We consider the linear third order (in time) PDE known as the SMGTJ-equation, defined on a bounded domain, under the action of either Dirichlet or Neumann boundary control
We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [
- Award ID(s):
- 2112311
- NSF-PAR ID:
- 10326410
- Date Published:
- Journal Name:
- Discrete & Continuous Dynamical Systems
- Volume:
- 42
- Issue:
- 4
- ISSN:
- 1078-0947
- Page Range / eLocation ID:
- 1647
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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\begin{document}$ g $\end{document} 1 ], after [41 ], when\begin{document}$ g \in L^2(0, T;L^2(\Gamma)) \equiv L^2(\Sigma) $\end{document} \begin{document}$ \gamma = 0 $\end{document} 19 ], [17 ], [24 ,Vol Ⅱ]. The interior or boundary regularity theory is however the same, whether\begin{document}$ \gamma = 0 $\end{document} \begin{document}$ 0 \neq \gamma \in L^{\infty}(\Omega) $\end{document} \begin{document}$ \gamma \neq 0 $\end{document} \begin{document}$ g $\end{document} \begin{document}$ L^2(\Sigma) $\end{document} 17 ]. Similarly for the Neumann boundary case, by invoking the corresponding results for the wave equation as in [22 ], [23 ], [37 ] for control smoother than\begin{document}$ L^2(0, T;L^2(\Gamma)) $\end{document} 44 ] for control less regular in space than\begin{document}$ L^2(\Gamma) $\end{document} 42 ], [24 ,Section 9.8.2]. -
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A planned special event (PSE), such as a sports game or a concert, can greatly affect the normal operations of a transportation system. To facilitate traffic, the road network is usually reconfigured, which could include road closures, reversed lanes, and limited access to parking facilities. For recurring PSEs, event-goers are often provided with recommended routes to designated parking areas in advance. Such network reconfiguration and route and parking recommendations are, however, often ad hoc in practice. This paper focuses on the PSE traffic planning problem. We propose to simultaneously consider parking, ridesharing, and network configuration. The problem is formulated as an optimization problem with integer decision variables. We developed a flow-based traffic simulation tool that is able to incorporate parking and lane changing (which cannot be ignored around ridesharing drop-off locations) to evaluate the objective function. We also developed effective and efficient heuristic solution algorithms. The models and algorithms are tested using the real network and traffic data from Super Bowl XLIX in 2015. The results show that our methods and approaches are able to produce an effective comprehensive traffic plan with reasonable computation time. For the Super Bowl XLIX case study, the resulting optimal plan is able to save 39.6% of the total vehicle-hours associated with default network configurations. Sensitivity analysis has also been conducted with respect to the compliance rate of travelers following recommended routes. It is found that the resulting near-optimal PSE traffic plans are able to tolerate some uncertainty in the compliance rate.
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null (Ed.)The main question to address in this paper is to recommend optimal signal timing plans in real time under incidents by incorporating domain knowledge developed with the traffic signal timing plans tuned for possible incidents, and learning from historical data of both traffic and implemented signals timing. The effectiveness of traffic incident management is often limited by the late response time and excessive workload of traffic operators. This paper proposes a novel decision-making framework that learns from both data and domain knowledge to real-time recommend contingency signal plans that accommodate non-recurrent traffic, with the outputs from real-time traffic prediction at least 30 min in advance. Specifically, considering the rare occurrences of engagement of contingency signal plans for incidents, it is proposed to decompose the end-to-end recommendation task into two hierarchical models—real-time traffic prediction and plan association. The connections between the two models are learnt through metric learning, which reinforces partial-order preferences observed from historical signal engagement records. The effectiveness of this approach is demonstrated by testing this framework on the traffic network in Cranberry Township, Pennsylvania, U.S., in 2019. Results show that the recommendation system has a precision score of 96.75% and recall of 87.5% on the testing plan, and makes recommendations an average of 22.5 min lead time ahead of Waze alerts. The results suggest that this framework is capable of giving traffic operators a significant time window to access the conditions and respond appropriately.more » « less
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With the advances in autonomous vehicles and intelligent intersection management systems, traffic lights may be replaced by optimal travel plans calculated for each passing vehicle in the future. While these technological advancements are envisioned to greatly improve travel efficiency, they are still facing various challenging security hurdles since even a single deviation of a vehicle from its assigned travel plan could cause a serious accident if the surrounding vehicles do not take necessary actions in a timely manner. In this paper, we propose a novel security mechanism namely NWADE which can be integrated into existing autonomous intersection management systems to help detect malicious vehicle behavior and generate evacuation plans. In the NWADE mechanism, we introduce the neighborhood watch concept whereby each vehicle around the intersection will serve as a watcher to report or verify the abnormal behavior of any nearby vehicle and the intersection manager. We propose a blockchainbased verification framework to guarantee the integrity and trustworthiness of the individual travel plans optimized for the entire intersection. We have conducted extensive experimental studies on various traffic scenarios, and the experimental results demonstrate the practicality, effectiveness, and efficiency of our mechanism.more » « less
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The aim of this paper is to study the optimal investment problem by using coherent acceptability indices (CAIs) as a tool to measure the portfolio performance. We call this problem the acceptability maximization. First, we study the one-period (static) case, and propose a numerical algorithm that approximates the original problem by a sequence of risk minimization problems. The results are applied to several important CAIs, such as the gain-to-loss ratio, the risk-adjusted return on capital and the tail-value-at-risk based CAI. In the second part of the paper we investigate the acceptability maximization in a discrete time dynamic setup. Using robust representations of CAIs in terms of a family of dynamic coherent risk measures (DCRMs), we establish an intriguing dichotomy: if the corresponding family of DCRMs is recursive (i.e. strongly time consistent) and assuming some recursive structure of the market model, then the acceptability maximization problem reduces to just a one period problem and the maximal acceptability is constant across all states and times. On the other hand, if the family of DCRMs is not recursive, which is often the case, then the acceptability maximization problem ordinarily is a time-inconsistent stochastic control problem, similar to the classical mean-variance criteria. To overcome this form of time-inconsistency, we adapt to our setup the set-valued Bellman's principle recently proposed in [
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/dcds.2021167
