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Urban transportation systems' structure and functionality can be affected by unexpected disruptions for several reasons, such as natural hazards, intentional attacks, accidents, and so forth. The conventional definition of resilience is the capacity to withstand, assimilate, adjust, and expeditiously recuperate from various forms of perturbations such as shocks, disturbances, and deliberate attacks. Though multiple studies in the literature focus on resilience assessment and improving the resilience level of mobility services before disruption, few studies offer solutions for the operators of transportation systems during disruptions to alleviate their negative effects, such as reducing the recovery time. In this context, a new paradigm called ``resilience as a service'' (RaaS) has emerged in the field of operations management. The idea of RaaS is to integrate the available resources of different service providers to manage disruptions and maintain the system's resilience. This paper proposes a definition of RaaS dedicated to transportation systems. To provide a methodological example for the RaaS paradigm, we formulate a bi-level optimization problem to represent a solution example that RaaS providers can deliver. The upper-level model formulates the resource reallocation problem during disruption from the perspective of RaaS providers, while the lower-level model considers user perspectives. We provide a numerical example in a real test case of a French city to illustrate the benefits of implementing a RaaS solution. The results show that we can reduce the average travel delay of all users by 69%, including the delay results from the proposed RaaS strategy compared with the absence of RaaS.

Departure time choice models play a crucial role in determining the traffic load in transportation systems. Most studies that consider departure time user equilibrium (DTUE) problems make assumptions on the user characteristics (e.g., distribution of desired arrival time and trip length) or dynamic traffic model (e.g., classic bathtub or point queue models) in order to analyze the problem. This paper relaxes these assumptions and introduces a new framework to model and analyze the DTUE problem based on the so-called mean field games (MFGs) theory. MFGs allow us to define players at the microscopic level similar to classical game theory models, translating the effect of players’ decisions to macroscopic models. In this paper, we first present a continuous departure time choice model and investigate the equilibria of the system. Specifically, we demonstrate the existence of the equilibrium and characterize the DTUE. Then, a discrete approximation of the system is provided based on deterministic differential game models to numerically obtain the equilibrium of the system. To examine the efficiency of the proposed model, we compare it with the departure time choice models in the literature. We apply our framework to a standard test case and observe that the solutions obtained based on our model are 5.6% better in terms of relative cost compared with the solutions determined based on previous studies. Moreover, our proposed model converges with fewer iterations than the reference solution method in the literature. Finally, the model is scaled up to the real test case corresponding to the whole Lyon metropolis with a real demand pattern. The results show that the proposed framework is able to tackle a much larger test case than usual to include multiple preferred travel times and heterogeneous trip lengths more accurately than existing models.

TRB 2021, Transportation Research Board 100th Annual Meeting - A Virtual Event, Washington DC, ETATS-UNIS, 05-/01/2021 - 29/01/2021; Departure time choice models have a crucial role in transportation network planning in order to provide planners with predictions about the optimal traffic load. This paper introduces a new dynamic departure time choice framework based on the so-called Mean-field Games (MFGs) theory proposed by Lasry and Lions. MFGs models aim to analyze large population differential games. This feature gives us a unique opportunity to design a departure time choice equilibrium model in a scale-free transportation system. The proposed framework is the combination of two components: (i) the reaction of travelers to the traffic congestion by choosing their departure time to optimize the travel cost; (ii) the aggregation of the actions of the travelers, which determines the congestion level of the system. The first component corresponds to a classical game theory model, while the second one captures the interactions of the travelers at the macroscopic level. We use the generalized bathtub model recently proposed by Jin to represent the traffic dynamics at the network level. First, we provide a continuous model to investigate the equilibria and then give a discrete approximation of the system from deterministic differential games models. Finally, we show on a real test case that the model can represent the departure time choice equilibrium for multiple preferred travel time with heterogeneous trip lengths wile the framework is capable of considering a large number of players.

This work investigates network-related trajectory features to unravel trips that contribute most to system under-performance. When such trips are identified, feature analysis also permits determining the best alternatives in terms of routes to bring the system to its optimum. First, we define a combination of network-related trajectory features that helps us unravel the critical trips which contribute the most to the network under-performance, based on the literature review and a factor selection process. Second, based on supervised learning methods, we propose a two-step data-driven methodological framework to reroute a part of the users and make the system close to its optimum. The learning models are trained with trajectory features to identify which users should be selected, and which alternative routes should be assigned, thanks to the data and features obtained from two reference dynamic traffic assignment (DTA) simulations, under User-Equilibrium (UE) and System-Optimum (SO). We only focus on trajectory features that are accessible in real time, such as network features and regular travel time information, so that the methods proposed can be implemented without requiring cumbersome network monitoring and prediction. Finally, we evaluate the efficiency of the methods proposed through microscopic DTA simulations. The results show that by targeting 20% of the users according to our selection model and moving them onto paths predicted as optimal alternative paths based on our rerouting model, the total travel time (TTT) of the system is reduced by 5.9% in comparison to a UE DTA simulation. This represents 62.5% of the potential TTT reduction from UE to SO, when all the users choose their path under the SO condition.

This study reviews existing computational methods to calculate simulation-based dynamic network equilibrium. We consider a trip-based multi-modal approach for the dynamic network loading. Mode and path choices are carried out at the same level; therefore, travel times depend on the travel path and the mode attributes of travelers. This study develops a multi-class model with several parameters per class. Two different categories of algorithms (heuristic and meta-heuristic) are considered in order to solve the discrete DTA problem. Finally, we analyze the equilibrium in a large-scale multi-modal DTA test case (Lyon 6th + Villeurbanne) in order to investigate the performance of different optimization approaches to solve trip-based DTA. The results show that, in a multimodal and heterogeneous setting, the meta-heuristic methods provide better solutions than the heuristic methods in terms of optimality and computation time. These improvements are even more significant than in a homogeneous setting.

Analysing the properties of a network equilibrium can help to have a better view about network state, robustness, and the effect of any variation in the network. This study investigated the impacts of network design history on day-to-day multimodal user equilibrium. In particular, we analyze the long-term evolution of the network, including opening new multimodal options and its impacts on the final network equilibrium. First, the analysis focuses on static network loading with different successive configurations. Then, a more realistic setting is studied by simulation. A large-scale multimodal network with the flexible opening over time of three possible transport facilities shows that the final equilibrium is not unique; more importantly, significant differences can be observed in public transportation occupancy, while user equilibrium is enforced in all situations. Some solutions prove to be better from the collective viewpoint (shorter total travel time), thus giving new insight into public transport planning.

The aim of this study is to solve the large?scale dynamic traffic assignment (DTA) model using a simulation?based framework, which is computationally a challenging problem. Many studies have been performed on developing an efficient algorithm to solve DTA. Most of the existing algorithms are based on path?swapping descent direction methods. From the computational standpoint, the main drawback of these methods is that they cannot be parallelized. This is because the existing algorithms need to know the results of the last iteration to determine the next best path flow for the next iteration. Thus, their performance depends on the single initial or intermediate solution, which means they exploit a solution that satisfies the equilibrium conditions more than explore the solution space for the optimal solution. More specifically, the goal of this study is to overcome the drawbacks of serial algorithms by using meta?heuristic algorithms known to be parallelizable and that have never been applied to the simulation?based DTA problem. This study proposes two new solution methods: a new extension of the simulated annealing and an adapted genetic algorithm. With parallel simulation, the algorithm runs more simulations in comparison with existing methods, but the algorithm explores the solution space better and therefore obtains better solutions in terms of closeness to the optimal solution and computation time compared to classical methods.

hEART 2019, 8th Symposium of the European Association for Research in Transportation, Budapest, HONGRIE, 04-/09/2019 - 06/09/2019; Dynamic Traffic Assignment (DTA) refers to the procedure of assigning trips to paths in a given transportation system considering the Origin-Destination pair (OD) flow demand and the network dynamic traffic states. This problem can be represented as a fixed-point problem. In a large-scale and trip-based setting, it is not possible to guarantee that fixed point algorithms converge towards the optimal. From a computational point of view, the main drawback of these methods for addressing DTA on large-scale networks is that they cannot be parallelized. This is because the existing algorithms need to know the last iteration results to determine the next best path flow for the next iteration. The goal of this study is to overcome the drawbacks of serial algorithms by using meta-heuristic algorithms that are known to be parallelizable. This study proposes two new solution methods: the new extension of the Simulated Annealing and adaptive Genetic Algorithm. With parallel simulation, the algorithm is going to run more simulations in comparison with existing methods, but it is expected to carry out a better exploration of the solution space and consequently achieve better solutions in terms of closeness to the optimal solution and computation time in comparison with classic methods.

TRISTAN X, The Tenth Triennial Symposium on Transportation Analysis, Hamilton island, AUSTRALIE, 17-/06/2019 - 21/06/2019; Dynamic Traffic Assignment (DTA) refers to the procedure of assigning trips to paths in a given transportation system considering the Origin-Destination pair (OD) flow demand and the network dynamic traffic states. This problem can be represented as a fixed-point problem. In a large-scale and trip-based setting, it is not possible to guarantee that fixed point algorithms converge towards the optimal. From a computational point of view, the main drawback of these methods for addressing DTA on large-scale networks is that they cannot be parallelized. This is because the existing algorithms need to know the last iteration results to determine the next best path flow for the next iteration. The goal of this study is to overcome the drawbacks of serial algorithms by using meta-heuristic algorithms that are known to be parallelizable. This study proposes two new solution methods: the new extension of the Simulated Annealing and adaptive Genetic Algorithm. With parallel simulation, the algorithm is going to run more simulations in comparison with existing methods, but it is expected to carry out a better exploration of the solution space and consequently achieve better solutions in terms of closeness to the optimal solution and computation time in comparison with classic methods.

TRB 2019, Transportation Research Board 98th Annual Meeting, Washington, ETATS-UNIS, 13-/01/2019 - 17/01/2019; Calculating dynamic network equilibrium is a challenging problem. This study first analyzes the different frameworks for the simulation-based User Equilibrium (UE) in the literature. Most of them are based on solving a fixed-point problem by iterative methods. Two elements have to be determined: the path set between all origin-destination pairs and the optimal path flow distribution. The most advanced solution methods expressed the problem with two-layers, the outer and the inner loop, that tackle each element respectively. The goal of this study is to improve the inner loop, i.e. the path flow calculation. The first improvement is keeping the best assignment pattern during the inner loop iterations and send it to the outer loop. It improves the solution quality in trip-based traffic assignment because flows are then discretized into units of user, which makes the point-fix calculation much harder. This study proposes three new swapping methods and two new methods for the step size initialization that is used in each descent iteration. Moreover, this study proposes two alternative methods to initialize the path flow distribution at the beginning of the outer loop. Two quality indicators are considered to examine the quality of UE solution and then the methods are applied to three networks with different sizes (small, medium and large). The results show that the performance of different components of the solution algorithm is sensitive to the network size. Finally, the best configurations of the solution algorithms are recommended for all network sizes with a particular focus on the large-scale.

Transport systems are dynamically characterized not only by nonlinear interactions between the different components but also by feedback loops between the state of the network and the decisions of users. In particular, network congestion affects both the distribution of local demand by modifying route choices and overall multimodal demand. Depending on the conditions of the network, they may decide to change for example their transportation mode. Several equilibria can be defined for transportation systems. The user equilibrium corresponds to the situation where each user is allowed to behave selfishly and to minimize his own travel costs. The system optimum corresponds to a situation where the total transport cost of all the users is minimum. In this context, the study aims to calculate route flow patterns in a network considering different equilibrium conditions and study the network equilibrium in a dynamic setting. The study focuses on traffic models capable of representing large-scale urban traffic dynamics. Three main issues are addressed. First, fast heuristic and meta-heuristic methods are developed to determine equilibria with different types of traffic patterns. Secondly, the existence and uniqueness of user equilibria is studied. When there is no uniqueness, the relationship between multiple equilibria is examined. Moreover, the impact of network history is analyzed. Thirdly, a new approach is developed to analyze the network equilibrium as a function of the level of demand. This approach compares user and system optimums and aims to design control strategies in order to move the user equilibrium situation towards the system optimum.; Les systèmes de transport sont caractérisés de manière dynamique non seulement par des interactions non linéaires entre les différents composants, mais également par des boucles de rétroaction entre l'état du réseau et les décisions des utilisateurs. En particulier, la congestion du réseau impacte à la fois la répartition de la demande locale en modifiant les choix d’itinéraire et la demande multimodale globale. Selon les conditions du réseau, ils peuvent décider de changer, par exemple, leur mode de transport. Plusieurs équilibres peuvent être définis pour les systèmes de transport. L'équilibre de l'utilisateur correspond à la situation dans laquelle chaque utilisateur est autorisé à se comporter de manière égoïste et à minimiser ses propres frais de déplacement. L'optimum du système correspond à une situation où le coût total du transport de tous les utilisateurs est minimal. Dans ce contexte, l’étude vise à calculer les modèles de flux d'itinéraires dans un réseau prenant en compte différentes conditions d’équilibre et à étudier l’équilibre du réseau dans un contexte dynamique. L'étude se concentre sur des modèles de trafic capables de représenter une dynamique du trafic urbain à grande échelle. Trois sujets principaux sont abordés. Premièrement, des méthodes heuristiques et méta-heuristiques rapides sont développées pour déterminer les équilibres avec différents types de trafic. Deuxièmement, l'existence et l'unicité des équilibres d'utilisateurs sont étudiées. Lorsqu'il n'y a pas d'unicité, la relation entre des équilibres multiples est examinée. De plus, l'impact de l'historique du réseau est analysé. Troisièmement, une nouvelle approche est développée pour analyser l’équilibre du réseau en fonction du niveau de la demande. Cette approche compare les optima des utilisateurs et du système et vise à concevoir des stratégies de contrôle afin de déplacer la situation d'équilibre de l'utilisateur vers l'optimum du système

Transportation systems are dynamically driven not only by non-linear interactions between the different components but also by significant feedbacks between network state and user decision. In this work, we consider a trip-based multi-modal approach to network equilibrium. We assume that mode and path choice is carried out at the same level; therefore, travel time depends on the travel path and the mode attributes of travelers. First, we analyze the existing approaches in the literature to model users’ heterogeneity. Second, we present a formulation for static traffic network equilibrium and propose a hybrid formulation of the cost function for trip-based traffic assignment. Third, we consider dynamic traffic assignment (DTA) and propose a variational inequality formulation of the trip-based fixed demand function for the multi-class dynamic traffic equilibrium problem. Finally, we analyze the equilibrium in a large-scale DTA test case (Lyon 6e + Villeurbanne) by a simulation-based approach. Moreover, we propose a novel trip-based algorithm to solve the discrete DTA problem and compare it with the gap function-based method.

DTA 2018, 7th International Symposium on Dynamic Traffic Assignment , Hong Kong, CHINE, 06-/06/2018 - 08/06/2018; Unicity of the solution is an important character of the Dynamic Traffic Assignment (DTA) problem. Beckman et al. (1956) indicate the importance of unicity and stability of the solution. The conditions of unicity have been properly reviewed by Iryo (2013) for flow-based DTA by considering the different approach to solving the DTA problem. Moreover, many researches have been done to prove the unicity of DTA solutions on flow-based dynamic traffic model with several assumptions and limitations on traffic network model (Mounce, 2007; Mounce and Smith, 2007; Iryo 2011; Iryo 2015; Iryo and Smith, 2017). This study adapts the conditions to trip-based DTA wherein each traveler is defined as an individual. A key characteristic for unicity is strictly monotone path travel time function with respect to the number of travelers that use the path. There is no guaranty to hold the monotonicity condition in the multimodal urban transportation network (Mounce, 2001). This study aims to investigate the end result of the evolution of a transportation system over a long-term day to day learning process. Mathematically speaking, we are going to address the impact of initial solutions in the day-to-day multimodal DTA.

In this study, a unique fuzzy multi-control approach for continuous quality improvement is introduced and is implemented in radio therapy department. Treatment process is one of the most important concern in healthcare department. To control this process there is a critical issue, because the periods that the patients take to the recovery should be controlled by the physicians. This study tries to control this process using the common statistical quality control methods. In addition, this paper presents a control index for patient condition. Given the decision making situations including diagnosis, determining the medicine and its value and control limit, decision making (DM) models will be used at first step. Then, process control is analyzed using statistical process control (SPC) including histogram, Pareto chart, cause and effect diagram and new fuzzy control chart. This research aims at presenting a unique control approach with fuzzy DM and SPC tools for a real radio therapy department. Moreover, these processes could be controlled and improved continuously using Deming cycle (PDCA). The case study verified and validated the design model. This is the first study that presents a unique integrated fuzzy control approach for improved decision-making process in an actual radio therapy department.

Conference on Traffic & Granular Flow, WASHINGTON DC, ETATS-UNIS, 19-/07/2017 - 22/07/2017; In this work we consider a trip-based multi-modal approach to network equilibrium. We assume that mode and path choice are carried out at the same level, therefore travel time (TT) depends on travel path and the mode(s) attributes of travelers. This study develops a multi-class model with several parameters per class.

This study reviews existing computational methods to calculate simulation-based dynamic network equilibrium. We consider a trip-based multimodal approach for the dynamic network loading. Mode and path choices are carried out at the same level; therefore, travel times depend on the travel path and the mode attributes of travelers. This study develops a multiclass model with several parameters per class. Two different categories of algorithms (heuristic and metaheuristic) are considered in order to solve the discrete dynamic traffic assignment (DTA) problem. Finally, we analyze the equilibrium in a large-scale multimodal DTA test case (Lyon 6th + Villeurbanne) in order to investigate the performance of different optimization approaches to solve trip-based DTA. The results show that, in a multimodal and heterogeneous setting, the metaheuristic methods provide better solutions than the heuristic methods in terms of optimality and computation time. These improvements are even more significant than in a homogeneous setting.

hEART 2018, 7th Symposium of the European Association for Research in Transportation, Athènes, GRECE, 05-/09/2018 - 07/09/2018; Unicity of the solution is an important issue in the Dynamic Traffic Assignment (DTA) problem (Beckmann et al. (1956)). The conditions of unicity have been properly reviewed by Iryo (2013) for flow-based DTA by considering the different approach to solving the DTA problem. Moreover, many researches have been done to prove the unicity of DTA solutions on flow-based dynamic traffic model with several assumptions and limitations on traffic network model (Mounce (2007); Mounce & Smith (2007); Iryo (2011); Iryo (2015); Iryo & Smith (2017)). This study adapts the conditions to trip-based DTA wherein each traveler is defined as an individual.

The purpose of this study is to compare network loadings related to different network equilibria by a simulation-based framework. The direct comparison of path flows or trajectory patterns is hard to achieve so here we propose a more aggregate approach based on the comparison of demand level breakpoints. A breakpoint is a demand threshold value that leads to significant changes in path flow loading. More specifically, we set in this paper a demand breakpoint when the list of effective route alternatives differs by at least one path. This is for example the case when one route is no longer considered for one equilibrium while being used by some vehicles in the second one. We are going to investigate both static and dynamic network loading while scanning all demand levels to identify the breakpoints. We focus on discrete demand formulation and choices and use a trip-based traffic simulator. This study analyzes the breakpoints for the solution of three popular equilibrium conditions: User equilibrium (UE), System optimum (SO) and Boundary Rational User Equilibrium (BRUE). First, we investigate breakpoints on a well-known network (Braess) in the static case in order to better define this concept. Second, breakpoints are investigated on a real network (Lyon, France) where dynamic travel times are provided by a microscopic traffic simulator. When the breakpoints are obtained for a given scenario, we focus on identifying demand ranges where some paths are not used in SO while being travelled in UE or BRUE. Following the concept of Braess paradox, this permits to design banning strategies at some key locations in the network to prevent some alternatives from being used and thus to improve the system performance. We show by simulation that such a strategy is effective, which demonstrates the importance of breakpoint identification.