arXiv subjects

Debojjal Bagchi

Publications and source records attributed to Debojjal Bagchi.

3 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↗

arXiv2025

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↗

arXiv2024

A Bi-criterion Steiner Traveling Salesperson Problem with Time Windows for Last-Mile Electric Vehicle Logistics

This paper addresses the problem of energy-efficient and safe routing of last-mile electric freight vehicles. With the rising environmental footprint of the transportation sector and the growing popularity of E-Commerce, freight companies are likely to benefit from optimal time-window-feasible tours that minimize energy usage while reducing traffic conflicts at intersections and thereby improving safety. We formulate this problem as a Bi-criterion Steiner Traveling Salesperson Problem with Time Windows (BSTSPTW) with energy consumed and the number of left turns at intersections as the two objectives while also considering regenerative braking capabilities. We first discuss an exact mixed-integer programming model with scalarization to enumerate points on the efficiency frontier for small instances. For larger networks, we develop an efficient local search-based heuristic, which uses several operators to intensify and diversify the search process. We demonstrate the utility of the proposed methods using benchmark data and real-world instances from Amazon delivery routes in Austin, US. Comparisons with state-of-the-art solvers shows that our heuristics can generate near-optimal solutions within reasonable time budgets, effectively balancing energy efficiency and safety under practical delivery constraints.

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