UNIVERSITY OF CINCINNATI

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1 UNIVERSITY OF CINCINNATI Date: I,, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair:

2 Railway Capacity Management and Planning by Steven Harrod B.S. Mechanical Engineering, Trinity College, Hartford M.S. Transportation, MIT M.S. Quantitative Analysis, University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy at University of Cincinnati Department of Quantitative Analysis and Operations Management College of Business July 25, 2007 Committee Co-Chairs: Michael J. Magazine & Michael F. Gorman Committee Members: Jeffrey D. Camm, Uday Rao c Copyright Steven Harrod, 2007

3 Abstract This research presents a novel model of the railway master scheduling problem, applies it to a theoretical study of railway line capacity under representative conditions, and offers a method for applying this model to practical railway scheduling problems. Contemporary market demands for different classes of rail transportation service are not adequately served because of the inability to assess the cost to the network of disparate services, as well as the inability to determine optimal scheduling. Disputes over cost and scheduling also arise between entities managing disparate services that must share common infrastructure. This new model represents railway schedules as binary multicommodity flows on discrete time scales, mapped on a hypergraph. The objective function calculates network value as a linear combination of viable train paths, en route delay, and destination tardiness. Studies are presented that estimate the cost of imposing a non-conforming, high speed train on an existing congested, homogeneous railway network flow. The analysis is provided for two formats of single track railway and for one common format of double track railway. A significant benefit is demonstrated when track networks are configured to allow complex train interactions that are not limited to pairwise meets and passes. In addition, a novel claim is made that under some conditions of single track operation, a higher speed nonconforming train is less costly to the network. A method is proposed and demonstrated for applying this model to a practical railway network scheduling problem. When applying the model, the primary decisions are the choice of track segment boundaries and the dimension of the discrete time unit. ii

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5 Acknowledgements This research was made possible by the support of my family, the trust and confidence of my committee, and extraordinary financial support from the University of Cincinnati, the Department of Quantitative Analysis and Operations Management, the Siddall Fund, and the Graduate Student Government Association. In the spring of 2001 I proposed to my family that I should obtain a PhD and pursue an academic career, and observed among them a considerable apprehension. That summer my wife and I and our children attended the INFORMS Cincinnati/Dayton Chapter picnic where I met Dr. Michael Magazine and Dr. Jeff Camm. After a short conversation, Magazine and Camm made an excellent sales pitch for the University of Cincinnati and guided me to the application process for the University Distinguished Graduate Fellowship. I subsequently won that fellowship, which provided superior financial support for my studies and made my return to school credible in the eyes of my family, and in retrospect also prevented me from accepting an offer at another university that would have been completely unsatisfactory. After difficult analysis (quantitative analysis), we decided that our home would remain in Lexington, Kentucky for the benefit of the children s schooling, and so began a four-year commute to Cincinnati and the status of near-single parenthood for my wife. Over those years there were many tense words, but quit was never one of them. My wife never, ever suggested that I should abandon my degree. As the original three-year plan stretched to four and ultimately spilled over to five plus, I am thankful that my wife s support and encouragement only grew stronger as each graduation requirement was attained. My children have also been understanding of my absence, and their welcoming on my return from qualifying exams, Congratulasons Daddy on your Eggsam!, was the highlight of the year. Finally, when the majority of available financial support was exhausted in my fifth year, I am thankful for my mother s iv

6 generous financial support of my family. When faced with the prospect of delaying my dissertation to obtain an income, my mother s mantra of graduation first, job later kept me focused on completing this work. On the academic front, I am thankful to my committee (Michael Magazine, Michael Gorman, Jeff Camm, Uday Rao) and to Doctors W. David Kelton, Martin Levy, Amit Raturi, David Rogers, and Craig Froehle. Each of these individuals tolerated an opinionated, naive, and green student who entered the program with just enough knowledge to be dangerous, but not enough to know better. In particular I am thankful to Dr. Froehle for insisting that I begin writing a paper in my first year, to Dr. Kelton for guiding my first publication, and to Dr. Levy for his constant words of encouragement. I am thankful to my committee for approving my chosen field of research, railway scheduling. The topic is not part of the general field of knowledge within this department, and there was some risk in allowing me to pursue this topic. Finally, I am grateful to Dr. Gorman (of the University of Dayton) for accepting the majority of committee chair responsibilities. This research topic would not have been approved or feasible without his familiarity with railway scheduling literature and career experience with BNSF Railway. Dr. Gorman was enlisted with a bit of bait-andswitch tactics ( No big deal, you just need to attend a few meetings... ), but I believe we will both benefit from the research relationship subsequently formed. v

7 Table of Contents Abstract ii Acknowledgements iv List of Tables x List of Figures xii 1 Introduction Definition of Scheduling in This Research Infrastructure Reduction as a Motivating Factor Growth in Both Passenger and Freight Traffic Recent Efforts to Address Capacity Research Methodology Organization of Dissertation A Survey of the Master Scheduling Problem in Operations Research A Railroad Technology Primer Freight Services Passenger Services The Operating Plan Advance Scheduling and Dispatching Resolving Train Conflicts Annotated Bibliography vi

8 2.2.1 Fundamental Concept Development Prior to Parametric Studies Probabilistic Models, Applied Simulation, and Timetable-Free Operation Train Pathing with Branch and Bound A Revival in Master Scheduling with Large Scale Integer Programming Summary and Comparison of the Literature A Railroad Master Scheduling Model with Operationally Feasible Solutions Literature Review and Comparison Operational Infeasibilities in Prior Models Pairwise Train Interactions Limit the Solution Stochastic Issues Not Addressed Model Formulation The Hypergraph Model Integer Programming Formulation Hypergraph Model Extensions Pre-processing Problem Model Validation Estimates of Problem Size A Lagrangian Relaxation of the Hypergraph Model Implementing the Hypergraph Model in Commercial Software Conclusion Capacity Factors of a Mixed Speed Network Literature Review and Experimental Design vii

9 4.2 Capacity Characteristics of a Single Track Railway Enroute Waiting Incurred by Base Flow Effect of Lengthening the Network Conclusion of Single Track Analysis Capacity Characteristics of a Double Track Railway Adding a Siding to a Double Track Network Cyclical Time Horizon Analysis Analysis of Capacity Factors Conclusion of Capacity Factor Analysis Applying the Hypergraph Model to a Representative Scenario: The BNSF Transcontinental Railway Determining Block Segments and the Discrete Time Unit for the Hypergraph Model Preparing the Source Data Abstracting the Data Capacity Analysis of the BNSF Transcontinental: Winslow to Flagstaff, Arizona Conclusion to Practical Application Research Conclusion and Recommended Future Research 121 A Database System and Ampl Program 123 A.1 File SchedFeasible.amp A.2 File SchedParam.amp A.3 File SchedOpt.amp A.4 File Schedule.amp viii

10 A.5 File SchedLagrangian.amp Bibliography 190 ix

11 List of Tables Table 1.1 Reported U.S. Mileage Statistics Table 2.1 Example North American Heavy Traffic Routes Table 2.2 Comparison of Scheduling Literature Since Table 2.3 Technical Comparison of Literature Table 2.4 Matrix of Literature Citations Table 3.1 Features of Prior Related Models Table 3.2 Components of Problem (P) Table 4.1 Base Data Set for Network Scheduling Table 4.2 Single Track Overlay Results, T 1 Network Table 4.3 Single Track Overlay Results, T 2 Network Table 4.4 Base Flow Incurred Waiting Time, T 1 Network Table 4.5 Base Flow Incurred Waiting Time, T 2 Network Table 4.6 Longer (7 Blocks) T 1 Network Table 4.7 Longer (7 Blocks) T 2 Network Table 4.8 Double Track, Roundtrip Overlay Results Table 4.9 Double Track With Siding, Roundtrip Overlay Results Table 4.10 Double Track, Roundtrip Overlay Results, Cyclical Network Table 4.11 Double Track, Roundtrip Overlay Results, Cyclical Network With Siding 98 Table 4.12 Reduction in Marginal Cost Due to Speed Change, 80 mph to 120 mph 101 Table 4.13 Reduction in Marginal Cost Due to T 2 or Siding Upgrade Table 5.1 Components of Problem x

12 Table 5.2 Discrete Timings for u = Table 5.3 Roundtrip Overlay Results, Winslow to Flagstaff xi

13 List of Figures Figure 1.1 Productivity Growth Since Figure 2.1 Example Track Diagram Between Cities A, B, and C Figure 2.2 A Train Meet Figure 2.3 A Train Pass ; train at C is faster than train at A Figure 3.1 Concept of a Dynamic Graph Figure 3.2 Time-Expanded Matrix of Track Blocks in Br annlund et al. (1998). 40 Figure 3.3 Example of Operational Infeasibility in Br annlund et al. (1998) Figure 3.4 Example of Infeasible Waiting Condition in Şahin et al. (2006) Figure 3.5 Example of Infeasible Meeting Condition in Şahin et al. (2006) Figure 3.6 Frank System T 1 (2, 5) Figure 3.7 Frank System T 2 (2, 5) Figure 3.8 Comparison of Arc Formulations (Top to Bottom): Br annlund et al. (1998), Şahin et al. (2006), Hypergraph Model Figure 3.9 Hypergraph of Train Paths Figure 3.10 Example Train Path Figure 3.11 Hypergraph as Defined in Formulation Figure 3.12 Fleeting on a Single Track Line Figure 3.13 Maximum Capacity on a T 1 Line, No Timing Incentives Figure 3.14 Maximum Capacity on a T 1 Line With Incentives Figure 3.15 Model Solution for a T 1 (3, 4) Data Set Figure 3.16 Model Solution for a T 2 (3, 4) Data Set Figure 3.17 Relational Diagram of Database Implementation xii

14 Figure 3.18 Sample Graphical Train Scheduling Solution Figure 4.1 Homogeneous Network of 60 mph Trains Figure 4.2 Track Layout of T 1 and T 2 Networks Figure 4.3 Overlay of One-Way 80mph Train onto 60mph T 1 Network, No Priority (Run 2) Figure 4.4 Overlay of Roundtrip 120mph Train onto 60mph T 1 Network, No Priority (Run 20) Figure 4.5 Overlay of Roundtrip Priority 120mph Train onto 60mph T 2 Network (Run 25) Figure 4.6 Overlay of Roundtrip Priority 80mph Train onto 60mph T 1 Network (Run 10) Figure 4.7 Overlay of Roundtrip Priority 120mph Train onto 60mph T 1 Network (Run 22) Figure 4.8 Homogeneous Network of 60 mph Trains on Double Track Network 92 Figure 4.9 Overlay of Roundtrip 80mph Train, Double Track (Run 104) Figure 4.10 Overlay of Roundtrip 120mph Train, Double Track (Run 110) Figure 4.11 Overlay of Priority Roundtrip 120mph Train, Double Track (Run 112) 93 Figure 4.12 Overlay of Priority Roundtrip 120mph Train, Double Track With Siding (Run 212) Figure 4.13 Overlay of Priority Roundtrip 80mph Train, Double Track With Siding (Run 206) Figure 4.14 Homogeneous Network of 60 mph Trains on Double Track, Cyclical Time Network Figure 4.15 Overlay of Roundtrip 80mph Train, Cyclical Double Track (Run 304) 97 xiii

15 Figure 4.16 Overlay of Roundtrip 120mph Train, Cyclical Double Track (Run 310) 97 Figure 4.17 Overlay of Priority Roundtrip 120mph Train, Cyclical Double Track (Run 312) Figure 4.18 Overlay of Priority Roundtrip 120mph Train, Cyclical Network With Siding (Run 412) Figure 4.19 Comparison of Solution Times to Optimality for Roundtrip Overlays on Double Track Networks Figure 4.20 Solution Progress for Run Figure 5.1 Track Network Database Figure 5.2 Source Train Movement Data Figure 5.3 Example Track Segment Combination Process Figure 5.4 Induced Error and Complexity as a Function of Discrete Time Unit. 115 Figure 5.5 Run 500, Base Flow Winslow to Flagstaff Figure 5.6 Run 501, Overlay of Amtrak Southwest Chief Without Priority Figure 5.7 Run 503, Priority Overlay of Amtrak Southwest Chief Figure 5.8 Run 506, Priority Overlay of High Speed Rail Figure A.1 Problem Instance Entry Screen in Database xiv

16 Chapter 1 Introduction We all know that for passenger trains, a timetable is the schedule they are always running behind. But for freight trains, it gets ridiculous. If the timetable has a freight train scheduled to leave at 2 p.m., all it means is that the train can t leave before 2 p.m. (God forbid it should arrive early.) It can leave just about any time afterwards. (Blatchford 1980) Scheduled operation is generally considered an obsolete concept in North America. Railroad operation has been almost entirely improvised for over twenty years. (White & Krug 2005, page 50) On July 18, 2006 President David Hughes of Amtrak, Chief Operating Officer Tony Ingram of CSX, and a number of additional senior officers met to negotiate solutions to recurring delays to Amtrak passenger trains, which operate under trackage rights on a number of CSX owned and managed routes. Amtrak s premise for the meeting was that Amtrak trains were suffering delays largely due to dispatching decisions, that dispatching was under the control of CSX, and therefore it was the responsibility of CSX to enact changes. The options and outcomes were grave for both parties. CSX s position was that offering priority dispatching to all Amtrak trains at all junctions would significantly reduce network capacity, below the minimum capacity necessary to carry existing freight commitments, and that Amtrak trains must slow their schedules. Amtrak s rebuttal position was that Federal law guaranteed Amtrak trains priority dispatching over any host railroad s other trains, and it was obvious to Amtrak riders that this priority was not honored. In June of 2006, 29% of Amtrak s Washington D.C. to Florida trips were greater than 4 hours late. A similar conflict 1

17 exists between Amtrak and Union Pacific over delays to long-distance trains in the western United States (Frailey 2006). Resolution of conflicts between passenger and freight trains is extremely important because Amtrak s current business plan emphasizes passenger trains operating at 80 to 100 mph on mixed use corridors (Machalaba 2006). This research presents a mathematical model and documents an application methodology appropriate for the optimal planning and scheduling of train movements on North American railways. The model offers a total value calculation for a mix of trains over a given time horizon, and does not pre-determine the behavior of individual trains. This model shares multicommodity flow concepts with earlier models, but to our knowledge is the first railway scheduling model utilizing hypergraph network theory. The hypergraph formulation is essential to the calculation of practical, operationally feasible, train movement schedules. It is proposed that with the aid of this model, conflicting railway users and interested parties may better quantify their positions, railway management may implement better operations plans, and better forecasts and estimates may be obtained of the operational impact, costs, and benefits of infrastructure changes. The formulation produces a large scale binary, dynamic multicommodity flow network on a discrete time scale, and the success of its application depends upon both careful calibration of the input data set and creative solution methods. Specific methods are demonstrated in this research to evaluate the effects of a change in train speed relative to other trains, a change in track configuration, or a change in dispatch policy. The benefits of this research are not limited to passenger trains, because conflicts between freight trains of different speeds are also a serious issue. Higher speeds are necessary for railways to attract higher value traffic from competing highway lanes. Frailey (2005) reports on United Parcel Service s inability to reduce its 5 day package trip time via BNSF and CSX due to conflicts with slower freight traffic. Although test trains successfully completed the Los Angeles to New York City journey in 65 hours, BNSF found the priority schedule created 2

18 significant conflicts with other traffic. Johnston (2005) reports that careful scheduling allows a varied mix of passenger train speeds on the 48 mile San Jose to San Francisco Caltrain route. Caltrain (2006) currently schedules eleven round trips which make the journey in 25% less time than adjacent departures. Thus it is possible that the market demand for high speed freight and passenger service could be met by better operational tools and planning, and closer attention to scheduling. 1.1 Definition of Scheduling in This Research Scheduling holds different meanings in different contexts. This research addresses master scheduling as defined in Europe and as practiced in North America many decades ago under the label timetable operation. In Europe, the emphasis is on passenger service, and the explicit, punctual movements of trains on congested, high-speed railways. European management will derive explicit schedules that direct the occupation of specific tracks in increments of one minute, and refers to this activity as master scheduling. In North America prior to 1970, for both passenger and freight trains, a train schedule was defined by a timetable published and distributed in advance. North American railways ceased publishing timetables and converted to improvised operation by Under improvised operation, specific train movements were not determined until each train presented itself ready to move in the dispatcher s territory. The only schedule information remaining was the transportation schedule provided to the marketing department, which defined an approximate cutoff time for receiving freight and an approximate trip time. White (2005) offers a detailed history of North American train scheduling policies, operating plans, and definition of terms. North American railroads are currently paying increased attention to the scheduling and planning of train operations, and many railroads have adopted, or are in the process of adopting, scheduled operating plans. However, these are not master schedule operating plans, but car routing plans. In North America the term Scheduled Railroad refers to the 3

19 advance assignment of one or more connecting trains for a freight car s journey. A dedicated stream of research has evolved covering scheduled railroading and related activities such as car blocking and the reliability of connections at yards and terminals. The current generation of railroad management was educated in an era of improvised train operations. Motivated by a regulatory structure in which revenue was fixed prior to 1980, railroad management best practice was to minimize cost while attaining the minimum service level dictated by regulatory authorities. This was achieved by holding all departing trains at terminals as long as necessary to fill them to maximum capacity (Beshers et al. 2004). The dramatic decline in passenger train service in the 1960 s eliminated the last firm motivation to schedule services, the need to operate around and avoid delaying passenger trains. Inflexible service led to declines in railroad traffic, which reduced train frequencies, which further facilitated unscheduled operation by reducing the number of trains requiring mutual coordination. In cases where a priority train still existed, the practice was to force all other traffic to stop and provide clearance for the priority train to pass (Brunner 2004), causing further delays for the non-priority traffic. The Staggers Rail Act of 1980 removed the vast majority of railroad price regulation, and also removed the majority of regulations dictating specific service levels. Two of the conditions that encouraged unscheduled operating plans thirty years ago, discontinuance of passenger services and low track network utilization, have since reversed their trends. Public perceptions notwithstanding, allocations of track time to passenger rail services are increasing. Meanwhile, after a continuous thirty year period of track abandonment, the North American railway network no longer has numerous parallel routes with low utilization, and freight traffic is continuing to grow year after year. Management s focus has shifted from abandonment of trunk lines to aggressive management of existing lines, and in some cases the re-opening of closed trunk lines. In this environment, this research advocates the reconsideration of master schedule operating plans. 4

20 1.1.1 Infrastructure Reduction as a Motivating Factor The U.S. class 1 railroads (the major railroads) have reduced their mileage by 40% since 1980, while the volume of freight has increased 69% in the same period (Federal Railroad Administration 2003). While it is not known exactly which routes are included in this statistic, many well known through routes have been abandoned since Examples include the Conrail route from New York to Michigan through Canada (McDonnell 1985); the Milwaukee Road from Minneapolis to Seattle (Kooistra 1979); the Erie-Lackawanna from New York to Chicago (DeYoung 2005); and the Seaboard Air Line from Virginia to Florida (Wrinn 2005). Much of the class 1 mileage reduction is attributable to transfer of trackage from class 1 ownership to smaller railroads, but from Table 1.1 there still remains 14,000 miles of route reduction attributable to class 1 abandonments. It should also be understood that the majority of mileage transferred to smaller railroads ceases to become a through route or has significant speed limits. The abandonment trend is only now leveling off for two reasons: in many origin-destination pairs there is now only one single track line, and secondly, freight volume in many instances exceeds the sustainable capacity of the existing infrastructure. Sustainable capacity refers to the activity level which allows for adequate idle time to properly maintain the railroad track. Many tracks are today so heavily utilized that it is necessary to completely halt traffic on selected lines to carry out accelerated maintenance programs (Kovalev 1998). For example, Amtrak had to cancel one of its three New York to Florida trains for two months in 2004 to allow CSX a daily 10 hour idle time window for major maintenance (Johnston Table 1.1: Reported U.S. Mileage Statistics Source Difference 109 Congress (2006) 155,000 99,000 - (56,000) American Short Line (2007) 8,000-50,000 42,000 5

21 2004b) Growth in Both Passenger and Freight Traffic The debate over the future of long distance, multi-day journey passenger trains, which are operated by Amtrak in the United States and VIA Rail in Canada, obscures the very significant growth of regional, commuter, and other day-coach rail services in the last twenty years. From a low point in the 1980 s, just after the 1979 Amtrak budget cuts and the abandonment of commuter rail services in Detroit and Pittsburgh (PTJ 1984, TR8 1989, Morgan 1979), new passenger services have started in Miami, Nashville, Los Angeles, Dallas, Washington DC (VRE), Albuquerque, and Seattle. Further new services are in advanced implementation stages for markets such as Salt Lake City and Minneapolis. The potential growth or re-introduction of passenger services on lines shared with freight trains is a significant element that must be included in any model of North American rail capacity. In fact, the potential interactions between passenger services popular with the public and commercial freight services are themselves now a point of political debate (Cox 2001, 2003). The Sacramento to Oakland,CA line of Union Pacific has seen daily passenger round-trips increase from four to sixteen in the last twenty years, and similar increases have occurred between Oakland and Bakersfield, and San Diego and San Luis Obispo (Johnston 2004a). Further expansion of these services is facing resistance from the host railroads because of their own need for additional capacity. North American railways have exhibited symptoms of severe congestion since the mid s, due mostly to continuing traffic growth and limited expansion options. AAR Policy and Economics Department (2007) reports that freight traffic (revenue ton-miles) per mile of track has increased 105% since This congestion has itself led to severe customer service problems and economic disruption (Machalaba 2003, 2004b,e, Valentine & Manelli 2005a). Line congestion has also led to warnings on the future investment performance of 6

22 the railway companies (Machalaba 1998b, 2005b, Wadewitz et al. 2005). Numerous sources predict strong rail freight traffic grown in the coming decades. The U.S. Federal Railroad Administration predicts growth into the 2020 s (Federal Railroad Administration 2003), and the Association of American Railroads forecasts as much as a 70% increase in tonnage in the same period (AAR Policy and Economics Department 2005). The Union Pacific Railroad has already seen a 30% increase in its Los Angeles (Sunset Route) traffic in the period alone, largely due to increases in container traffic of Asian imports (Hemphill et al. 2004) Recent Efforts to Address Capacity There is no universally agreed remedy to rising demand for limited track time. Many representatives of the industry have argued that the railway infrastructure, the routes and track, is overextended and past due for investment and expansion (Machalaba 2000, 2004a, Ritchie 2004). However, there remain others within the industry who believe the current infrastructure can be better managed to handle greater traffic flows, and that there is no financial justification for expansion of the track infrastructure (Larkin & Taylor 2005a,b, Machalaba 1998a, 2004d, Valentine & Manelli 2005b). The debate is complicated by the lack of mutually agreed quantitative measures with which to compare alternatives. When comparing alternative track investments or service patterns, prior models or simulation tools require the assignment of sometimes subjective values to various performance measures, and it is difficult to evaluate the impact of policies on the network as a whole. For example, it is common for a dispatch decision tool or simulation program to arbitrate the conflict between two trains at a meeting place according to a function of their independent assigned values or priorities and individual accumulated delay at that point, while disregarding the resulting impact of that decision upon the network flow as a whole. In the 1980 s railroads responded to traffic growth by implementing longer trains, made 7

23 Figure 1.1: Productivity Growth Since 1980 Source: (Federal Railroad Administration 2003) possible by improved braking and power systems, and larger capacity freight cars, made possible by heavier rail in the track itself (Ritchie 2004). Following these methods, railways have been very successful in increasing network capacity, measured in freight tonnage (see Figure 1.1), but all options for train capacity expansion are considered exhausted for the foreseeable future. Rail technology has largely reached its limits in tonnage per train, leaving train scheduling or expansion of the track itself as the last capacity expansion option. Congestion reduction efforts to date have concentrated on double or triple tracking main lines (Vantuono 2005), lowering speed limits of priority trains (passenger or intermodal) to force trains to move in a homogenous flow (Machalaba 2004c), and implementing unidirectional flow across vast territories (Saunders 2003, page 333). However, there remain many city pairs that do not have sufficient traffic to justify a double track line, and the homogenous train speeds prevent railroads from offering customized service levels for different market segments. Greater attention is being paid by management to scheduling (Machalaba 2005a), and some results are forthcoming from stricter interpretations of schedules and a migration 8

24 towards the master scheduling methods of the Europeans. Although academics in operations research and associated disciplines have considered the railway capacity and scheduling problem since the 1960 s, the range of solutions remains incomplete due to the unique complexities and variety of railway operations, and the large size of the problem formulations. North American operations in particular require solutions that satisfy the needs of a complex heterogeneous traffic mix and offer capacity adjustments less dramatic than complete doubling or tripling of main line track. 1.2 Research Methodology This research addresses the motivating problem of how to best manage or schedule an increasingly diverse mix of train types on a congested, capacity limited network. In particular, methods are demonstrated to quantify alternative network flows in order to aid the settling of disputes between competing users of a network. These fundamental experimental questions are addressed: 1. How do mixed train speeds affect the network? 2. What role does train priority play? 3. How do alternative track configurations affect network capacity? 4. What are the preferred daily management strategies? These questions are investigated by quantifying the network outputs as a sum of the value of service of the completed train journeys and the sum of linear penalties and incentives for timekeeping relative to a given schedule. Optimal schedules are derived relative to these outputs by maximizing them as the objective function of a linear scheduling model. Pricing for each scenario or schedule change is derived from the change in objective function relative to the prior or control network schedule. The change in objective function due to a schedule 9

25 change or introduction of a new service is then considered the marginal cost of that service. A range of common network configurations and train service patterns are examined and best management practices are proposed. Finally, procedures are offered for simplifying typical application data to reduce problem complexity within fixed limits of model accuracy. 1.3 Organization of Dissertation This work is divided into six chapters, the first of which is this introduction and motivating problem. Chapter 2 offers a tutorial on railroad operations and a general survey of operations research in the area of railroad master scheduling, both in North America and abroad. Chapter 3 presents the model formulation and describes in detail how the hypergraph formulation resolves limitations of earlier models. In Chapter 4 abstractions of typical railroad operating modes are studied in an experimental sample and general conclusions stated on the performance of each mode. Particular attention is paid to the interaction of dispatch strategy, infrastructure, and the diversity of train speeds. Chapter 5 describes the data manipulations necessary to apply the model to typical sample data and an example analysis is performed on the BNSF Transcontinental route segment between Winslow and Flagstaff, Arizona. Final conclusions and research recommendations are presented in Chapter 6. 10

26 Chapter 2 A Survey of the Master Scheduling Problem in Operations Research Railway operations involve large sums of money both in infrastructure and direct operating expenses, and their services are valued by both the traveling public and primary industries. Consequently there exists a rich history of research on railway management and operations planning. This survey is offered to provide context in which to place the current research amongst all of the other attempts at solving the master scheduling problem and the methodologies employed. Later chapters make numerous claims concerning the operational feasibility of various scheduling models, and so to properly define operational feasibility this chapter begins with a concise description of important operating rules and characteristics of railroad operations. After this introduction, a review of train scheduling and dispatching literature since 1960 forms the bulk of the chapter. The literature surveyed is very broad from the distant past, but is more focused as the timeline approaches the current day, limited to that which would be relevant to North American operating conditions and which offers mathematical tools to determine optimal network flow. 2.1 A Railroad Technology Primer The fundamental properties and constraints of railway operations are identical worldwide, however the differences in geography, traffic density, and a legacy of up to two centuries of railway operations in some countries lead to differences in vocabulary, subjective operating preferences, and a large installed base of actively used historic infrastructure. Unless stated otherwise, the statements made here are generally applicable to all railway operations, with 11

27 some bias towards North American vocabulary. References to specific national practices are made where necessary to clarify the discussion for a broad range of readers Freight Services The fundamental unit of the railway is the freight car. Almost without exception, railways no longer participate in the traffic of individual packages or partial loads of freight. Rail freight is measured in terms of integer carloads, with secondary emphasis on the weight measurement or tonnage of the freight. Freight cars vary in outside dimensions and length, but for the purposes of discussion can be considered uniform size objects. Railway customers, shippers and consignees, ship and are billed for services in units of freight cars. The shipper initiates service by requesting empty freight cars, called empties, from the railway company, to be delivered to the shipper s point of origin. The shipper fills the car, now called a load, and then requests that the railway pick up the load. The railway will retrieve the load using a switch engine or local train and move it to a yard, where longer mainline trains are formed. Management consolidates cars from many sources with similar destinations into trains. The blocking plan is a set of rules and strategic plans that define how this consolidation is to be realized (Huntley et al. 1995). At destination yards, the process is reversed, as trains are uncoupled and individual cars delivered to consignees by local switching crews. After the consignee unloads the car, a local switching crew returns, retrieves the empty car, and returns it to the railway s inventory of empty freight cars. The response time for each party, which is relevant to scheduling constraints and buffer times, in this process is regulated by various contractual agreements, fees and charges, and government regulations. For very high volume shippers, some of these steps may be simplified or automated. 12

28 2.1.2 Passenger Services Passenger train services are much simpler in contrast, because, of course, passengers can load and unload themselves. There is no comparable mixing and collating of passenger cars, no blocking plan for passenger cars. Passenger trains are generally equipped with more power per ton of train weight and faster acting braking systems, allowing for faster starting, higher travel speeds, and shorter braking distances. However, passenger trains must make station stops at regular intervals to serve passengers, while freight trains will run nonstop between yards if conditions allow. The dwell time at passenger station stops may significantly reduce the speed advantage of passenger trains calculated over the full journey The Operating Plan Railway management must devise an operating plan that specifies how and when trains will be operated to satisfy freight and passenger service standards. It is rarely advisable to simply copy the operating plans of other successful railways because lines with similar revenue, geography, and employment may yet be differentiated by the specific mix and speed priority of trains (see Table 2.1). The operating plan must frequently favor one traffic over another, according to railway company marketing goals (Blanchard 2005). The operating plan consists of many parts, including the aforemention blocking plan; the scheduling problem of dispatching trains within a constrained track network; and the assignment problem of train crews and locomotives to trains. Of these, the problems of advance scheduling or live dispatching are the focus of this survey Advance Scheduling and Dispatching The core activity in dispatching is the planning and giving of movement instructions to train crews. When these instructions are issued in advance, and typically published and distributed, they form a timetable. Orders are ad hoc instructions for movements and 13

29 Table 2.1: Example North American Heavy Traffic Routes Operator Line Freight Passenger a Union Pacific Powder River, Wyoming Unit Train Coal None Norfolk Southern Cincinnati - Knoxville All Kinds None Amtrak New York - Washington, D.C. High Value b 50+ Daily c CSX Albany - Buffalo, NY All Kinds 8 Daily Canadian National Chicago - Carbondale, IL All Kinds 4 Daily Union Pacific Sacramento - Oakland, CA All Kinds 28 Daily Source: 2005 Amtrak timetables, Frailey (1989), Johnston (2004a), Middleton (2003), author s observations a trip counts are one-way b typically auto racks, intermodal, local freight c plus NJ Transit and Maryland Rail Commuter (MARC) changes to timetable instructions. The planning of a timetable, including a complete master schedule of all stops, track locations, and train interactions, for a significant length of track, such as between two major cities, is called the over-the-road master scheduling problem, and master scheduling refers to the complete enumeration of the times of all of a train movements necessary to enforce a coordinated timetable. Any train operated outside an enforced timetable is an extra. Within the scheduling activity are various levels of detail. Pathing refers to the planning of a train s exact route through the track network, including its priority with respect to other trains. The meet/pass planning problem can be a component of either master scheduling or improvised operations. Its solution provides the strategic priority of conflicting trains at sidings or multiple track locations, and can be applied both to advance master scheduling and to the determination of orders in improvised operations. Tactical scheduling refers to the frequency within defined time intervals that trains are to run. The tactical schedule is referred to as the transportation schedule in North America. A railroad operating exclusively on orders without a master schedule plan is operating under timetable-free or improvised operations, and many years ago would also have been labeled an unscheduled railroad. A railroad that adheres primarily to a timetable is a 14

30 scheduled railroad, but this label has acquired an alternate meaning in the last 10 years. The label scheduled railroad is currently applied to operations where cars have advance train assignments and connection plans (White 2005), but the underlying trains are not required to have master schedules, and this leads to confusion in the literature. To maintain clarity here, these two environments will always be referred to as master scheduled or car scheduled respectively. The majority of North American operations are currently timetable-free. Many lines are currently operating in a hybrid fashion, where a transportation schedule is in force, but operations are improvised. This leads to conditions where where on time is measured in hours, not minutes, and trains are canceled if the day s traffic falls below minimum levels (Beshers et al. 2004). In most of the rest of the developed world, where rail traffic densities are very high, master scheduling to a tolerance of +/- one minute is standard practice (Pachl 2002, page 187). For operational and safety reasons, track is segregated by the owning railroad into unique segments called blocks (not to be confused with the alternate usage of the term in reference to car consolidation in 2.1.1). The block is the primary unit of operating authority dynamically granted to trains and their crews. Aside from special conditions, the fundamental operating rule is that a block may never be occupied by more than one train. The status of any block is then a binary condition of occupied or unoccupied. In places where parallel track exists, each track offers a separate block, so for example in Figure 2.1 the immediate region outside city A has three parallel tracks, allowing occupancy for a maximum of three trains (regardless of direction of travel). Under current technology, blocks are defined by the fixed infrastructure on the ground. A block is defined either by the location of signals, switches (connections from one track to another), or by geographic points published in company regulations and clearly recognized by train crews. Thus in the immediate planning horizon, blocks are fixed resources or constraints. Of course, blocks can be increased, decreased, or modified over the long term planning horizon by changes in the fixed plant, but 15

31 C B Crossover : switch in both directions Plain track switch A One block each route One block 3 blocks 2 blocks 2 blocks 3 blocks Figure 2.1: Example Track Diagram Between Cities A, B, and C these decisions are not made lightly due to the cost of restructuring track and signals, and of training crew Resolving Train Conflicts Railways have inherent dispatching constraints not seen in any other transport mode. The most obvious case is that of the single track railway in which opposing trains must pass each other. Trains must be dispatched with orders to coordinate passing each other at sidings (short sections of parallel track), completing what is called a meet, where two opposing trains pass (see Figure 2.2), or a pass, where one train overtakes another (see Figure 2.3). The strategic location and timing of these train intersections is frequently referred to as meet/pass planning, and that term is adopted here. In any meet or pass, the stopped or waiting train is inferior and the train passing through is superior. Provision of two tracks does not eliminate the necessity of meet/pass planning, because many multi-track lines are signalled for operation in either direction on all tracks, and even on dedicated one-way tracks, heterogeneous train speeds require frequent passing. On busy A C Figure 2.2: A Train Meet 16

32 A C Figure 2.3: A Train Pass ; train at C is faster than train at A passenger networks, there is a great deal of jockeying of position as express trains pass local stopping trains. The same overtaking movements also occur on lines dominated with freight traffic, but with less frequency. In the case of freight service, slower trains exist because of the great operating cost differential between slow and fast trains, and a great deal of freight is only viable in the lower cost service. The mix of high valued intermodal traffic and low value coal, grain, etc. common to most lines in North America requires multiple meets and passes, even on multiple-track routes. An important scenario that dispatchers must avoid is line blockage, also called lockup in other countries. This occurs when sidings and main tracks are occupied with sufficient trains in a particular pattern such that no train may move forward without forcing another train to back up. It is more severe than the analogous highway gridlock, because while highway traffic may eventually dissipate, railway line blockage is a catastrophic status that can only be remedied by reversing trains. Simulation or dispatching algorithms must include a provision for prevention of line blockage. Petersen & Taylor (1983) offer mathematical models for the prevention of line blockage. 17

33 2.2 Annotated Bibliography Nearly all railroad operations research of record has been funded by a single railroad or government sponsor to address a specific operational challenge or economic development goal at a specific geographic location. Unlike the general global standards of operation for transportation by air, sea, or roadway, railroad operations are very specific to the population density, industrial development, and political priorities of the host nation. There are, for example, fundamental operational differences between the Russian and German signalling systems (Pachl 2002) that affect the timing and spacing of trains, and even today in the United States it is possible to discern the corporate heritage of many routes by observing the signal installations. Even the fundamental label railroad or railway lacks standardization, so it should be no surprise that research streams are closely identified by national labels. References are made to the national or corporate identity of each research center largely because those labels correctly categorize the traffic flow and operating rules of the railway network, as well as identifying the source of funding and leadership for research. The scheduling topics reviewed here are limited to timetabling, enroute train dispatching, and the planning of whole train movements. There are many other forms of railroad scheduling and planning, such as the allocation of locomotives and crews, statistical estimates of capacity and value of service, the route planning of individual freight cars, and the makeup of trains in yards and terminals, which are not reviewed here. Interesting and still relevant publications in railway scheduling can be found as long ago as the 1960 s. The most prolific research centers have been in Canada, in Pennsylvania at the University of Pennsylvania, in Australia, and most recently in the Netherlands, in that chronological sequence. The earliest mathematical scheduling model of interest, which addresses deterministic and cyclical schedules, comes from Swedish author Ove Frank (1966), and is cited frequently over the following 20 years. Another work, in Russian, cited by a few early authors is Chernyavski (1971a,b), however it was not reviewed for this paper because no 18