Lily Elefteriadou

Detecting critical nodes in sparse graphs

Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the critical node problem has applications in several fields including biomedicine, telecommunications, and military strategic planning. We show that the recognition version of the problem is NP-complete and derive a mathematical formulation based on integer linear programming. In addition, we propose a heuristic for the problem which exploits the combinatorial structure of the graph. The heuristic is then enhanced by the application of a local improvement method. A computational study is presented in which we apply the integer programming formulation and the heuristic to real and randomly generated data sets. For all instances tested, the heuristic is able to efficiently provide optimal solutions in a fraction of the time required by a commercial software package.

Safety Effectiveness of Intersection Left- and Right-Turn Lanes

The results of research involving a well-designed before-and-after evaluation of the safety effects of providing left- and right-turn lanes for at-grade intersections are presented. Geometric design, traffic control, traffic volume, and traffic accident data were gathered for a total of 280 improved intersections as well as 300 similar intersections that were not improved during the study period. The types of improvement projects evaluated included installation of added left-turn lanes, added right-turn lanes, and extension of the length of existing left- or right-turn lanes. An observational before-and-after evaluation of these projects was performed by using several alternative evaluation approaches. Three contrasting approaches to before-and-after evaluation were used: the yoked comparison or matched-pair approach, the comparison group approach, and the empirical Bayes approach. The research not only evaluated the safety effectiveness of left- and right-turn lane improvements but also compared the performances of these three alternative approaches in making such evaluations. The research developed quantitative safety effectiveness measures for installation design improvements involving added left-turn lanes and added right-turn lanes. The research concluded that the empirical Bayes method provides the most accurate and reliable results. Further use of this method is recommended.

DEFINING FREEWAY CAPACITY AS FUNCTION OF BREAKDOWN PROBABILITY

The need for an enhanced freeway capacity definition that incorporates the probabilistic nature of the freeway breakdown process is addressed. This is investigated through an extensive analysis of speed and volume data collected at two freeway bottleneck sites in Toronto, Ontario, Canada. At each site, the freeway breakdown process was examined in detail for more than 40 congestion events occurring during the course of nearly 20 days. Preliminary models were developed for each site. These models are used to describe the probability of breakdown versus the observed flow rate and to examine the implications that this probabilistic approach to breakdown has on the current definition of freeway capacity. A revised, probabilistic freeway capacity definition is proposed for use in future editions of the Highway Capacity Manual.

A simulation study of truck passenger car equivalents (PCE) on basic freeway sections

Trucks have an effect on the quality of traffic flow on freeways. The passenger car equivalency of a truck represents the number of passenger cars that would have an equivalent effect on the quality of the traffic flow. This research estimated truck passenger car equivalents using simulation, based on traffic density. It investigates the effect of several characteristics related to freeway design, vehicle performance, and the traffic stream on truck passenger car equivalents. Traffic density is a good indicator of the drivers freedom to maneuver and proximity to other vehicles, and is consistent with the measure of effectiveness for freeways used in the Highway Capacity Manual (HCM)[TRB (Transportation Research Board), 1994. Special Report 209: Highway Capacity Manual, Third ed. Transportation Research Board, Washington, DC]. The Freeway Simulation (FRESIM) model, developed by the Federal Highway Administration, was used in this research. FRESIM is a microscopic, stochastic computer simulation model, capable of simulating the operations of traffic on freeways. Based on the output of numerous simulation runs, flow-density curves were developed, and passenger car equivalents were estimated for a wide range of design and traffic conditions, and a range of vehicle performance characteristics. These passenger car equivalents were compared to values provided in the 1994 HCM.

DEVELOPMENT OF PASSENGER CAR EQUIVALENTS FOR FREEWAYS, TWO-LANE HIGHWAYS, AND ARTERIALS

Passenger car equivalents (PCEs) have been used extensively in the Highway Capacity Manual to establish the impact of trucks, buses, and recreational vehicles on traffic operations. PCEs are currently being used for studying freeways, multilane highways, and two-lane highways. A heavy-vehicle factor is directly given for the impact of heavy vehicles at signalized intersections (and indirectly along arterials). These PCE values are typically based on a limited number of simulations and on older simulation models. In addition, the impact of variables such as traffic flow, truck percentage, truck type (i.e., length and weight/horsepower ratio), grade, and length of grade on PCEs has not been evaluated in depth for all facility types. The methodology for developing PCEs for different truck types for the full range of traffic conditions on freeways, two-lane highways, and arterials is described. Given the scope of this research and the variability of traffic conditions to be examined, simulation was selected as the most appropriate tool. The resulting PCE values for freeways, two-lane highways, and arterials indicated that some variables, such as percentage of trucks, do not always have the expected effect on PCEs, whereas other variables, such as vehicle type, are crucial in the calculations. Generally, major differences in PCEs occurred for the longer and steeper grades. There was great variability in PCE values as a function of the weight/horsepower ratio as well as of vehicle length.

Evaluating horizontal alignment design consistency of two-lane rural highways : Development of new procedure

Design consistency refers to the condition wherein the roadway geometry does not violate driver expectations. Operating-speed profile models are used to evaluate the consistency of a design by identifying locations with large speed variability between successive design elements. There is a direct correlation between safety and variability in speeds. Recent operating-speed models predict the 85th percentile speeds on horizontal curves and compare this value with the expected 85th percentile speed on the approach tangent. There is a direct correlation between speed variability between successive design elements and crash rates. Eighty-fifth percentile speeds, however, do not necessarily represent the speed reductions experienced by drivers. The primary objective of the research was to assess the efficacy of the use of 85th percentile speed by operating-speed profile models to evaluate the consistency of a design. Speed data were collected at 21 horizontal curve sites. These data were used to evaluate the implication of using 85th percentile speed for evaluating design consistency. A new parameter was investigated for analyzing design consistency: the 85th percentile maximum reduction in speed (85MSR). This parameter is calculated by using each driver’s speed profile from an approach tangent through a horizontal curve and determining the maximum speed reduction each driver experiences. These maximum speed reductions are sorted, and the 85th percentile value becomes the statistic of interest, or 85MSR. 85MSR was compared with the difference in 85th percentile speeds (85S), and it was found that 85MSR is significantly larger than 85S. The data showed that, on average, 85MSR is approximately two times larger than 85S. Models were developed that predict 85MSR as a function of geometric design elements, and these models could be used to complement existing operating-speed models.

A methodology for estimating capacity at ramp weaves based on gap acceptance and linear optimization

Freeway weaving areas are those formed when the paths of two or more traffic streams cross, i.e., when a merge area is closely followed by a diverge area, and the two are joined by an auxiliary lane. Previous research on weaving areas has mostly focused on developing methods for estimating speeds for the weaving and non-weaving traffic streams, and on determining freeway weaving level of service; there are no methods available for estimating freeway weaving capacity. The recently published Highway Capacity Manual (HCM, 2000) presents capacity values for weaving areas that are solely based on a density of 27 pc/km/ln. The objective of this study is to develop a method for estimating capacity of ramp weaves based on gap acceptance and linear optimization. The methodology provides estimates of the capacity of ramp weaves, as a function of the capacity of the equivalent basic freeway segment lane, and for given proportions of origin-destination demands within the weave. The paper presents the methodology along with results of the capacity estimation for the range of possible weaving and non-weaving flows. It also presents the results of sensitivity analyses conducted to assess the impact of the assumptions used in the methodology. Finally, the results obtained by this method are compared to the HCM (2000) capacity values.

Research and Implementation of Lane-Changing Model Based on Driver Behavior

Lane-changing algorithms have attracted increased attention during recent years. However, limited research has been conducted to address the probability of changing lanes and vehicle interactions that occur. The objective of this study is to model urban lane-changing maneuvers by using data related to driver behavior. Two components were developed from field data, for lane-changing probability and for gap acceptance. Two experiments were conducted to collect the corresponding lane-changing data: a focus group study and an in-vehicle driving test. The proposed lane-changing model was implemented in the CORSIM microscopic simulator. Traffic data collected from a busy arterial street were used for model calibration and validation, and the simulation capabilities of the newly developed model were compared with the original lane-changing model embedded in CORSIM. Results indicate that the new model replicates observed traffic under different levels of congestion better than the original model does.

Speed Prediction Models for Trucks on Two-Lane Rural Highways

In the design consistency literature, the development of speed prediction models has concentrated on passenger cars, with little attention given to truck speed models. On some two-lane rural highways, however, trucks represent a large enough percentage of vehicles that they may be considered the design vehicle. The objective of the study was to develop operating speed prediction models for trucks on two-lane rural highways. A series of regression models was developed using a combination of field data and simulated data. First, the “Traffic on Rural Roads” and “Two-Lane with Passing” (TWOPAS) simulation models were critically assessed, and TWOPAS was selected to be used in further analysis. Next, field data from 17 sites were used to evaluate TWOPAS’s capability in the prediction of passenger car speeds and truck speeds. On the basis of the results of this evaluation, 13 sites were selected for use in simulating truck operating speeds. These sites were used to generate additional speed data for inclusion in the database for model development. Finally, a series of regression models was developed to predict 85th percentile truck operating speeds upstream, along, and downstream of a horizontal curve. These models consider the effect of length and grade of approach tangent, horizontal curve radius, and length and grade of departure tangent.

Capacity Estimations for Type B Weaving Areas Based on Gap Acceptance

Although weaving areas are one of the major types of highway facilities that have long been investigated by many researchers, the estimation of capacity along weaving areas has not been well researched or validated. Most of the literature concentrates on methods for the estimation of the speeds of weaving and nonweaving vehicles and of level of service (LOS). The 2000 Highway Capacity Manual (HCM) weaving methodology includes methods for the estimation of capacities for weaving segments, which are based on the assumption that the density at capacity is the boundary of LOS E–LOS F, 27 passenger cars/km/lane. The objective was to develop a method for the estimation of the capacities of Type B weaving areas based on gap acceptance and linear optimization. In addition, traffic data were obtained from a site located on the Queen Elizabeth Way in Toronto, Ontario, Canada, and were analyzed to identify capacity. Field estimates of capacity were compared with those resulting from the new methodology and from the 2000 HCM methodology. It was concluded that the proposed methodology provides better estimates of the capacity of the study site than the 2000 HCM methodology does when the results obtained by both methodologies were compared with field observations. The collection of additional data is required to validate the proposed model for a variety of Type B weaving segments and for various traffic and highway design conditions.