Train Timetable Design for Shared Railway Systems using a Linear Programming Approach to Approximate Dynamic Programming

In the last 15 years, the use of rail infrastructure by different train operating companies (shared railway system) has been proposed as a way to improve infrastructure utilization and to increase efficiency in the railway industry. Shared use requires coordination between the infrastructure manager and multiple train operators in a competitive framework, so that regulators must design appropriate capacity pricing and allocation mechanisms. However, the resulting capacity utilization from a given mechanism in the railway industry cannot be known in the absence of operations. Therefore assessment of capacity requires the determination of the train timetable, which eliminates any potential conflicts in bids from the operators. Although there is a broad literature that proposes train timetabling methods for railway systems with single operators, there are few models for shared competitive railway systems. This paper proposes a train timetabling model for shared railway systems that explicitly considers network effects and the existence of multiple operators requesting to operate several types of trains traveling along different routes in the network. The model is formulated and solved both as a mixed integer linear programming (MILP) problem (using a commercial solver) and as a dynamic programming (DP) problem. We solve the DP formulation with a novel algorithm based on a linear programming (LP) approach to approximate dynamic programming (ADP) that can solve much larger problems than are computationally intractable with commercial MILP solvers. The model simulates the optimal decisions by an infrastructure manager for a shared railway system with respect to a given objective function and safety constraints. This model can be used to evaluate alternative capacity pricing and allocation mechanism. We demonstrate the method for one possible capacity pricing and allocation mechanism, and show how the competing demands and the decisions of the infrastructure manager under this mechanism impact the operations on a shared railway system for all stakeholders

An approximate dynamic programming approach for designing train timetables

Traditional approaches to solving the train timetabling problem—the optimal allocation of when each train arrives and departs each station—have relied on Mixed-Integer Programming (MIP) approaches. We propose an alternative formulation for this problem based on the modeling and algorithmic framework of approximate dynamic programming. We present a Q-learning algorithm in order to tractably solve the high-dimensional problem. We compare the performance of several variants of this approach, including discretizing the state and the action spaces, and continuous function approximation with global basis functions. We demonstrate the algorithms on two railway system cases, one minimizing energy consumption subject to punctuality constraints, and one maximizing capacity subject to safety constraints. We demonstrate that the ADP algorithm converges rapidly to an optimal solution, and that the number of iterations required increases linearly in the size of the rail system, in contrast with MIP approaches whose computation time grows exponentially. We also show that an additional benefit to the ADP approach is the intuition gained from visualizing the Q-factor functions, which graphically capture the intuitive tradeoffs between efficiency and constraints in both examples

Analysis of Capacity Pricing and Allocation Mechanisms in Shared Railway Systems: Lessons for the Northeast Corridor

Recently, governments have started promoting the use of shared railway systems as a way to take advantage of the existing capital-intensive railway infrastructure. Until 1988, all major railways both managed the infrastructure and operated the trains. In contrast, in shared railway systems, multiple train operators utilize the same infrastructure. Such systems can achieve high utilization, but also require coordination between the infrastructure manager and the train operators. Such coordination, in turn, requires capacity planning and regulation that determines which trains can access the infrastructure at each time, capacity allocation, and the access price they need to pay, capacity pricing. The need to establish capacity pricing and allocation mechanisms in the railway system is relatively new and the comparative performance of alternative mechanisms to price and allocate capacity is still a matter of study. This paper proposes a framework to analyze the performance of shared railway systems under alternative capacity pricing and allocation mechanisms. The paper focuses on how the introduction of price-based and capacity-based mechanisms affect the train operators’ ability to access the infrastructure capacity in the context of the Northeast Corridor in the US. The results of this paper suggest that there are trade-offs associated with each mechanism and none of them is superior to the other on all dimensions. As a result, Northeast Corridor stakeholders should carefully analyze the implications of alternative pricing and allocation mechanisms before locking the system into one of them

Capacity pricing schemes to implement open-access rail in Tanzania

We analyze alternative capacity pricing schemes (access charges) to implement an open-access railway system in Tanzania. We show that the implementation of variable access charges widely used in the railway industry may result in levels of traffic lower than the traffic operated by an integrated railway company. We propose the use of fixed access charges to avoid this problem and discuss the main advantages and disadvantages to implement them in the context of multiple freight train services in Tanzania

Analyzing the Financial Relationship between Railway Industry Players in Shared Railway Systems: The Train Operator’s Perspective

Capacity pricing and allocation play an important role in efficient management of railway corridors, especially shared ones. This paper analyzes how Train Operators (TOs) would respond to different track-access charges, as a first step to understand the relationship between Train Operators and Infrastructure Manger (IM) in railway systems with some level of vertical separation. By modeling a corridor whose users are long-distance high-speed trains and freight trains along the entire corridor, and commuter trains offering services around large urban areas in the corridor, this paper narrows down the focus on each individual operator, looking at the factors that drive each operator's ultimate service levels. Assuming an environment where the TOs are competing for capacity, financial goals and boundary conditions of each TO are derived, and a number of sensitivity analyses for various typical and extreme conditions are performed. This model allows to anticipate how TOs would respond to track-access charges, and can thus help the government, the regulators, and the IMs in the design of appropriate capacity pricing and allocation schemes

Rail Infrastructure Manager Problem: Analyzing Capacity Pricing and Allocation in Shared Railway System

This paper proposes a train timetabling model for shared railway systems. The model is formulated as a mixed integer linear programming problem and solved both using commercial software and a novel algorithm based on approximate dynamic programming. The results of the train timetabling model can be used to simulate and evaluate the behavior of the infrastructure manager in shared railway systems under different capacity pricing and allocation mechanisms. This would allow regulators and decision makers to identify the implications of these mechanisms for different stakeholders considering the specific characteristics of the system

Analysis of High-Speed Rail Implementation Alternatives in the Northeast Corridor: the Role of Institutional and Technological Flexibility

In this paper, an engineering systems framework using the CLIOS Process, scenario analysis, and flexibility analysis is used to study the implementation of a high-speed rail corridor in the Northeast Corridor of the United States. Given the tremendous uncertainty that characterizes high-speed rail projects, the implementation of the alternatives proposed, which are very similar to other commonly accepted ways to implement high-speed rail in the corridor, are analyzed under different scenarios. The results motivate incorporation of flexibility into the alternatives to allow decision makers to adapt as situations evolve. While designing-in this flexibility has a cost, it may facilitate the implementation of the alternatives by enabling adaptation to uncertain outcomes, thereby improving performance

NEC FUTURE Tier I Scoping Process: Public Comment

Utilizing its special expertise, the Regional Transportation Planning and High Speed Rail Research Group at the Massachusetts Institute of Technology (MIT) sought to provide input via public comment to the NEC FUTURE Tier I scoping process. Earlier in 2012, we completed a comprehensive look at the complexities and challenges associated with mobility in the NEC. This submittal is based on a report prepared for and funded by the Institute for Transportation Policy Studies (ITPS) in Tokyo, Japan, entitled Transportation in the Northeast Corridor of the U.S.: A Multimodal and Intermodal Conceptual Framework. We applied novel combinations of system analysis methods to seek new insights for planning in this corridor. With the lessons learned from this account, we seek to provide input to the NEC FUTURE scoping process, and enrich the NEC FUTURE Tier I EIS study. We recognize that the Purpose and Need and a comprehensive and carefully articulated range of alternatives are of utmost importance for the EIS process, and we are focusing our comments in these two areas. With our lessons learned, we hope to offer insights useful in formulating and refining the project’s Purpose and Need, and as well in defining the alternatives to be considered

NEC FUTURE Preliminary Alternatives Report: Public Comment

The United States Department of Transportation's Federal Railroad Administration (FRA) is currently in the early stages of a planning process to define a 30-year passenger rail investment plan for the Northeast Corridor (NEC), between Boston and Washington, D.C. In the Spring of 2013, NEC FUTURE (the name of the planning process), released a Preliminary Alternatives Report, containing 15 possible alternatives for passenger rail infrastructure investment. This working paper contains a memo from the Regional Transportation Planning and High Speed Rail Research Group at the Massachusetts Institute of Technology (MIT) responding to the Preliminary Alternatives Report, as well as following up on the group's previous public comments to NEC FUTURE (ESD-WP-2012-27 NEC FUTURE Tier I Scoping Process: Public Comment). The memo focuses on the group's reactions in three areas: “goals and objectives, and evaluation of the alternatives,” “planning under uncertainty and flexible alternatives,” and “institutional assumptions.” These comments also build on the knowledge gained from report prepared for and funded by the Institute for Transportation Policy Studies (ITPS) in Tokyo, Japan, entitled Transportation in the Northeast Corridor of the U.S.: A Multimodal and Intermodal Conceptual Framework

Measurement of the Higgs boson production rate in association with top quarks in final states with electrons, muons, and hadronically decaying tau leptons at s√=13TeV

The rate for Higgs (H) bosons production in association with either one (tH) or two (tt¯H) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of 13TeV by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137fb−1. The analysis is aimed at events that contain H→WW, H→ττ, or H→ZZ decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among tH, tt¯H, and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the tt¯H and tH signals correspond to 0.92±0.19(stat)+0.17−0.13(syst) and 5.7±2.7(stat)±3.0(syst) of their respective standard model (SM) expectations. The corresponding observed (expected) significance amounts to 4.7 (5.2) standard deviations for tt¯H, and to 1.4 (0.3) for tH production. Assuming that the Higgs boson coupling to the tau lepton is equal in strength to its expectation in the SM, the coupling yt of the Higgs boson to the top quark divided by its SM expectation, κt=yt/ySMt, is constrained to be within −0.9<κt<−0.7 or 0.7<κt<1.1, at 95% confidence level. This result is the most sensitive measurement of the tt¯H production rate to date.SCOAP