereby vehicles do not travel more than

two levels; and

z Entrance points or exit points for left-turn and right-turn movements that are

staggered along mainlines.

The main difference in the geometric features between the parallel nano interchange and the reversed nano interchange is that the parallel nano interchange keeps the mainlines parallel and horizontally separate from each other, whereas the reversed nano interchange features mainlines stacked in opposite directions over each other (west over east and north over south, for example).

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differences in operational performances between the two interchanges are likely to be evident. In addition, because the right-of-way needs of the reversed interchange are much fewer than those of the parallel interchange, the reversed interchange is more likely to be suitable for building in compact urban areas than the parallel interchange. Thus, this study compares a conventional interchange with the reversed nano interchange only.

Figure 3.3 shows the three-dimensional geometric configuration of the reversed nano interchange created in VISSIM, based on the ramp design speed of 35 mph. The reversed curve segment is shown in Figure 3.4.

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Figure 3.4 Reverse curve segment heading into the reversed nano interchange

Table 3.2 shows the key design elements for the reversed nano interchange.

Table 3.2 Geometric Design Elements by Ramp Design Speeds for Reversed Nano Interchange [2]

Ramp Design Speed (mph) Design Element

35 45 55 Acceleration 1,230 ft Min. 820 ft Min. 580 ft Min.

Speed-change Length (ft)

Deceleration 490 ft Min. 390 ft Min. 340 ft Min.

Freeway Max. 4% Max. 4% Max. 4% Grade (%)

Ramp proper Max. 4% Max. 4% Max. 4%

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3.1.2 Conventional Directional Four-level Interchange

A conventional directional four-level interchange was chosen as a competitor to the reversed nano interchange for this study. Although several system interchange types exist [2], the conventional directional four-level interchange is the most widely accepted in the United States as a system interchange without loops. Thus, it serves as the best comparison with the nano interchange in terms of operation and safety effects.

The design efforts for the four-level interchange are based on the same design criteria as the nano interchanges. The particular configuration of the four-level interchange used in this study has all the ramps passing over mainlines located on the two lowest levels, thus resulting in construction cost reductions [2]. Figure 3.5 shows the three-dimensional geometric configuration of the conventional interchange created in VISSIM.

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Table 3.3 shows the key design characteristics of the conventional directional four-level interchanges.

Table 3.3 Geometric Design Elements by Ramp Design Speeds for Conventional Interchanges [2]

Ramp Design Speed (mph) Design Element

35 45 55 Acceleration 1,500 ft 1,500 ft 1,500 ft

Speed-change Length

(ft) Deceleration 1,500 ft 1,500 ft 1,500 ft

Freeway Max. 4% Max. 4% Max. 4% Grade (%)

Ramp proper Max. 4% Max. 4% Max. 4%

Typical Ramp Controlling Radius (ft) 340 ft Min. 643 ft Min. 1,060 ft Min.

3.2 Operational Analysis Experiment

The main objective of this experiment is to estimate whether the nano interchange handles typical freeway and ramp volume patterns effectively compared to the conventional interchange.

3.2.1 Methodology

The two general types of simulation models are: (1) macro-simulation models and (2) micro-simulation models. A macro-micro-simulation model estimates overall measures of effectiveness (MOEs) for a particular facility during a time period such as 15 minutes, whereas a micro-simulation model evaluates MOEs of a network by tracking and summing the operational performances of individual vehicle movements.

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and identify LOS. In addition, the HCM procedures consider the operational effects of grades and speed-changing lanes within influence areas, along with approaching freeway and ramp flow and free-flow speeds in the immediate upstream or downstream of the influence areas.

As Figure 3.6 shows, the nano interchanges have simultaneous direct left-hand and right-hand ramps on each level; thus, there is an overlap in influence areas between the left-right-hand and right-hand ramps. That is, vehicles would operate through a more complicated zone due to the overlap of the influence areas where merging or diverging vehicles maneuver simultaneously from the left-hand and right-hand ramps. These simultaneous merging or diverging maneuvers also differ in lane distribution and use from the HCM ramp analysis procedures. The HCM procedures are used for isolated ramp influence areas with adjacent upstream or downstream ramps; therefore, the HCM models for predicting freeway flow quality in the influence areas cannot account for operational turbulence and lane utilization due to the coincident existence of left-hand and right-hand ramps.

(a) Left-hand Ramp

Right-hand Ramp

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(b)

Figure 3.6 Typical right-hand and left-hand off-ramps and on-ramps in the nano interchange model

Furthermore, the vertical alignments near the ramp influence areas in nano interchanges are complex. Figure 3.7 shows the composite grades of the highest level of a nano interchange with a ramp design speed of 55 mph. The diverging influence area is connected to the upstream mainline using two grade segments, 4% and 3.2%. Diverging vehicles exit onto the left-hand and right-hand off-ramps with grades of -1.4% and -3.6%, respectively. The merging influence area is connected to the downstream mainline using two composite grades of -3.6% and -4.0%. Also, ramp flows that approach the merging influence area depart from the two on-ramps with a rising grade. These complicated vertical alignments would affect individual vehicle performances. In addition, the operational performance of the freeway and the ramp flow approaching the merging or diverging influence areas in the nano interchanges would vary according to the particular design features. However, the HCM ramp methodologies have no special cases that would reflect the operational effects of the upstream or downstream influence areas of the nano interchanges. Also, the HCM average speed equations for the ramp influence areas, which are based on free-flow speeds, freeway and ramp flow rates, and speed-changing lane lengths, would not be sufficient to estimate the space speeds for the influence areas of the nano interchanges, because the HCM equations are for all vehicles traveling within ramp influence areas and, therefore, would not reflect the

Left-hand Ramp Right-hand Ramp

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Figure 3.7 Typical composite grades in the nano interchange design

Thus, it is concluded that the HCM does not have the capability to model the operational characteristics of the merging or diverging maneuvers inherent of the specific design features of the nano interchanges.

3.2.2 Traffic Simulation Model

The micro-simulation models currently used in research are CORSIM, VISSIM, PARAMICS, and AIMSUM. All these models can simulate freeways relatively accurately, especially the merging and diverging maneuvers at on- and off-ramps, based on the movements of individual vehicles. Of these models, CORSIM has been validated and used in many older studies that compare operations associated with interchange types, and VISSIM has been used and validated more recently more. Then, CORSIM and VISSIM were compared in order to select the better of these two models as a traffic simulation model suitable for estimating the operational effects among the interchanges of interest.

3

2 1

4

3.2 % 4.0 % 0 %

- 3.6 % - 4.0 %

0 %

- 3 .6 %

- 1.4 %

2.4 %

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There are only a few differences between CORSIM 5.1 and VISSIM 4.1 in their abilities to simulate complicated transportation systems. CORSIM 5.1 requires a minimum of spacing (at least 50 ft) between two nodes [22]. Bonneson et al. point out through engineering experience that 800 ft or more between two nodes are needed for CORSIM to simulate typical volume levels [23]. They also state that a special modeling method to make reasonable lane-changing maneuvers is required for short links. Furthermore, because CORSIM uses link-based routing, if vehicles cannot find available gaps to merge or diverge prior to an entrance or exit point, then they pass through that point and travel regardless of the predefined routes assigned to each vehicle. Such erratic maneuvers for short segments might produce unreasonable operational results. Because the nano interchange has nearly simultaneous left-hand and right-hand on-ramps and off-ramps, operational problems may be expected near the ramp junctions of the nano interchange using the CORSIM node. In addition, the link node-based network of CORSIM is unfriendly for creating the nano interchange in which one mainline freeway direction is directly over the mainline in the opposite direction.

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medium), corresponding to LOS, E and D, respectively. The volume levels of ramps also have two groups: high and medium. Because the basic freeway sections of the nano and conventional interchanges were designed for a speed of 70 mph, the demands of each level are based on the LOS criteria corresponding to free-flow speeds of 70 mph in the HCM 2000 [24]. If the demand at the high level is set near the upper value of LOS E, breakdowns will easily occur due to the interactions among vehicles across an entire interchange and will continue through a simulation period. Therefore, given 20% heavy vehicles (the highest studied during this effort), the demands at LOS E and LOS D are set to 2,000 and 1,666 for vehicles per hour per lane (veh/h/lane) for each freeway, respectively.

The high demand on ramps was set to near capacity for ramps with free-flow speeds of 30– 40 mph, which is shown in the HCM as 2,000 passenger cars per hour (pc/h). The medium volume is fixed at about two-thirds of the high volume. Given 20% heavy vehicles and the ramp capacity, the high and medium levels for ramps were set to 1,600 veh/h and 1,000 veh/h, respectively.

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Figure 3.8 Distribution of ramp turning movements

The percentage of heavy vehicles was varied because maneuver differentials between passenger cars and heavy vehicles may affect operations significantly. The percentage of heavy vehicles across all the volume scenarios was set at either 10% or 20% to estimate the relative operational effects of heavy vehicles for each volume scenario on each interchange.

Table 3.4 shows the volume scenarios considered for each ramp design speed and interchange type in this study by the two percentages of heavy vehicles. There are five freeway mainline volume cases, two ramp volume cases, and three turning movement ratios for the ramp volume cases, or 30 cases all together.

1,600 veh/h

1,12

0 v

eh

/h

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Table 3.4 Volume Scenarios

Freeway1 Entering Volume (veh/h)

Freeway2 Entering Volume (veh/h) Scenarios

Eastbound Westbound Northbound Southbound

Ramp (veh/h)

Direction ratio*

1 6,000 6,000 6,000 6,000 1,600 70:30

2 6,000 6,000 6,000 6,000 1,600 50:50

3 6,000 6,000 6,000 6,000 1,600 30:70

4 6,000 6,000 6,000 6,000 1,000 70:30

5 6,000 6,000 6,000 6,000 1,000 50:50

6 6,000 6,000 6,000 6,000 1,000 30:70

7 6,000 6,000 6,000 5,000 1,600 70:30

8 6,000 6,000 6,000 5,000 1,600 50:50

9 6,000 6,000 6,000 5,000 1,600 30:70

10 6,000 6,000 6,000 5,000 1,000 70:30

11 6,000 6,000 6,000 5,000 1,000 50:50

12 6,000 6,000 6,000 5,000 1,000 30:70

13 6,000 5,000 6,000 5,000 1,600 70:30

14 6,000 5,000 6,000 5,000 1,600 50:50

15 6,000 5,000 6,000 5,000 1,600 30:70

16 6,000 5,000 6,000 5,000 1,000 70:30

17 6,000 5,000 6,000 5,000 1,000 50:50

18 6,000 5,000 6,000 5,000 1,000 30:70

19 6,000 5,000 5,000 5,000 1,600 70:30

20 6,000 5,000 5,000 5,000 1,600 50:50

21 6,000 5,000 5,000 5,000 1,600 30:70

22 6,000 5,000 5,000 5,000 1,000 70:30

23 6,000 5,000 5,000 5,000 1,000 50:50

24 6,000 5,000 5,000 5,000 1,000 30:70

25 5,000 5,000 5,000 5,000 1,600 70:30

26 5,000 5,000 5,000 5,000 1,600 50:50

27 5,000 5,000 5,000 5,000 1,600 30:70

28 5,000 5,000 5,000 5,000 1,000 70:30

29 5,000 5,000 5,000 5,000 1,000 50:50

30 5,000 5,000 5,000 5,000 1,000 30:70

* = ratio of left-turn to right-turn volumes for each freeway.

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made to determine if the combination of the freeway and ramp volumes could be handled adequately. Before simulating the volume scenarios, the following calibration steps were taken:

z Calibrate the capacity given in the HCM for freeways and ramp sections by

adjusting the simulation parameters that influence the capacity of a highway until the maximum flow occurred at the value shown in the HCM.

z Observe the calibrated parameters that are commonly applied to mixed traffic flows,

including heavy vehicles and maximum mixed-vehicle flows, to ensure that tested networks could handle them; and check that the mixed vehicle maximum flows were adjusted to an equivalent flow in passenger cars and matched to the HCM maximum flows. Note: These efforts were performed for several percentages of heavy vehicles.

z Perform several preliminary runs to determine if high through and ramp volumes

could be handled adequately in the simulation model and if input volumes discharge into the subject network or on-ramps without prolonged breakdowns. Note: Although the model parameters were calibrated for HCM capacity, a microscopic simulation using driver-vehicle units may not generate expected input volumes into the tested networks if congestion occurs in specific sections.

3.2.4 Measures of Effectiveness (MOEs)

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Table 3.5 Measures of Effectiveness for an Entire Interchange and Key Freeway Segments Study Area: Entire Interchange Key Freeway Segments

Travel times (hours)

Density

(passenger car per mile per lane) Total delay

(hours)

Speed (mph) Average speed

(mph) LOS

MOE

Travel times of ramp flows (hours)

For the entire interchange, the total travel time (in vehicle hours) over one hour is appropriate as the entire interchange performance-related MOE. The total travel time MOE encompasses delays and extra travel distances involved in the unique geometric features of each interchange type. Besides the travel time MOE, total delay (in vehicle hours) and average speed (miles per hour) are used as additional MOEs. Furthermore, one of the supposed advantages of the new interchange, the short travel distance for ramp flows, will be compared to the conventional interchanges by estimating the total travel time for ramp traffic. The boundary area for evaluating the MOEs of the system interchanges across the entire interchange is the area within one mile from the center point of each interchange. Adopting a consistent distance allows fair estimates of the performance for each of the subject interchanges, including ramps and freeway mainlines. The same networks were used to evaluate the MOEs under all volume scenarios for a particular interchange type and ramp design speed. Thus, the effects of the various volume scenarios and the various percentages of heavy vehicles are easy to discern.

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criterion for determining LOS for each segment is density (pc/m/l), and VISSIM can easily measure volume, average speed, and density in a segment for each vehicle type by each lane.

3.2.5 Number of Replications

Because the VISSIM model is stochastic, 15 repetitions for each case are performed in this study; the number of repetitions is estimated if the number of runs is appropriate to obtain the representative population mean.

The nano interchange with a ramp design speed of 55 mph and the worst volume condition was selected for estimating the number of runs, because the variation in travel times could result in the highest number of runs possible. The average travel time (hours) and the standard deviation of the subject interchange for the 15 runs using different random number seeds are 976 hours and 38.3 hours, respectively.

For this study, α = 0.05 was chosen as a reasonable error rate, and the travel time of 30 hours at 95% was selected as the user-specified allowable error, which is the minimum range of the difference between the real population mean and the sample mean, as specified by the null hypothesis. The user-specified allowable error is based on about 3% of the average travel time. The relevant equation to determine the absolute minimum number of runs is as follows [25]:

n ts

=

ε , (3-1)

where n is the sample size; t is the t-score for the significant level (α = 0.05) and degree of

freedom (df = n-1); s is the standard deviation of the sample data; and ε is the calculated allowable error.

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2 . 21 15

3 . 38 145 .

2 × =

= =

n ts

ε , (3-2)

where the t-score was estimated using α = 0.05 and df = 14. Because the calculated allowable error is less than the user-specified error, 15 runs are adequate to estimate the mean total travel time to within ± 15 hours with 95% confidence.

Finally, the VISSIM model was run 15 times for one hour per run after a 5-minute warm-up for each combination of variables tested for each interchange type. Each replication used a different random number seed. All together, the number of VISSIM runs is calculated as follows:

z 30 volume scenarios × 2 heavy vehicle percentages × 3 ramp design speeds × 2

interchanges × 15 replications = 5,400 runs

3.3 Sensitivity Analysis and Calibration Process for VISSIM

This section describes the sensitivity analysis and calibration process for VISSIM. The sensitivity analysis describes the ways trucks and cars operate in VISSIM relative to various vertical and horizontal curves. The calibration process was undertaken to insure that VISSIM behaves like the HCM [24] in basic freeways and ramp sections.

3.3.1 Vertical Sensitivity Analysis

AASHTO documents that whereas most passenger cars can readily maintain the same speed on steep grades (4 to 5%) as on a level section, truck speeds depend on the length and grade of vertical curves [3]. This section shows vehicle speed performances produced by VISSIM according to various vertical alignment conditions.

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each detector point installed every 500 ft, and the speeds were averaged. The simulation was run using default vehicle physical characteristics. In addition, the initial speeds of all the vehicles entering the test section were set at 70 mph.

The simulated speed-distance curves on the grades are shown in Figures 3.9 and 3.10 for trucks and passenger cars, respectively. The results indicate that the average truck performances in VISSIM are dependent on the lengths and steepness of the grades. Passenger cars maintain the initial speed through the 6% grade, whereas the 7 and 8% grades have only a slight effect on the average speeds. Figure 3.9 also superimposes the speed-distance curves of a typical heavy truck obtained from AASHTO [3] on the simulated results. Although there are slight differences in the performance patterns between the simulated and the AASHTO speed-distance curves, it is concluded that VISSIM has the capability to model vehicle operation patterns on vertical alignments that match expected results.

Figure 3.9 Speed-distance curves for heavy trucks on upgrade in VISSIM Distance (ft)

Speed (m

p

h)

0 10 20 30 40 50 60 70 80

0 2000 4000 6000 8000 10000

1% 2% 3% 4% 5% 6%

1% (AASHTO)

2% (AASHTO) 3%

(AASHTO)

4% (AASHTO) 5%

(AASHTO)

6% (AASHTO)

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Figure 3.10 Speed-distance curves for cars on upgrade in VISSIM

3.3.2 Horizontal Sensitivity Analysis

When vehicles maneuver on a horizontal curved path, the superelevation, side friction, and radius help govern the vehicle speeds. Unlike vehicle performance on vertical alignments, VISSIM cannot directly simulate vehicle performances on horizontal curves. Instead, in VISSIM, a ‘Reduced Speed Area’ function can be used to model the speed effect of horizontal curves. The function dictates that, upon approaching a horizontal curve section, vehicles start to decelerate to reach the desired curve operational speeds and accelerate to the original speeds near the end of the curve.

This analysis considers the combination of two horizontal and four vertical curves to estimate the effect on speeds. The horizontal curve average operational speeds were set at 30 mph and 40 mph, and the grades of the vertical curves were level, 2%, 4%, and 5%. The speed measurement method was undertaken in the same manner as for the vertical sensitivity analysis.

50 55 60 65 70 75 80

0 2000 4000 6000 8000 10000

Distance (ft)

Spe

e

d (m

ph)

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The simulated passenger car and truck operations on the curves are shown in Figure 3.11 to 3.14. The results indicate that the lower the design speed, the further away from the start points of horizontal curves the average vehicle speeds start to decrease to reach the desired operation speed, and that the effect of the combined alignment conditions on the average truck speeds is much more pronounced than on the average passenger car speeds. Results also show that after passing the curve sections, the passenger cars return to the initial speeds quickly, unlike the trucks. Overall, this sensitivity analysis shows that VISSIM can replicate real-world vehicle performance adequately under various alignment conditions.

Figure 3.11 Speed- distance curves for heavy trucks on selected horizontal curves and upgrades (radius = 340 ft)

0 10 20 30 40 50 60 70 80

0 400 800 1200 1600 2000 2400

Distance (ft)

Sp

ee

d (

m

ph

)

Level 2% 4% 5%

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Figure 3.12 Speed-distance curves for heavy trucks on selected horizontal curves and upgrades (radius = 640 ft)

Figure 3.13 Speed-distance curves for passenger cars on selected horizontal curves and upgrades (radius = 340 ft)

0 10 20 30 40 50 60 70 80

0 400 800 1200 1600 2000 2400 2800 3200

Distance (ft)

Speed (mph)

2% 4% 5% Level

Horizontal Curve Start Point Horizontal Curve End Point

0 10 20 30 40 50 60 70 80

0 400 800 1200 1600 2000 2400

Distance (ft)

S

peed (m

p

h)

Level 2% 4% 5%

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Figure 3.14 Speed-distance curves for passenger cars on selected horizontal curves and upgrades (radius = 640 ft)

3.3.3 Calibration Analysis

The basic freeway sections of the nano and conventional interchanges have a design speed of 70 mph, and the ramps have a design speed of 35 mph, 45 mph, and 55 mph, respectively. The design speed of 70 mph corresponds to free-flow speeds of 70 mph in the HCM, and the ramp design speeds correspond to ramp free-flow speeds of 30 to 40 mph, 40 to 50 mph, and above 50 mph in the HCM, respectively. Table 3.6 shows the HCM capacities relative to the design speeds of the freeway components. The VISSIM model was calibrated such that the simulation replicates the HCM capacities as closely as possible for each freeway type.

However, this study does not undertake a calibration process for the merging or diverging influence areas of ramps. The proportion of freeway traffic flows entering influence areas is one of the most influential factors that determine density and speed in the HCM, but VISSIM

0 10 20 30 40 50 60 70 80

0 400 800 1200 1600 2000 2400 2800 3200

Distance (ft)

Sp

e

e

d

(m

p

h

)

Level 2% 4% 5%

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future study. This study checks the capacity of the freeway segments upstream or downstream of the influence areas as well as the capacity of the ramp itself.

Table 3.6 Capacities of Freeway Types [4]

Segment Design Speeds (mph) Free-Flow Speeds (mph) Capacity (pc/h/ln)

Basic Freeway 70 70 2,400

55 > 50 2,200

45 40 - 50 2,100

Ramp

35 30 - 40 2,000

Identifying Calibration Parameters

Recently, a few studies have been conducted on VISSIM model calibration. Most of the studies are for congested freeway situations. These studies show the extent to which VISSIM parameters are related to driving behaviors and contribute to replicating the HCM capacity. Two car-following models are available in VISSIM: Wiedemann 71 and Wiedemann 99. Whereas the former model is used for urban streets, the latter model is suitable for freeways. The Wiedemann 99 car-following model consists of ten parameters [39]: standstill distance (CC0), headway time (CC1), following variation (CC2), threshold for entering following (CC3), following thresholds (CC4 and CC5), speed dependency of oscillation (CC6), oscillation acceleration (CC7), standstill acceleration (CC8), and acceleration at 80 km/h (CC9). A review of the literature indicates that of the parameters, CC1 (headway time) has the most influence on capacity. CC1 is a factor of the safety distance that drivers want to keep; the safety distance is computed as follows [26]:

v CC

CC0 1*

distance

Safety = + , (3-3) where v is a speed (mph). CC0 relates to the desired distance between stopped vehicles but not to the desired distance between moving vehicles.

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conducted by adjusting the main influence, CC1, and the desired speed ranges until flows were found to be close to the corresponding maximum flows given in the HCM.

Calibration Test Segment

Micro-simulations show a general tendency wherein the higher the number of lanes provided, the more vehicles are discharged into the network because of frequent lane-changing maneuvers. Once a calibration process is undertaken on a road segment with multiple lanes, the calibrated capacities are difficult to replicate. Therefore, a straight segment 1 mile long with one lane was chosen for this VISSIM calibration process, which is sufficient to reflect the concept of the HCM capacity, defined in the HCM 2000 [24] as “the maximum hourly rate at which persons or vehicles can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions.” The calibration process ran 15 repetitions using 15 randomly selected seeds.

Basic Freeway Capacity Calibration

Figure

Figure 1.1 Schematic of typical conventional, directional, four-level system interchange design [2]
Table 1.1 Ramp Configuration of Nano Interchange [2]
Figure 1.3 Schematic for scope of the study
Figure 3.7 Typical composite grades in the nano interchange design
+7

References

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Parents are indifferent between having different types of kids if their actions are identical cases 1 and 2 for investors and case 1 for receivers.. Consider first the population

identification or authorization of the interchange sender or the data in the interchange; the type of information is set by the Authorization Information Qualifier (I01)..

2.3 Types, sketch, specification , material , applications and methods of using of fitting cutting tools- hacksaw, chisels, twist drill, taps, files, dies.. 2.4 Types, sketch,

In the analysis of first births we keep track of time since migration (for migrants) and time since marriage formation (for the married) beside the respondent’s age (for women at

Iteration will occur in a raid group as groups perform the patterns of behaviour in order to attack mobs during the raid.. Members exhibit different