arXiv subjects

David Rey

Publications and source records attributed to David Rey.

At least 19 recordsLinked to original sources

arXiv2024

Optimizing Traffic Signal Control for Continuous-Flow Intersections: Benchmarking against a State-of-Practice Model

Continuous-Flow Intersections (CFI), also known as Displaced Left-Turn (DLT) intersections, aim to improve the efficiency and safety of traffic junctions. A CFI introduces additional sub-intersections upstream of the main intersection to split the left-turn flow from the through movement before it arrives at the main intersection, decreasing the number of conflict points between left-turn and through movements. This study develops and examines a two-step optimization model for CFI traffic signal control design and demonstrates its performance across more than 300 different travel demand scenarios. The proposed model is compared against a benchmark state-of-practice CFI signal control model. Microsimulation results suggest that the proposed model reduces average delay by 17% and average queue length by 32% for a full CFI compared with the benchmark signal control model.

math.OC↗

arXiv2024

Thermal melting of a vortex lattice in a quasi two-dimensional Bose gas

We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by an abrupt change in the decay of orientational correlations, associated to a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the KTHNY scenario for two-dimensional melting.

cond-mat.quant-gas↗

arXiv2024

Data-driven Optimization for Drone Delivery Service Planning with Online Demand

In this study, we develop an innovative data-driven optimization approach to solve the drone delivery service planning problem with online demand. Drone-based logistics are expected to improve operations by enhancing flexibility and reducing congestion effects induced by last-mile deliveries. With rising digitalization and urbanization, however, logistics service providers are constantly grappling with the challenge of uncertain real-time demand. This study investigates the problem of planning drone delivery service through an urban air traffic network to fulfil online and stochastic demand. Customer requests, if accepted, generate profit and are serviced by individual drone flights as per request origins, destinations and time windows. We cast this stochastic optimization problem as a Markov decision process. We present a novel data-driven optimization approach which generates predictive prescriptions of parameters of a surrogate optimization formulation. Our solution method consists of synthesizing training data via lookahead simulations to train a supervised machine learning model for predicting relative link priority based on the state of the network. This knowledge is then leveraged to selectively create weighted reserve capacity in the network and via a surrogate objective function that controls the trade-off between reserve capacity and profit maximization to maximize the cumulative profit earned. Using numerical experiments based on benchmarking transportation networks, the resulting data-driven optimization policy is shown to outperform a myopic policy. Sensitivity analyses on learning parameters reveal insights into the design of efficient policies for drone delivery service planning with online demand.

math.OC↗

arXiv2022

Loading a quantum gas from a hybrid dimple trap to a shell trap

Starting from a degenerate Bose gas in a hybrid trap combining a magnetic quadrupole trap and an attractive optical trap resulting from a focused laser beam, we demonstrate the efficient loading of this quantum gas into a shell-shaped trap. The shell trap is purely magnetic and relies on adiabatic potentials for atoms in an inhomogeneous magnetic field dressed by a radiofrequency (rf) field. We show that direct rf evaporation in the hybrid trap enables an efficient and simple preparation of the cold sample, well adapted to the subsequent loading procedure. The transfer into the shell trap is adiabatic and limits the final excitation of the center-of-mass motion to below 2 micrometres.

cond-mat.quant-gas↗

arXiv2022

Aircraft Conflict Resolution with Trajectory Recovery Using Mixed-Integer Programming

To guarantee the safety of flight operations, decision-support systems for air traffic control must be able to improve the usage of airspace capacity and handle increasing demand. In this study, we address the aircraft conflict avoidance and trajectory recovery problem. The problem of finding least deviation conflict-free aircraft trajectories that guarantee the return to a target waypoint is highly complex due to the nature of the nonlinear trajectories that are sought. We present a two-stage iterative algorithm that first solves initial conflict by manipulating their speed and heading control and then identifying each aircraft's optimal time to recover its trajectory towards their nominal. The avoidance stage extends existing mixed-integer programming formulations, and for the recovery stage, we propose a novel mixed-integer formulation. We assume that speed and heading control are continuous variables for this approach while the recovery time is treated as a discrete variable. In this approach, it is shown that the trajectory recovery costs can be anticipated by inducing avoidance trajectories with higher deviation, therefore obtaining earlier recovery time within few iterations. Numerical results on benchmark conflict resolution problems show that this approach can solve instances with up to 30 aircraft within 10 minutes.

math.OC↗

arXiv2021

Vaccine allocation policy optimization and budget sharing mechanism using Thompson sampling

The optimal allocation of vaccines to population subgroups over time is a challenging health care management problem. In the context of a pandemic, the interaction between vaccination policies adopted by multiple agents and the cooperation (or lack thereof) creates a complex environment that affects the global transmission dynamics of the disease. In this study, we take the perspective of decision-making agents that aim to minimize the size of their susceptible populations and must allocate vaccine under limited supply. We assume that vaccine efficiency rates are unknown to agents and we propose an optimization policy based on Thompson sampling to learn mean vaccine efficiency rates over time. Furthermore, we develop a budget-balanced resource sharing mechanism to promote cooperation among agents. We apply the proposed framework to the COVID-19 pandemic. We use a raster model of the world where agents represent the main countries worldwide and interact in a global mobility network to generate multiple problem instances. Our numerical results show that the proposed vaccine allocation policy achieves a larger reduction in the number of susceptible individuals, infections and deaths globally compared to a population-based policy. In addition, we show that, under a fixed global vaccine allocation budget, most countries can reduce their national number of infections and deaths by sharing their budget with countries with which they have a relatively high mobility exchange. The proposed framework can be used to improve policy-making in health care management by national and global health authorities.

math.OC↗

arXiv2021

Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets

Mobility-as-a-Service (MaaS) is an emerging business model driven by the concept of "Everything-as-a-Service" and enabled through mobile internet technologies. In the context of economic deregulation, a MaaS system consists of a typical two-sided market, where travelers and transportation service providers (TSPs) are two groups of agents interacting with each other through a MaaS platform. In this study, we propose a modeling and optimization framework for the regulation of two-sided MaaS markets. We consider a name-your-own-price (NYOP)-auction mechanism where travelers submit purchase-bids to accommodate their travel demand via MaaS platform, and TSPs submit sell-bids to supply mobility resources for the MaaS platform in exchange for payments. We cast this problem as a single-leader multi-follower game (SLMFG) where the leader is the MaaS regulator and two groups of follower problems represent the travelers and the TSPs. The MaaS regulator aims to maximize its profits by optimizing operations. In response to the MaaS regulator's decisions, travelers (resp. TSPs) adjust their participation level in the MaaS platform to minimize their travel costs (resp. maximize their profits). We analyze cross-group network effects in the MaaS market, and formulate SLMFGs without and with network effects leading to mixed-integer linear bilevel programming and mixed-integer quadratic bilevel programming problems, respectively. We propose customized branch-and-bound algorithms based on strong duality reformulations to solve these SLMFGs. Extensive numerical experiments conducted on large scale simulation instances generated from realistic mobility data highlight that the performance of the proposed algorithms is significantly superior to a benchmarking approach, and provide meaningful managerial insights for the regulation of two-sided MaaS markets in practice.

math.OC↗

arXiv2021

Expansion of a quantum gas in a shell trap

We report the observation of the controlled expansion of a two-dimensional quantum gas confined onto a curved shell-shaped surface. We start from the ellipsoidal geometry of a dressed quadrupole trap and introduce a novel gravity compensation mechanism enabling to explore the full ellipsoid. The zero-point energy of the transverse confinement manifests itself by the spontaneous emergence of an annular shape in the atomic distribution. The experimental results are compared with the solution of the three-dimensional Gross-Pitaevskii equation and with a two-dimensional semi-analytical model. This work evidences how a hidden dimension can affect dramatically the embedded low-dimensional system by inducing a change of topology.

cond-mat.quant-gas↗

arXiv2020

Robust aircraft conflict resolution under trajectory prediction uncertainty

We address the aircraft conflict resolution problem under trajectory prediction uncertainty. We consider that aircraft velocity vectors may be perturbed due to weather effects, such as wind, or measurement errors. Such perturbations may affect aircraft trajectory prediction which plays a key role in ensuring flight safety in air traffic control. Our goal is to solve the aircraft conflict resolution problem in the presence of such perturbations and guarantee that aircraft are separated for any realization of the uncertain data. We propose an uncertainty model wherein aircraft velocities are represented as random variables and the uncertainty set is assumed to be polyhedral. We consider a robust optimization approach and embed the proposed uncertainty model within state-of-the-art mathematical programming formulations for aircraft conflict resolution. We then adopt the approach of Bertsimas and Sim (2004) to formulate the robust counterpart. We use the complex number reformulation and the constraint generation algorithm proposed by Dias et al. (2020a) to solve the resulting nonconvex optimization problem on benchmarking instances of the literature. Our numerical experiments reveal that perturbations of the order of $\pm 5\%$ on aircraft velocities can be accounted for without significantly impacting the objective function compared to the deterministic case. Our tests also show that for greater levels of uncertainty, several instances fail to admit conflict-free solutions, thus highlighting existing risk factors in aircraft conflict resolution. We attempt to explain this behavior by further analyzing pre- and post-optimization aircraft trajectories. Our findings show that most infeasible instances have both a relatively low total aircraft pairwise minimal distance and a high number of conflicts.

math.OC↗

arXiv2020

Traffic Assignment Problem for Footpath Networks with Bidirectional Links

The estimation of pedestrian traffic in urban areas is often performed with computationally intensive microscopic models that usually suffer from scalability issues in large-scale footpath networks. In this study, we present a new macroscopic user equilibrium traffic assignment problem (UE-pTAP) framework for pedestrian networks while taking into account fundamental microscopic properties such as self-organization in bidirectional streams and stochastic walking travel times. We propose four different types of pedestrian volume-delay functions (pVDFs), calibrate them with empirical data, and discuss their implications on the existence and uniqueness of the traffic assignment solution. We demonstrate the applicability of the developed UE-pTAP framework in a small network as well as a large scale network of Sydney footpaths.

eess.SY↗

arXiv2020

A chance-constrained dial-a-ride problem with utility-maximizing demand and multiple pricing structures

The classic Dial-A-Ride Problem (DARP) aims at designing the minimum-cost routing that accommodates a set of user requests under constraints at an operations planning level, where users' preferences and revenue management are often overlooked. In this paper, we present a mechanism for accepting/rejecting user requests in a Demand Responsive Transportation (DRT) context based on the representative utilities of alternative transportation modes. We consider utility-maximizing users and propose a mixed-integer programming formulation for a Chance Constrained DARP (CC-DARP), that captures users' preferences in the long run via a Logit model. We further introduce class-based user groups and consider various pricing structures for DRT services. A customised local search based heuristic is developed to solve the proposed CC-DARP. We report numerical results for both DARP benchmarking instances and a realistic case study based on New York City yellow taxi trip data. Computational experiments performed on 105 benchmarking instances with up to 96 nodes yield an average optimality gap of 2.69% using the proposed local search heuristic. The results obtained on the realistic case study reveal that a zonal fare structure is the best strategy in terms of optimising revenue and ridership. The proposed CC-DARP formulation provides a new decision-support tool to inform on revenue and fleet management for DRT systems at a strategic planning level.

math.OC↗

arXiv2020

Incentive-compatible mechanisms for online resource allocation in mobility-as-a-service systems

In the context of `Everything-as-a-Service', the transportation sector has been evolving towards user-centric business models in which customized services and mode-agnostic mobility resources are priced in a unified framework. Yet, in the vast majority of studies on Mobility as a Service (MaaS) systems, mobility resource pricing is based on segmented travel modes, e.g. private vehicle, public transit and shared mobility services. This study attempts to address this research gap by introducing innovative auction-based online MaaS mechanisms where users can bid for any amount of mode-agnostic mobility resources based on their willingness to pay and preferences. We take the perspective of a MaaS regulator which aims to maximize social welfare by allocating mobility resources to users. We propose two mechanisms which allow users to either pay for the immediate use of mobility service (pay-as-you-go), or to subscribe to mobility service packages (pay-as-a-package). We cast the proposed auction-based mechanisms as online resource allocation problems where users compete for MaaS resources and bid for travel time per trip. We propose (integer-) linear programming formulations to accommodate user bids based on available mobility resources in an online optimization approach. We show that the proposed MaaS mechanisms are incentive-compatible, develop customized online algorithms and derive performance bounds based on competitive analysis. Extensive numerical simulations are conducted on large scale instances generated from realistic mobility data, which highlight the benefits of the proposed MaaS mechanisms and the effectiveness of the proposed online optimization approaches.

math.OC↗

arXiv2020

Online Incentive-Compatible Mechanisms for Traffic Intersection Auctions

We present novel online mechanisms for traffic intersection auctions in which users bid for priority service. We assume that users at the front of their lane are requested to declare their delay cost, i.e. value of time, and that users are serviced in decreasing order of declared delay cost. Since users are expected to arrive dynamically at traffic intersections, static pricing approaches may fail to estimate user expected waiting time accurately, and lead to non-strategyproof payments. To address this gap, we propose two Markov chain models to determine the expected waiting time of participants in the auction. Both models take into account the probability of future arrivals at the intersection. In a first model, we assume that the probability of future arrivals is uniform across lanes of the intersection. This queue-based model only tracks the number of lower- and higher-bidding users on access lanes, and the number of empty lanes. The uniformness assumption is relaxed in a second, lane-based model which accounts for lane-specific user arrival probabilities at the expense of an extended state space. We then design a mechanism to determine incentive-compatible payments in the dynamic sense. The resulting online mechanisms maximize social welfare in the long run. Numerical experiments on a four-lane traffic intersection are reported and compared to a static incentive-compatible mechanism. Our findings show that static incentive-compatible mechanisms may lead users to misreport their delay costs. In turn, the proposed online mechanisms are shown to be incentive-compatible in the dynamic sense.

cs.GT↗

arXiv2020

A two-stage algorithm for aircraft conflict resolution with trajectory recovery

As air traffic volume is continuously increasing, it has become a priority to improve traffic control algorithms to handle future air travel demand and improve airspace capacity. We address the conflict resolution problem in air traffic control using a novel approach for aircraft collision avoidance with trajectory recovery. We present a two-stage algorithm that first solves all initial conflicts by adjusting aircraft headings and speeds, before identifying the optimal time for aircraft to recover towards their target destination. The collision avoidance stage extends an existing mixed-integer programming formulation to heading control. For the trajectory recovery stage, we introduce a novel exact mixed-integer programming formulation as well as a greedy heuristic algorithm. The proposed two-stage approach guarantees that all trajectories during both the collision avoidance and recovery stages are conflict-free. Numerical results on benchmark problems show that the proposed heuristic for trajectory recovery is competitive while also emphasizing the difficulty of this optimization problem. The proposed approach can be used as a decision-support tool for introducing automation in air traffic control.

math.OC↗

arXiv2019

Freeway network design with exclusive lanes for automated vehicles under endogenous mobility demand

Automated vehicles (AV) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions. Additional resource allocation at the network level, such as AV-exclusive lanes, can further foster the usage of AVs rendering this mode of travel more attractive than legacy vehicles (LV). However, it is necessary to find the crucial locations in the network where providing these dedicated lanes would reap the maximum benefits. In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on freeway networks which accounts for commuters' demand split among AVs and LVs via a logit model incorporating class-based utilities. We incorporate the link transmission model (LTM) as the underlying traffic flow model due to its computational efficiency for system optimum dynamic traffic assignment. The LTM is modified to integrate two vehicle classes namely, LVs and AVs with a lane-based approach. The presence of binary variables to represent lane design and the logit model for endogenous demand estimation results in a nonconvex mixed-integer nonlinear program (MINLP) formulation. We propose a Benders' decomposition approach to tackle this challenging optimization problem. Our approach iteratively explores possible lane designs in the Benders' master problem and, at each iteration, solves a sequence of system-optimum dynamic traffic assignment (SODTA) problems which is shown to converge to fixed-points representative of logit-compatible demand splits. Further, we prove that the proposed solution method converges to a local optima of the nonconvex problem and identify under which conditions this local optima is a global solution. The proposed approach is implemented on three hypothetical freeway networks with single and multiple origins and destinations.

math.OC↗

arXiv2019

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

We address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the traditional nonlinear conditions for aircraft separation. Further, we characterize conflict-free pairwise aircraft trajectories and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimization formulation that aims to minimize the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimization formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed disjunctive formulations are compared against state-of-the-art formulations based on the so-called shadow separation condition. Our numerical results show that the proposed disjunctive linear separation conditions outperform existing formulations in the literature and can solve significantly more instances to global optimality. For reproducibility purposes, all formulations and instances are made available on a public repository.

math.OC↗

arXiv2019

Integrating Travel Demand and Network Modelling: a Myth or Future of Transport Modelling

In this paper, a novel transport planning model system (TPMS) is formulated which is built on the concepts of supernetworks, multi-modality, integrity and calibration. In the proposed formulation, activity travel pattern (ATP) choice facets including the choices of activity, activity sequence, mode, departure time, and parking location, are all unified into a time-dependent supernetwork. The proposed model accounts for the dynamicity of the network, including time-of-day and congestion effects. These help capturing the interdependencies among all different attributes of a full transport planning system. Moreover, the proposed TPMS explicitly formulates an operating capacitated public transport system. To allow visiting locations multiple times and to alleviate the complexity of the proposed supernetwork, a novel multi-visit vehicle routing problem is proposed which does not enumerate the node and link visits. In order to calibrate the model based on the major travel attributes of the travel survey data, a set of splitting ratios are introduced to distribute trips on the supernetwork. The model uses the splitting ratios to integrate the supernetwork and the traffic assignment model in a unified TPMS structure. At last, numerical examples are provided to demonstrate the advantages of the proposed approach.

physics.soc-ph↗

arXiv2018

Blue Phase: Optimal Network Traffic Control for Legacy and Autonomous Vehicles

With the forecasted emergence of autonomous vehicles in urban traffic networks, new control policies are needed to leverage their potential for reducing congestion. While several efforts have studied the fully autonomous traffic control problem, there is a lack of models addressing the more imminent transitional stage wherein legacy and autonomous vehicles share the urban infrastructure. We address this gap by introducing a new policy for stochastic network traffic control involving both classes of vehicles. We conjecture that network links will have dedicated lanes for autonomous vehicles which provide access to traffic intersections and combine traditional green signal phases with autonomous vehicle-restricted signal phases named blue phases. We propose a new pressure-based, decentralized, hybrid network control policy that activates selected movements at intersections based on the solution of mixed-integer linear programs. We prove that the proposed policy is stable, i.e. maximizes network throughput, under conventional travel demand conditions. We conduct numerical experiments to test the proposed policy under varying proportions of autonomous vehicles. Our experiments reveal that considerable trade-offs exist in terms of vehicle-class travel time based on the level of market penetration of autonomous vehicles. Further, we find that the proposed hybrid network control policy improves on traditional green phase traffic signal control for high levels of congestion, thus helping in quantifying the potential benefits of autonomous vehicles in urban networks.

math.OC↗