PRIORITIZATION OF INFRASTRUCTURE INVESTMENT FOR RAIL SAFETY PROJECTS: A CORRIDOR-LEVEL APPROACH

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1 Arellano, Mindick-Walling, Thomas, Rezvani PRIORITIZATION OF INFRASTRUCTURE INVESTMENT FOR RAIL SAFETY PROJECTS: A CORRIDOR-LEVEL APPROACH Johnny R Arellano Moffatt & Nichol Fifth Avenue, th Floor, New York, NY 00 Tel: --; jrarellano@moffattnichol.com Amy Mindick-Walling, PE Moffatt & Nichol 00 Falls of Neuse Road, Suite 00, Raleigh, NC 0 Tel: --; amindick-walling@moffattnichol.com Andrew Thomas, PE NCDOT Rail Division Mail Service Road (MAIL), Raleigh, NC Tel: --; dthomas@ncdot.com Ali Z. Rezvani, PhD Moffatt & Nichol Fifth Avenue, th Floor, New York, NY 00 Tel: --; arezvani@moffattnichol.com Word count:, + table/ figures x 0 words (each) =,0 November 0

2 Arellano, Mindick-Walling, Thomas, Rezvani 0 ABSTRACT This paper summarizes the North Carolina Department of Transportation (NCDOT) Rail Division s efforts in developing a methodology for prioritizing safety improvement projects for highway-rail atgrade crossings at the corridor-level. The goal is to optimize the use of limited funding to improve rail system reliability. By leveraging previous research which identifies and prioritizes individual projects using procedures such as benefit cost analysis, this approach aims to improve project selection by focusing on freight corridors rather than individual crossings. The proposed approach defines a metric that relates system reliability to crossing safety. It then uses binary programming to select an optimal set of safety improvement actions which maximize the improvement in system reliability. The defined framework can be expanded beyond crossing safety to include a more diverse set of projects and help decision makers with selecting projects that maximize overall system improvement. Keywords: Rail; Corridor; Safety; Prioritization; Optimization, System Reliability; Infrastructure; Investment

3 Arellano, Mindick-Walling, Thomas, Rezvani INTRODUCTION The continuous investment in the United States transportation infrastructure network is an essential part of its economy and future growth. The United States heavily invested in infrastructure for all modes of transportation over the past two-centuries, but in the last few decades has failed to allocate sufficient funding for the maintenance of this infrastructure. The shortage in maintenance funding necessitates for different approaches aimed towards the allocation of available funds. () At the state level, North Carolina has implemented a data-driven prioritization program for more efficiently and effectively using its funding in improving infrastructure known as the Strategic Transportation Investment (STI) Program. At the federal level, there are various government programs that have begun to award funding to infrastructure projects that contribute to the improvement of the United States transportation network, such as the Fostering Advancements in Shipping and Transportation for the Long-term Achievement of National Efficiencies (FASTLANE) program and the Transportation Infrastructure Generating Economic Recovery (TIGER) Grant. FASTLANE will award $. billion between 0 and 00 to selected freight and highway projects that address transportation system challenges such as the improvement of safety and reliability of the movement of freight (). Meanwhile, TIGER Grant will award $00 million in 0 to projects that improve transportation reliability and safety, and generate economic development (). FASTLANE, TIGER and other sources of funding usually have a set of requirements for projects in terms of viability and benefit they bring to the general public. Although these programs have guidelines to evaluate individual projects in terms of their costs and benefits to society, they do not investigate the benefits of combining multiple projects (i.e. multiple rail projects along a corridor). While the current approaches generate solid outcomes in term of the benefit to cost ratio of public expenditure, looking at individual projects independently could lead to less than optimal decisions in improving overall system efficiency. This paper proposes a framework for prioritizing highway-rail at-grade crossing safety improvement projects, from a set of feasible projects with benefit to cost ratios greater than one, with a goal of maximizing system efficiency while adhering to budgetary constraints. Furthermore, this paper extends prior crossing centric research () into a corridor-level approach. The remainder of this paper is structured as follows: Problem Statement further explains the problem that this research is addressing. Methodology proposes a safety related metric that can be used as a medium for measuring system reliability and uses it for optimizing safety improvement actions. Potential Number of Crashes per Corridor provides guidance on how to calculate the potential number of crashes on a corridor. Corridor Closure Time expands the calculation for number of crashes into expected corridor closure time. Total Train Delay Time uses the closure time to estimate delay times at corridor-level. Prioritization of Projects illustrates the use of the defined metric for prioritizing safety projects. Conclusion and Future Work discusses conclusions and future work. PROBLEM STATEMENT The NCDOT s Comprehensive State Rail Plan (State Plan) aims, amongst other goals, to analyze and prioritize rail corridors, rail programs and proposed projects (). In its State Plan, North Carolina identifies a total of rail corridors. Improving the combined performance of these corridors through the prioritization of safety improvement actions is the basis of this study. A freight rail corridor provides connectivity between two or more inland points enabling a frequent flow of cargo. Cargo flow performance metrics normally measure transportation costs, transportation time, and transportation reliability. Safety improvement projects, generally, do not have a major impact on transportation costs or time, however, they do impact transportation reliability and, consequently, impact system fluidity by reducing unplanned delays caused by crashes. Therefore, total unplanned delay times can be used as a means to calculate system reliability. This study expands previous efforts and processes developed by NCDOT in the development of a prioritization approach for improving highway-rail at-grade crossings. The input to this approach is a list of feasible at-grade crossing safety improvement projects, which is the typical output of a benefit-cost

4 Arellano, Mindick-Walling, Thomas, Rezvani analysis study. The proposed corridor-level prioritization approach seeks to improve the overall reliability and fluidity of the system by minimizing system-wide train delays caused by highway-rail crashes, by selecting the optimal safety improvement actions, under budget constraints. METHODOLOGY The primary challenge in developing a corridor-level prioritization approach is defining a performance metric that relates crossing safety to system reliability. As mentioned earlier, crashes at highway-rail atgrade crossings lead to a decrease in system reliability by causing unplanned delays. Hence, any action that leads to a reduction in unplanned delays will also lead to an improvement in system reliability. Unplanned corridor-level delays depend on (a) frequency of crashes and (b) severity of crashes. At the same level of severity, corridors with a higher number of crashes are expected to have higher unplanned delays. Similarly, at the same frequency of crashes, corridors with a higher representation of severe crashes tend to have higher unplanned delays dues to longer closure times of crossings. The proposed methodology estimates future unplanned corridor-level delays by estimating the likelihood of crashes and their severity levels on different corridors. It then provides a binary programming model to select the optimal set of safety improvement actions that maximize the reduction in unplanned delay. Potential Number of Crashes per Corridor The frequency of crashes on a freight rail corridor depends both on the number of crossings on that corridor and the likelihood of having a crash on its individual crossings. The probability of a crash happening on an individual crossing, as discussed by Ogden (), depends on multiple factors including highway traffic, train speed, etc. For a corridor with n total crossings, the chance of having m crashes (CP m n ) is calculated as follows: n CP m n = ( P ) ( i ) i P ( P ) ( i ) i P ( P n ) ( i n ) i P n n i j = m () i =0 i =0 i n =0 j= Where: CP m n : Probability of having m crashes on a corridor with n crossings. P i : Probability of having a crash on crossing i. The computational complexity of equation () exponentially increases as the number of crossings and crashes increase, which makes probability calculations extremely time consuming for larger corridors. For example, there are only possible crash combinations for a corridor with crossings that experiences two crashes. However, there are, possible combinations for a corridor with 0 crossings that experiences the same number of crashes. Therefore, the proposed approach uses an estimation for the formula in the above equation to measure the probability of having m crashes on a corridor with n crossings. The maximum average error between the actual and estimated probabilities was calculated to be less than 0.% for all corridors. The estimate equation is defined as follows: CP m n = ( n m ) P acc m ( P acc ) n m () Where: P acc = n i= P i n = average corridor crash probability Using the defined metric, different corridors can be compared in terms of number of crashes. Figure maps NCDOT s rail system and highlights three selected corridors: corridor, corridor, and corridor. For the remainder of this paper, these three corridors will be used for illustrating various calculations and comparing their results.

5 Cumulative Probability Arellano, Mindick-Walling, Thomas, Rezvani 0 FIGURE Map of selected rail corridors. Figure shows that corridor has approximately a % chance of experiencing one crash or less next year while corridor has only an % chance. It could also be inferred from Figure that corridor has approximately a % chance of experiencing seven crashes or less next year. Therefore, corridor has a higher chance of experiencing a crash and consequent delays, which will be calculated further in the following sections, than corridor or. 00% 0% 0% 0% 0% Number of Crashes % FIGURE Corridor Crash CDF. Corridor Closure Time To identify the expected closure time of a corridor, it is necessary to estimate closure likelihood and duration. Closure duration depends both on the frequency of crashes and their severity. According to NCDOT assumption based on the findings of NCHRP Report (), in the occurrence of an at-grade crossing crash, the crossing will be closed to rail traffic for an average of minutes for fatal crashes, and it would be closed for minutes for injury or property damage only crashes. Using these assumptions, the total closure time of a crossing can be calculated for all potential crash outcomes (Table ). Table shows that having one crash with zero fatalities will lead to an average closure time of minutes while having two crashes with one fatality will lead to an average closure time of minutes.

6 Arellano, Mindick-Walling, Thomas, Rezvani TABLE Closure time matrix (minutes). Number of Crashes Number of Fatalities ,,0,,0 00,0,0,0,0,,,,,,0,,,,0,0,,,0,,,,,, 0 0,0,,,,,0,,,,0 The likelihood of any given closure time (Table ) can be estimated by calculating the probability of crashes and fatalities. Therefore, it is necessary to first calculate the probability of any number of fatal crashes based on the total number of crashes. For a given m number of crashes, the probability of having k fatalities is calculated as follows: FP k m = ( Pf ) ( i) i Pf ( Pf ) ( i) i Pf ( Pf m ) ( m) i Pf m i j = k () i =0 i =0 i m =0 Where: FP k m Probability of having k fatalities when the number of crashes is m. Pf i : Probability of crash i being a fatal crash calculated based on Ogden (). Similar to the crash count calculation, the computational complexity of calculating fatality probabilities increases exponentially by the increase in number of crashes and fatalities. Fatality probabilities can also be estimated using a similar approach to crash probability equation estimates as follows: FP m k = ( m k ) P acfc k ( P acfc ) m k () Where: P acfc = m i= P f i m = average corridor fatality crash probability. Consequently, the probability of having k fatalities out of m crashes on a corridor with n crossings is calculated as: P nmk = CP n m FP m k () Table shows the probability of different crash outcomes for corridor based on the P nmk. As it can be observed from Table, the chance of having zero crashes and zero fatalities is equal to.%. (Note: this is the same probability of having zero crashes in Figure.) The chance of having two crashes and one fatality is equal to.0% while the chance of having two fatal crashes is equal to 0.%. m j=

7 Cumulative Probability Cumulative Probability Arellano, Mindick-Walling, Thomas, Rezvani 0 TABLE Delay probability matrix of corridor. Number of Crashes Number of Fatalities %.% 0.% 0.%.0% 0.%.%.% 0.% 0.0%.%.%.% 0.% 0.0%.%.%.% 0.% 0.0% 0.0%.%.%.% 0.% 0.0% 0.0% 0.0%.%.%.0% 0.% 0.0% 0.0% 0.0% 0.0%.%.% 0.% 0.% 0.0% 0.0% 0.0% 0.0% 0.0% 0.% 0.% 0.% 0.% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 0.% 0.% 0.% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% The expected closure time of a corridor depends on the number and types of crashes, and their probabilities. Therefore, a closure time cumulative distribution function (CDF) can be built, for each corridor, from the combination of closure times and delay probability matrices (Table and Table ) as shown in Figure, left. Figure, right represents a smoothed version of the original cumulative probability function which is used in future calculations. The smoothed version is created by fitting a logistics curve on the original cumulative distribution functions. According to Figure, corridor has a % chance of experiencing a closure time of minutes or less while corridor has the same chance of having minutes of closure time. 00% 00% 0% 0% 0% 0% 0% 0% 0% 0% ,000,0,00 Closure Time (minutes) ,000,0,00 Closure Time (minutes) % % 0 FIGURE Closure Time CDF. Total Train Delay Time Total train delay time of a corridor depends on both unexpected closure times, as explained in section., and train frequency. Train frequency is defined by calculating the average number of daily trains traveling through each crossing on that corridor. Figure illustrates how total delay time resulting from the same closure time duration could differ for different corridors. Corridor A has an inter-arrival time of 0 minutes while corridor B has an inter-arrival time of 0 minutes of through trains. In the occurrence of a 0-minute closure at a crossing, train delays will vary by corridor. Corridor A will experience a total

Arellano, Mindick-Walling, Thomas, Rezvani train delay of 00 minutes, with four trains being affected, while corridor B will experience a total train delay of 0 minutes, with only two trains being

For any specific corridor, the total delay time resulting from a closure with a length of c minutes can be calculated as follow: (x + ) Total Delay Time = f x Where: f = train inter-arrival time at

8 Arellano, Mindick-Walling, Thomas, Rezvani train delay of 00 minutes, with four trains being affected, while corridor B will experience a total train delay of 0 minutes, with only two trains being affected FIGURE Total delay time calculation. For any specific corridor, the total delay time resulting from a closure with a length of c minutes can be calculated as follow: (x + ) Total Delay Time = f x Where: f = train inter-arrival time at Corridor (min.) c = closure time at the crossing on Corridor (min.) x = c f Using equation (), total delay times of all of the corridors are calculated based on the frequency and outcome of crashes to estimate the corridor delay time at % confidence. The delays for selected corridors are presented in Table. TABLE Calculated delay times by corridor. Corridor Crossing Count Daily Trains Train Delay (min.), Prioritization of Projects The objective of the proposed corridor-level prioritization approach is to minimize total unplanned train delays along the corridors. This objective can be achieved by selecting a set of safety improvement actions which minimize total train delay times. As illustrated in Figure, the process uses a list of potential safety improvement actions as input and generates different action-sets based on the input list. Applying each action-set to individual corridors will lead to new train delays for North Carolina rail corridors, action-sets could impact all or some of the corridors. In aggregate, the action-set that minimizes the total train delay (maximizes the total reduction in delays) is the optimal action-set. The new train delays are calculated using crash modification factors and the process explained in previous sections. ()

9 Arellano, Mindick-Walling, Thomas, Rezvani FIGURE Prioritization Process. This objective can mathematically be presented as: Maximize Z = dr i x i Subject to k i= k c i x i budget i= x i, for all action i related to a unique corridor () 0 x i = {0,} for all i Where: k = total action-sets x i = binary variable of action-set i dr i = delay reduction due to implementation of action-set i c i = cost related to implementation of action-set i This proposed model is further explained through an illustrative case-study. In this case study, a total of six feasible projects with identical cost and crash modification factors (CMF) of $ and 0., respectively, on corridors, and, are considered (Table ).

10 Arellano, Mindick-Walling, Thomas, Rezvani TABLE Proposed safety projects. Project Crossing ID Cost CMF A H $ 0. B A $ 0. C 0W $ 0. D U $ 0. E H $ 0. F U $ 0. These six projects lead to distinct action-sets which could reduce total corridor delay times (Table ). An action-set represents one of all possible combinations for identified projects on a corridor. TABLE Complete action-sets. Action Project Corridor Action-Set Project Cost Original Delay Improved Delay Reduction in Delay A $ B $...0 C $... BC $.. 0. D $,.,.. E $,.,.. DE $,.,.. F $,.,..0 DF $,.,.. 0 EF $,.,. 0. DEF $,.,. 0.0 Assuming a budget constraint of $, and using the mathematical formulation presented above, the optimization function for this case study can be illustrated as: Maximize Z = 0.x +.0x +.x + 0.x +.x +.x +.x +.0x Subject to +.x + 0.x x x + x + x + x + x + x + x + x + x + x 0 + x (Ensure budget constraint) x (Maximum of one action from corridor ) x + x + x (Maximum of one action from corridor ) x + x + x + x + x + x 0 + x (Maximum of one action from corridor ) x i = {0,} for all i ( is the action is selected and 0 if the action is not selected) Under the current assumptions and budget constraints, and are the optimal action-sets for minimizing unplanned system delay. Implementation of these actions is expected to reduce total unplanned system delay by. minutes (Table ).

11 Arellano, Mindick-Walling, Thomas, Rezvani 0 0 TABLE Linear program solution. Action Project Corridor Action-Set Project Cost Original Delay Improved Delay Reduction in Delay B $...0 DE $,.,.. CONCLUSIONS AND FUTURE WORK The proposed framework looks at a set of individually feasible projects and evaluates their implementation from a system improvement perspective. A system perspective allows this approach to select an optimal set of projects which maximize system improvement. The developed framework is an extension of already existing project valuation procedures, such as benefit cost analysis, and extends them from a pool of individual crossings into a multi-project optimization approach along multiple corridors. The rail corridor-level methodology facilitates communication with Rail Division stakeholders in both the public and private sectors. This approach mirrors USDOT s efforts to establish an overall infrastructure investment funding process that can be applied across all modes and objectives, such as safety and mobility. The expanded framework will also have the ability of prioritizing projects under limited budget by expanding the planning horizon beyond one year and sequencing the corridor-level projects in a way that yields the maximum quantifiable benefits to society. Future steps include the implementation of this method into a test case utilizing a designated funding source tasked with improving rail infrastructure. The corridor-level method will run in parallel to the existing prioritization method with continuous comparison of both systems in project selection, funding allocation, and infrastructure improvements. Its secondary purpose will involve the design and implementation of this methodology into web-based systems supported by existing metrics. This tool will be tasked with offering dynamic analysis for what if scenarios further assisting Rail Division s management in the selection and visualization of impacts to the rail infrastructure.

12 Arellano, Mindick-Walling, Thomas, Rezvani 0 REFERENCES. National Economic Council and the President s Council of Economic Advisers. An Economic Analysis of Transportation Infrastructure Investment. National Economic Council. 0.. Office of the Secretary of Transportation. Significant Freight and Highway Projects (FASTLANE Grants) for Fiscal Year 0. DOT-OST U.S. Department of Transportation. 0.. TIGER Discretionary Grants. U.S. Department of Transportation. Accessed July, 0.. Rezvani A. Z, Peach M., Thomas A., Cruz R., Kemmsies W. Benefit-cost methodology for highway-railway grade crossing safety protocols as applied to transportation infrastructure project prioritization processes. European Transport Conference, 0.. McCrory P., Tennyson N., Weatherly K., Worley P. C. NCDOT Rail Division Comprehensive Rail Plan. North Carolina Department of Transportation Rail Division. 0.. Ogden, Brent D. Railroad-Highway Grade Crossing Handbook - Revised Second Edition 00. FHWA-SA Federal Highway Administration Brod, D., Weisbrod, G., Williges, C., Moses, S. J., Gillen, D. B., Martland, C. D. Comprehensive Costs of Highway-Rail Grade Crossing Crashes. Transportation Research Board of the National Academies, Washington, D.C., 0, pp..

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