Online Estimation of Dynamic Origin-Destination Matrices Using Reinforcement Learning with Link-Flow Propagation Guidance
Donggyu MinDong-Kyu Kim
Sep 2026
Artificial IntelligenceMachine Learning
Abstract
Online dynamic origin-destination (OD) matrix estimation (DODE) calibrates time-dependent OD demand to reproduce observed link-flow trajectories. In online, OD demand should be estimated from current observations and propagated network states while subsequent observations and stochastic dynamic network loading (DNL) outcomes remain uncertain. Recently, reinforcement learning (RL) has emerged as a promising alternative, reducing computational burden by replacing iterative algorithms while being applicable to stochastic environments. However, because the policy is trained offline and deployed online, it must handle varying target link-flow trajectories; since each target trajectory defines the link-flow error used in the reward, the same OD demand vector can require different adjustments, making conventional scalar feedback ambiguous. To address this gap, this study proposes LFPG-RL, which integrates link-flow propagation guidance (LFPG) into proximal policy optimization (PPO). LFPG combines link-flow error sensitivities with the contribution of each OD-time demand component to simulated link flows, transforming aggregate mismatch into OD-specific advantage shaping for PPO actor updates. At deployment, the policy requires only a single forward pass. LFPG-RL is developed and evaluated on 250 weekday trajectories of 15-min link-flow data from a Melbourne arterial network modeled by a link transmission model with stochastic route choice. On held-out trajectories, LFPG-RL achieved an RMSE of 4.69, MAPE of 20.15%, and Pearson correlation of 0.995. These results support the contention that our method is a more efficient and accurate online OD demand calibration method compared to existing ones.
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
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Carmine Giardino, Xiaofeng Wang, P. Abrahamsson· International Conference on...· 174 citations· ⚡19
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Anh Nguyen-Duc, P. Abrahamsson· International Conference on...· 92 citations· ⚡9
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