This paper presents an overview of recovery models and algorithms for real-time railway disturbance and disruption management. This area is currently an active research area in Operations Research, including real-time timetable rescheduling and real-time rescheduling of the rolling stock and crew duties. These topics are addressed in this paper. Also research dealing with the integration of more than one rescheduling phase is discussed. Currently, the developed methods have been tested mainly in an experimental setting, thereby showing promising results, both in terms of their solution quality and in terms of their computation times. The application of these models and algorithms in real-life railway systems will be instrumental for increasing the quality of the provided railway services, leading to an increased utilization of the involved railway systems.

The efficiency of a transport system depends on several elements, such as available technology, governmental policies, the planning process, and control strategies. Indeed, the interaction between these elements is quite complex, leading to intractable decision making problems. The planning process and real-time control strategies have been widely studied in recent years, and there are several practical implementations with promising results. In this paper, we review the literature on Transit Network Planning problems and real-time control strategies suitable to bus transport systems. Our goal is to present a comprehensive review, emphasizing recent studies as well as works not addressed in previous reviews.

► Minimizing emissions does not imply minimizing operational costs in vehicle routing. ► CO emission cost estimates do not seem to be as important as fuel or labor costs. ► High variation in customer demand implies more room for reducing energy. ► The use of fewer vehicles generally implies lower fuel consumption. The amount of pollution emitted by a vehicle depends on its load and speed, among other factors. This paper presents the Pollution-Routing Problem (PRP), an extension of the classical Vehicle Routing Problem (VRP) with a broader and more comprehensive objective function that accounts not just for the travel distance, but also for the amount of greenhouse emissions, fuel, travel times and their costs. Mathematical models are described for the PRP with or without time windows and computational experiments are performed on realistic instances. The paper sheds light on the tradeoffs between various parameters such as vehicle load, speed and total cost, and offers insight on economies of ‘environmental-friendly’ vehicle routing. The results suggest that, contrary to the VRP, the PRP is significantly more difficult to solve to optimality but has the potential of yielding savings in total cost.

Although ridesharing can provide a wealth of benefits, such as reduced travel costs, congestion, and consequently less pollution, there are a number of challenges that have restricted its widespread adoption. In fact, even at a time when improving communication systems provide real-time detailed information that could be used to facilitate ridesharing, the share of work trips that use ridesharing has decreased by almost 10% in the past 30 years. In this paper we present a classification to understand the key aspects of existing ridesharing systems. The objective is to present a framework that can help identify key challenges in the widespread use of ridesharing and thus foster the development of effective formal ridesharing mechanisms that would overcome these challenges and promote massification.

► Network fundamental diagram is exploited to improve mobility in saturated traffic conditions. ► Based on a simple but efficient feedback control structure, gating is applied to control urban congestion. ► Application of the gating strategy leads to substantial improvements compared to the non-gating case. Traffic signal control for urban road networks has been an area of intensive research efforts for several decades, and various algorithms and tools have been developed and implemented to increase the network traffic flow efficiency. Despite the continuous advances in the field of traffic control under saturated conditions, novel and promising developments of simple concepts in this area remains a significant objective, because some proposed approaches that are based on various meta-heuristic optimization algorithms can hardly be used in a real-time environment. To address this problem, the recently developed notion of network fundamental diagram for urban networks is exploited to improve mobility in saturated traffic conditions via application of gating measures, based on an appropriate simple feedback control structure. As a case study, the proposed methodology is applied to the urban network of Chania, Greece, using microscopic simulation. The results show that the total delay in the network decreases significantly and the mean speed increases accordingly.

► Transportation and power networks coupled by plug-in hybrid electric vehicles. ► Equilibrium analysis of the coupled networks. ► Optimal allocation of public charging stations to maximize social welfare. This paper develops an equilibrium modeling framework that captures the interactions among availability of public charging opportunities, prices of electricity, and destination and route choices of plug-in hybrid electric vehicles (PHEVs) at regional transportation and power transmission networks coupled by PHEVs. The modeling framework is then applied to determine an optimal allocation of a given number of public charging stations among metropolitan areas in the region to maximize social welfare associated with the coupled networks. The allocation model is formulated as a mathematical program with complementarity constraints, and is solved by an active-set algorithm. Numerical examples are presented to demonstrate the models and offer insights on the equilibrium of the coupled transportation and power networks, and optimally allocating resource for public charging infrastructure.

In a heavily congested metro line, unexpected disturbances often occur to cause the delay of the traveling passengers, infeasibility of the current timetable and reduction of the operational efficiency. Due to the uncertain and dynamic characteristics of passenger demands, the commonly used method to recover from disturbances in practice is to change the timetable and rolling stock manually based on the experiences and professional judgements. In this paper, we develop a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains. To capture the complexity of passenger traveling characteristics, the arriving ratio of passengers at each station is modeled as a non-homogeneous poisson distribution, in which the intensity function is treated as time-varying origin-to-destination passenger demand matrices. By considering the number of on-board passengers, the total energy usage is modeled as the difference between the tractive energy consumption and the regenerative energy. Then, we design an approximate dynamic programming based algorithm to solve the proposed model, which can obtain a high-quality solution in a short time. Finally, numerical examples with real-world data sets are implemented to verify the effectiveness and robustness of the proposed approaches.

In this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation urban networks by utilizing the Macroscopic Fundamental Diagram (MFD), a widely observed relation between network-wide space-mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, two modeling variations lead to two alternative optimal control methodologies for the design of perimeter and boundary flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system’s throughput is maximized. Based on the two control methodologies, perimeter and boundary control actions may be computed in real-time through a linear multivariable feedback regulator or a linear multivariable integral feedback regulator. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. To this end, the heterogeneous network of San Francisco is partitioned into three homogeneous reservoirs and the proposed feedback regulators are compared with a pre-timed signal plan and a single-reservoir perimeter control strategy. Finally, the impact of the perimeter and boundary control actions is demonstrated via simulation by the use of the corresponding MFDs and other performance measures. A key advantage of the proposed approach is that it does not require high computational effort and future demand data if the current state of each reservoir can be observed with loop detector data.

Pre-positioning of emergency supplies is one mechanism of increasing preparedness for natural disasters. The goal of this research is to develop an emergency response planning tool that determines the location and quantities of various types of emergency supplies to be pre-positioned, under uncertainty about if, or where, a natural disaster will occur. The paper presents a two-stage stochastic mixed integer program (SMIP) that provides an emergency response pre-positioning strategy for hurricanes or other disaster threats. The SMIP is a robust model that considers uncertainty in demand for the stocked supplies as well as uncertainty regarding transportation network availability after an event. Due to the computational complexity of the problem, a heuristic algorithm referred to as the Lagrangian L-shaped method (LLSM) is developed to solve large-scale instances of the problem. A case study focused on hurricane threat in the Gulf Coast area of the US illustrates application of the model.

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.

A field experiment in Yokohama (Japan) reveals that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. The experiment used a combination of fixed detectors and floating vehicle probes as sensors. It was observed that when the somewhat chaotic scatter-plots of speed vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped neatly along a smoothly declining curve. This evidence suggests, but does not prove, that an MFD exists for the complete network because the fixed detectors only measure conditions in their proximity, which may not represent the whole network. Therefore, the analysis was enriched with data from GPS-equipped taxis, which covered the entire network. The new data were filtered to ensure that only full-taxi trips (i.e., representative of automobile trips) were retained in the sample. The space-mean speeds and densities at different times-of-day were then estimated for the whole study area using relevant parts of the detector and taxi data sets. These estimates were still found to lie close to a smoothly declining curve with deviations smaller than those of individual links – and entirely explained by experimental error. The analysis also revealed a fixed relation between the space-mean flows on the whole network, which are easy to estimate given the existence of an MFD, and the trip completion rates, which dynamically measure accessibility.

The paper presents a statistical model for urban road network travel time estimation using vehicle trajectories obtained from low frequency GPS probes as observations, where the vehicles typically cover multiple network links between reports. The network model separates trip travel times into link travel times and intersection delays and allows correlation between travel times on different network links based on a spatial moving average (SMA) structure. The observation model presents a way to estimate the parameters of the network model, including the correlation structure, through low frequency sampling of vehicle traces. Link-specific effects are combined with link attributes (speed limit, functional class, etc.) and trip conditions (day of week, season, weather, etc.) as explanatory variables. The approach captures the underlying factors behind spatial and temporal variations in speeds, which is useful for traffic management, planning and forecasting. The model is estimated using maximum likelihood. The model is applied in a case study for the network of Stockholm, Sweden. Link attributes and trip conditions (including recent snowfall) have significant effects on travel times and there is significant positive correlation between segments. The case study highlights the potential of using sparse probe vehicle data for monitoring the performance of the urban transport system.

The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.

This paper comprehensively reviews recent developments in modeling lane-changing behavior. The major lane changing models in the literature are categorized into two groups: models that aim to capture the lane changing decision-making process, and models that aim to quantify the impact of lane changing behavior on surrounding vehicles. The methodologies and important features (including their limitations) of representative models in each category are outlined and discussed. Future research needs are determined.

Due to increasing environmental concerns and energy prices, what is very important but has not been given due consideration is the energy efficiency of metro rail systems. Train energy-efficient operation consists of timetable optimization and speed control. The former synchronizes the accelerating and braking actions of trains to maximize the utilization of regenerative energy, and the latter controls the train driving strategy to minimize the tractive energy consumption under the timetable constraints. To achieve a better performance on the net energy consumption, i.e., the difference between the tractive energy consumption and the utilization of regenerative energy, this paper formulates an integrated energy-efficient operation model to jointly optimize the timetable and speed profile. We design a genetic algorithm to solve the model and present some numerical experiments based on the actual operation data of Beijing Metro Yizhuang Line of China. It is shown that a larger headway leads to smaller energy saving rate, and the maximum energy saving rate achieved is around 25% when we use the minimum allowable headway of 90 s. In addition, compared with the two-step approach optimizing the timetable and speed profile separately, the integrated approach can reduce the net energy consumption around 20%.

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.

► We partition transportation networks based on spatial features of congestion. ► A three-step partitioning mechanism for transportation networks is designed. ► The spatial compactness of the clusters is obtained after partitioning. ► Several homogeneity metrics to evaluate the partitioning results are specified. ► Scatter of partitioned MFDs decreases for heterogeneous density of networks. It has been recently shown that a macroscopic fundamental diagram (MFD) linking space-mean network flow, density and speed exists in the urban transportation networks under some conditions. An MFD is further well defined if the network is homogeneous with links of similar properties. This collective behavior concept can also be utilized to introduce simple control strategies to improve mobility in homogeneous city centers without the need for details in individual links. However many real urban transportation networks are heterogeneous with different levels of congestion. In order to study the existence of MFD and the feasibility of simple control strategies to improve network performance in heterogeneously congested networks, this paper focuses on the clustering of transportation networks based on the spatial features of congestion during a specific time period. Insights are provided on how to extend this framework in the dynamic case. The objectives of partitioning are to obtain (i) small variance of link densities within a cluster which increases the network flow for the same average density and (ii) spatial compactness of each cluster which makes feasible the application of perimeter control strategies. Therefore, a partitioning mechanism which consists of three consecutive algorithms, is designed to minimize the variance of link densities while maintaining the spatial compactness of the clusters. Firstly, an over segmenting of the network is provided by a sophisticated algorithm (Normalized Cut). Secondly, a merging algorithm is developed based on initial segmenting and a rough partitioning of the network is obtained. Finally, a boundary adjustment algorithm is designed to further improve the quality of partitioning by decreasing the variance of link densities while keeping the spatial compactness of the clusters. In addition, both density variance and shape smoothness metrics are introduced to identify the desired number of clusters and evaluate the partitioning results. These results show that both the objectives of small variance and spatial compactness can be achieved with this partitioning mechanism. A simulation in a real urban transportation network further demonstrates the superiority of the proposed method in effectiveness and robustness compared with other clustering algorithms.

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.

► We model a reliable logistics network design problem with -robustness constraints. ► The model produces supply chain networks that perform well under both nominal and disruption scenarios. ► We propose a hybrid metaheuristic algorithm to efficiently solve the problem. ► The -robustness criterion is less conservative compared with other robustness measures. ► Substantial improvements in reliability are achievable with minimal increases in cost. This paper studies a strategic supply chain management problem to design reliable networks that perform as well as possible under normal conditions, while also performing relatively well when disruptions strike. We present a mixed-integer programming model whose objective is to minimize the nominal cost (the cost when no disruptions occur) while reducing the disruption risk using the -robustness criterion (which bounds the cost in disruption scenarios). We propose a hybrid metaheuristic algorithm that is based on genetic algorithms, local improvement, and the shortest augmenting path method. Numerical tests show that the heuristic greatly outperforms CPLEX in terms of solution speed, while still delivering excellent solution quality. We demonstrate the tradeoff between the nominal cost and system reliability, showing that substantial improvements in reliability are often possible with minimal increases in cost. We also show that our model produces solutions that are less conservative than those generated by common robustness measures.

This paper introduces the fleet size and mix pollution-routing problem which extends the pollution-routing problem by considering a heterogeneous vehicle fleet. The main objective is to minimize the sum of vehicle fixed costs and routing cost, where the latter can be defined with respect to the cost of fuel and CO emissions, and driver cost. Solving this problem poses several methodological challenges. To this end, we have developed a powerful metaheuristic which was successfully applied to a large pool of realistic benchmark instances. Several analyses were conducted to shed light on the trade-offs between various performance indicators, including capacity utilization, fuel and emissions and costs pertaining to vehicle acquisition, fuel consumption and drivers. The analyses also quantify the benefits of using a heterogeneous fleet over a homogeneous one.