arXiv subjects

Stephen D. Boyles

Publications and source records attributed to Stephen D. Boyles.

13 recordsLinked to original sources

arXiv2026

Spectral analysis of the logit mapping and implications for stochastic user equilibrium algorithms

We analyze the Jacobian of the logit mapping for stochastic user equilibrium (SUE) and use it to develop two improved algorithms for path-based SUE. We show that the Jacobian decomposes into two matrices: one that annihilates differences of feasible path flow vectors, and another whose eigenvalues are all non-positive reals, provided link costs are monotone non-decreasing and separable. Using these properties, we first show that the method of successive averages (MSA) with a small constant step-size $s$ converges linearly at a rate $1-s$, with the largest admissible step-size depending on the eigenvalues of the Jacobian of the logit mapping. Building on this result, we develop an adaptive constant step-size rule that retains the global convergence of MSA while achieving asymptotic linear convergence. Our second algorithm is a Newton-based method using a reformulation of SUE as a root-finding problem. Unlike gradient-projection approaches that operate on the Hessian of the SUE objective function (a dense matrix), our method exploits the structure of the Jacobian of the logit mapping, making computations tractable and removing the need for manifold optimization. Numerical experiments show superlinear convergence on most tested networks, with our methods outperforming existing approaches on large networks or when demand is high. To our knowledge, this article is the first to report runtimes for logit-based SUE on networks as large as Chicago Regional and Philadelphia, providing a benchmark for future algorithmic development.

math.OC↗

arXiv2026

Departure Time Choice with Parametric Heterogeneity: Equilibrium and Instability

Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day dynamics or from one of the simplifying assumptions of the basic model? This paper explores a variant of the basic model with a continuous distribution of schedule delay parameters which we intuitively expect to have more favorable stability properties. To attain tractability we assume a monotonic relationship between earliness and lateness parameters. We first verify the existence and uniqueness of the equilibrium solution for this model. We then study a broad class of day-to-day dynamics satisfying local pressure and order preservation conditions. Our main contribution is a formal proof that, surprisingly, all such day-to-day dynamics in this context are unstable.

cs.GT↗

arXiv2026

Measuring capacities in multimodal maritime port systems with anchorage queues

This paper presents a framework for estimating the capacity of a multimodal maritime port system handling vessels of multiple classes. Port system capacity can be categorized into two distinct types: operating capacity, defined as the maximum number of vessels that can be processed over an extended period under stable operating conditions, and ultimate capacity, defined as the absolute maximum vessel throughput achievable irrespective of stability. Distinguishing between these two capacity measures is critical for long-term planning and resilience analysis, as ports may temporarily operate above sustainable levels following disruptions or during demand surges. Despite the importance of this distinction, existing port capacity models generally do not provide methods to compute port-level capacity estimates that clearly differentiate between operating and ultimate capacity. We introduce methods to estimate both capacity measures for seaport systems. We apply the proposed framework using the Port of Houston, Texas as a case study. Operating capacity is estimated using a parsimonious queueing-theoretic model, while ultimate capacity is estimated by fitting an ordinary differential equation model to simulation outputs. We estimate an operating capacity of approximately 0.9 vph and an ultimate capacity of approximately 1.4 vph for the Port of Houston. Sensitivity analysis of key port resources indicates that liquid-bulk terminals constitute the primary bottlenecks under stable operating conditions, whereas pilot availability becomes the dominant bottleneck following disruptions. These methods can be used in port planning to determine the expected operational and resilience gains of a given infrastructure intervention, or to identify bottlenecks in a complex, multimodal port environment.

stat.ME↗

arXiv2025

A Comparative Study of Spline-Based Trajectory Reconstruction Methods Across Varying Automatic Vehicle Location Data Densities

Automatic vehicle location (AVL) data offers insights into transit dynamics, but its effectiveness is often hampered by inconsistent update frequencies, necessitating trajectory reconstruction. This research evaluates 13 trajectory reconstruction methods, including several novel approaches, using high-resolution AVL data from Austin, Texas. We examine the interplay of four critical factors -- velocity, position, smoothing, and data density -- on reconstruction performance. A key contribution of this study is evaluation of these methods across sparse and dense datasets, providing insights into the trade-off between accuracy and resource allocation. Our evaluation framework combines traditional mathematical error metrics for positional and velocity with practical considerations, such as physical realism (e.g., aligning velocity and acceleration with stopped states, deceleration rates, and speed variability). In addition, we provide insight into the relative value of each method in calculating realistic metrics for infrastructure evaluations. Our findings indicate that velocity-aware methods consistently outperform position-only approaches. Interestingly, we discovered that smoothing-based methods can degrade overall performance in complex, congested urban environments, although enforcing monotonicity remains critical. The velocity constrained Hermite interpolation with monotonicity enforcement (VCHIP-ME) yields optimal results, offering a balance between high accuracy and computational efficiency. Its minimal overhead makes it suitable for both historical analysis and real-time applications, providing significant predictive power when combined with dense datasets. These findings offer practical guidance for researchers and practitioners implementing trajectory reconstruction systems and emphasize the importance of investing in higher-frequency AVL data collection for improved analysis.

cs.RO↗

arXiv2025

Balancing Passenger Transport and Power Distribution: A Distributed Dispatch Policy for Shared Autonomous Electric Vehicles

Shared autonomous electric vehicles can provide on-demand transportation for passengers while also interacting extensively with the electric distribution system. This interaction is especially beneficial after a disaster when the large battery capacity of the fleet can be used to restore critical electric loads. We develop a dispatch policy that balances the need to continue serving passengers (especially critical workers) and the ability to transfer energy across the network. The model predictive control policy tracks both passenger and energy flows and provides maximum passenger throughput if any policy can. The resulting mixed integer linear programming problem is difficult to solve for large-scale problems, so a distributed solution approach is developed to improve scalability, privacy, and resilience. We demonstrate that the proposed heuristic, based on the alternating direction method of multipliers, is effective in achieving near-optimal solutions quickly. The dispatch policy is examined in simulation to demonstrate the ability of vehicles to balance these competing objectives with benefits to both systems. Finally, we compare several dispatch behaviors, demonstrating the importance of including operational constraints and objectives from both the transportation and electric systems in the model.

eess.SY↗

arXiv2025

Transportation Network Analysis, Volume I: Static and Dynamic Traffic Assignment

This book covers static and dynamic traffic assignment models used in transportation planning and network analysis. Traffic assignment is the final step in the traditional planning process, and recent decades have seen many advances in formulating and solving such models. The book discusses classical solution methods alongside recent ones used in contemporary planning software. The primary audience for the book is graduate students new to transportation network analysis, and to this end there are appendices providing general mathematical background, and more specific background in formulating optimization problems. We have also included appendices discussing more general optimization applications outside of traffic assignment. We believe the book is also of interest to practitioners seeking to understand recent advances in network analysis, and to researchers wanting a unified reference for traffic assignment content. A second volume is currently under preparation, and will cover transit, freight, and logistics models in transportation networks. A free PDF version of the text will always be available online at https://sboyles.github.io/blubook.html. We will periodically post updated versions of the text at this link, along with slides and other instructor resources.

math.OC↗

arXiv2022

Electric Vehicle Traveling Salesman Problem with Drone with Partial recharge Policy

In (Zhu et al., 2022), it proposes an electric vehicle traveling salesman problem with drone while assuming that the electric vehicle (EV) is a battery-electric vehicle whose energy could be refreshed in a battery swap station in minutes. In this paper, we extend the work in (Zhu et al., 2022) by relaxing the fixed-time-full-charge assumption, assuming that the EV is a plug-in hybrid electric vehicle that could be partially recharged in a charging station. This problem is named electric vehicle traveling salesman problem with drone with partial recharge policy (EVTSPD-P). A three-index MILP formulation is proposed to solve the EVTSPD-P with linear and non-linear charging functions where the concave time-state-of-charge (SoC) function is approximated using piecewise linear functions, a technique proposed in Montoya et al. (2017) and Zuo et al. (2019). Furthermore, a specially designed adaptive large neighborhood search (ALNS) meta-heuristic, which incorporates constraint programming (CP), is presented to solve EVTSPD-P problem instances of practical size. The numerical analysis results indicate that the proposed ALNS method is more efficient than variable neighborhood search and has an average optimality gap of about 3% when solving instances with ten nodes. Besides, using a piecewise linear function with a six-line-segments approximation has an average of 10.8% less cost than a linear approximation.

math.OC↗

arXiv2022

Electric Vehicle Traveling Salesman Problem with Drone with Fixed-time-full-charge Policy

The idea of deploying electric vehicles and unmanned aerial vehicles (UAVs), also known as drones, to perform "last-mile" delivery in logistics operations has attracted increasing attention in the past few years. In this paper, we propose the electric vehicle traveling salesman problem with drone (EVTSPD), in which the electric vehicle (EV) and the drone perform delivery tasks coordinately while the electric vehicle may need to visit charging stations occasionally to recharge. We further assume that the EV can refresh its energy to full battery capacity with fixed time at charging stations. Thus, the proposed problem is termed EVTSPD-FF. In this paper, an arc-based mixed-integer programming model defined in a multigraph is presented for EVTSPD-FF. An exact branch-and-price (BP) algorithm and a variable neighborhood search heuristic are developed to solve instances with up to 25 customers in one minute. Numerical experiments show that the heuristic is much more efficient than solving the arc-based model using the ILOG CPLEX solver and BP algorithm. A real-world case study on the Austin network and the sensitivity analysis of different parameters are also conducted and presented. The results indicate that drone speed has a more significant effect on delivery time than the EV's driving range.

math.OC↗

arXiv2021

Budget-constrained rail electrification modeling using symmetric traffic assignment -- a North American case study

We consider a budget constrained rail network electrification problem with associated changes in costs of energy usage (via path gradient and curvature), operations, and long-term maintenance. In particular, we consider that freight flows on such a network form a user equilibrium. Interactions between electric and diesel trains on the same corridor are represented with nonseparable link performance functions, which nevertheless have a symmetric Jacobian. This bi-level formulation is solved for the North American railroad network using a genetic algorithm (GA), incorporating domain-specific insights to reduce the number of solutions which must be considered. We analyze solution characteristics and decision-making implications. Results show that broad connectivity would be beneficial for most impact. Increasing demand shifts electrified corridors towards the more populous east and gulf coasts, while increased operational costs results in electrification of routes through mountainous terrains.

math.OC↗

arXiv2021

Unmanned Aerial Vehicle Path Planning for Traffic Estimation and Detection of Non-Recurrent Congestion

Unmanned aerial vehicles (UAVs) provide a novel means of extracting road and traffic information from video data. In particular, by analyzing objects in a video frame, UAVs can detect traffic characteristics and road incidents. Leveraging the mobility and detection capabilities of UAVs, we investigate a navigation algorithm that seeks to maximize information on the road/traffic state under non-recurrent congestion. We propose an active exploration framework that (1) assimilates UAV observations with speed-density sensor data, (2) quantifies uncertainty on the road/traffic state, and (3) adaptively navigates the UAV to minimize this uncertainty. The navigation algorithm uses the A-optimal information measure (mean uncertainty), and it depends on covariance matrices generated by a dual state ensemble Kalman filter (EnKF). In the EnKF procedure, since observations are a nonlinear function of the incident state variables, we use diagnostic variables that represent model predicted measurements. We also present a state update procedure that maintains a monotonic relationship between incident parameters and measurements. We compare the traffic/incident state estimates resulting from the UAV navigation-estimation procedure against corresponding estimates that do not use targeted UAV observations. Our results indicate that UAVs aid in detection of incidents under congested conditions where speed-density data are not informative.

stat.AP↗

arXiv2021

Book-Ahead & Supply Management for Ridesourcing Platforms

Ridesourcing platforms recently introduced the ``schedule a ride'' service where passengers may reserve (book-ahead) a ride in advance of their trip. Reservations give platforms precise information that describes the start time and location of anticipated future trips; in turn, platforms can use this information to adjust the availability and spatial distribution of the driver supply. In this article, we propose a framework for modeling/analyzing reservations in time-varying stochastic ridesourcing systems. We consider that the driver supply is distributed over a network of geographic regions and that book-ahead rides have reach time priority over non-reserved rides. First, we propose a state-dependent admission control policy that assigns drivers to passengers; this policy ensures that the reach time service requirement would be attained for book-ahead rides. Second, given the admission control policy and reservations information in each region, we predict the ``target" number of drivers that is required (in the future) to probabilistically guarantee the reach time service requirement for stochastic non-reserved rides. Third, we propose a reactive dispatching/rebalancing mechanism that determines the adjustments to the driver supply that are needed to maintain the targets across regions. For a specific reach time quality of service, simulation results using data from Lyft rides in Manhattan exhibit how the number of idle drivers decreases with the fraction of book-ahead rides. We also observe that the non-stationary demand (ride request) rate varies significantly across time; this rapid variation further illustrates that time-dependent models are needed for operational analysis of ridesourcing systems.

eess.SY↗

arXiv2020

Time-Equitable Dynamic Tolling Scheme For Single Bottlenecks

Dynamic tolls present an opportunity for municipalities to eliminate congestion and fund infrastructure. Imposing tolls that regulate travel along a public highway through monetary fees raise worries of inequity. In this article, we introduce the concept of time poverty, emphasize its value in policy-making in the same ways income poverty is already considered, and argue the potential equity concern posed by time-varying tolls that produce time poverty. We also compare the cost burdens of a no-toll, system optimal toll, and a proposed ``time-equitable" toll on heterogeneous traveler groups using an analytical Vickrey bottleneck model where travelers make departure time decisions to arrive at their destination at a fixed time. We show that the time-equitable toll is able to eliminate congestion while creating equitable travel patterns amongst traveler groups.

econ.TH↗

arXiv2019

Deep Reinforcement Learning Algorithm for Dynamic Pricing of Express Lanes with Multiple Access Locations

This article develops a deep reinforcement learning (Deep-RL) framework for dynamic pricing on managed lanes with multiple access locations and heterogeneity in travelers' value of time, origin, and destination. This framework relaxes assumptions in the literature by considering multiple origins and destinations, multiple access locations to the managed lane, en route diversion of travelers, partial observability of the sensor readings, and stochastic demand and observations. The problem is formulated as a partially observable Markov decision process (POMDP) and policy gradient methods are used to determine tolls as a function of real-time observations. Tolls are modeled as continuous and stochastic variables, and are determined using a feedforward neural network. The method is compared against a feedback control method used for dynamic pricing. We show that Deep-RL is effective in learning toll policies for maximizing revenue, minimizing total system travel time, and other joint weighted objectives, when tested on real-world transportation networks. The Deep-RL toll policies outperform the feedback control heuristic for the revenue maximization objective by generating revenues up to 9.5% higher than the heuristic and for the objective minimizing total system travel time (TSTT) by generating TSTT up to 10.4% lower than the heuristic. We also propose reward shaping methods for the POMDP to overcome the undesired behavior of toll policies, like the jam-and-harvest behavior of revenue-maximizing policies. Additionally, we test transferability of the algorithm trained on one set of inputs for new input distributions and offer recommendations on real-time implementations of Deep-RL algorithms. The source code for our experiments is available online at https://github.com/venktesh22/ExpressLanes_Deep-RL

eess.SY↗