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Coordinating dynamical routes with statistical physics on space-time networks

Physical Review E 2019年第4期99卷 042123-042123页

作者： Chi Ho Yeung Department of Science and Environmental Studies The Education University of Hong Kong Tai Po Hong Kong China

Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static or without intervehicle coordination. In this paper, we first apply the cavity approach in statistical physics to derive the theoretical behavior and an optimization algorithm for dynamical route coordination, but they become computationally intractable as the number of time segments increases. We therefore map static spatial networks to space-time networks to derive a computational feasible message-passing algorithm compatible with arbitrary system parameters; it agrees well with the analytical and algorithmic results of the conventional cavity approach and outperforms multistart greedy search in saving total travel time by as much as 15% in simulations. The study sheds light on the design of dynamical route coordination protocols and the solution to other dynamical problems via static analytical approaches on space-time networks.

关键词： network flow network flow optimization Transportation networks Disordered systems Cavity methods

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Risk-based inventory scheduling framework to fulfill multi-product orders within a production network

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期182卷

作者： Bourgeois, Christopher M. Soltanisehat, Leili Barker, Kash Gonzalez, Andres D. Univ Oklahoma Sch Ind & Syst Engn Norman OK 73019 USA Univ Massachusetts Charlton Coll Business Dept Decis & Informat Sci Dartmouth MA USA

Production facilities are critical components of the global economy and supply chain. Firms are forced to balance several competing objectives-from reducing operating costs by managing inventory to increasing profits by satisfying customer demand. The act of scheduling material through an interconnected production network is analytically challenging;therefore, stakeholders require statistical insights to strengthen the decision-making process. This inventory scheduling application allows decision-makers to monitor the status and impact of numerous production parameters while aiming to mitigate the propagation of schedule risk through the system. This work presents a material planning framework that (i) jointly represents work center and material relationships and (ii) integrates stochastic methods to assess potential risk. Using network flow optimization and Monte Carlo simulation, this work accommodates three primary considerations: (i) safety stock, and other inventory restrictions, (ii) multi-product order satisfaction, and (iii) costs derived from holding inventory and delaying orders. An illustrative example examines the impact of twelve experimental scenarios on order fulfillment, work center utilization, and material inventory and production.

关键词： Material requirements planning Monte Carlo simulation network flow optimization Production schedule risk

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Sustainable optimal transport in multilayer networks

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Physical Review E 2022年第6期105卷 064302-064302页

作者： Abdullahi Adinoyi Ibrahim Daniela Leite Caterina De Bacco Max Planck Institute for Intelligent Systems Cyber Valley Tübingen 72076 Germany

Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economic and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer network infrastructures is imperative. We consider an approach based on optimal transport theory to route passengers preferably along layers that are more carbon-efficient than the road, e.g., rails. By analyzing the impact of this choice on performance, we find that this approach reduces carbon emissions considerably compared to shortest-path minimization. Similarly, we find that this approach distributes traffic more homogeneously, thus alleviating the risk of traffic congestion. Our results shed light on the impact of distributing traffic flexibly across layers guided by optimal transport theory.

关键词： network flow network flow optimization Traffic Transport in networks Multilayer & multiplex networks Transportation networks

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Congestion Induced by the Structure of Multiplex networks

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Physical Review Letters 2016年第10期116卷 108701-108701页

作者： Albert Solé-Ribalta Sergio Gómez Alex Arenas Departament d’Enginyeria Informàtica i Matemàtiques Universitat Rovira i Virgili 43007 Tarragona Spain

Multiplex networks are representations of multilayer interconnected complex networks where the nodes are the same at every layer. They turn out to be good abstractions of the intricate connectivity of multimodal transportation networks, among other types of complex systems. One of the most important critical phenomena arising in such networks is the emergence of congestion in transportation flows. Here, we prove analytically that the structure of multiplex networks can induce congestion for flows that otherwise would be decongested if the individual layers were not interconnected. We provide explicit equations for the onset of congestion and approximations that allow us to compute this onset from individual descriptors of the individual layers. The observed cooperative phenomenon is reminiscent of Braess’ paradox in which adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. Similarly, in the multiplex structure, the efficiency in transportation can unbalance the transportation loads resulting in unexpected congestion.

关键词： Complex systems network flow optimization Scaling laws of complex systems Transport in networks Multilayer & multiplex networks Transportation networks

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Effective traffic-flow assignment strategy on multilayer networks

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Physical Review E 2019年第1期100卷 012310-012310页

作者： Lei Gao Panpan Shu Ming Tang Wei Wang Hui Gao College of Information Science and Engineering Shandong Agricultural University Taian 271018 China Web Sciences Center University of Electronic Science and Technology of China Chengdu 610054 China School of Sciences Xi'an University of Technology Xi'an 710054 China School of Mathematical Sciences Shanghai Key Laboratory of PMMP East China Normal University Shanghai 200241 China Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University Shanghai 200241 China Cybersecurity Research Institute Sichuan University Chengdu 610065 China

An efficient flow assignment strategy is of great importance to alleviate traffic congestion on multilayer networks. In this work, by considering the roles of nodes' local structures on the microlevel, and the different transporting speeds of layers in the macrolevel, an effective traffic-flow assignment strategy on multilayer networks is proposed. Both numerical and semianalytical results indicate that our proposed flow assignment strategy can reasonably redistribute the traffic flow of the low-speed layer to the high-speed layer. In particular, preferentially transporting the packets through small-degree nodes on the high-speed layer can enhance the traffic capacity of multilayer networks. We also find that the traffic capacity of multilayer networks can be improved by increasing the network size and the average degree of the high-speed layer. For a given multilayer network, there is a combination of optimal macrolevel parameter and optimal microlevel parameter with which the traffic capacity can be maximized. It is verified that real-world network topology does not invalidate the results. The semianalytical predictions agree with the numerical simulations.

关键词： Collective behavior in networks Continuous phase transition network flow optimization Multilayer & multiplex networks Transportation networks Betweenness Monte Carlo methods

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Optimal Transport flows for Distributed Production networks

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Physical Review Letters 2020年第20期124卷 208101-208101页

作者： Julius B. Kirkegaard Kim Sneppen Niels Bohr Institute University of Copenhagen 2100 Copenhagen Denmark

network flows often exhibit a hierarchical treelike structure that can be attributed to the minimization of dissipation. The common feature of such systems is a single source and multiple sinks (or vice versa). In contrast, here we study networks with only a single source and sink. These systems can arise from secondary purposes of the networks, such as blood sugar regulation through insulin production. Minimization of dissipation in these systems leads to vascular shunting, a single vessel connecting the inlet and outlet. We show instead how optimizing the transport time yields network topologies that match those observed in the insulin-producing pancreatic islets. These are patterns of periphery-to-center and center-to-periphery flows. The obtained flow networks are broadly independent of how the flow velocity depends on the flow flux, but continuous and discontinuous phase transitions appear at extreme flux dependencies. Lastly, we show how constraints on flows can lead to buckling of the branches of the network, a feature that is also observed in pancreatic islets.

关键词： Developmental pattern formation network flow optimization network phase transitions Physiological flows Cardiovascular networks Endocrine system Vascular system

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DISTRIBUTION-BASED OPTION PRICING ON LATTICE ASSET DYNAMICS MODELS

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International Journal of Theoretical and Applied Finance 2002年第6期5卷 599-618页

作者： YUJI YAMADA JAMES A. PRIMBS Graduate School of Business Sciences University of Tsukuba 3-29-1 Otsuka Bunkyo-ku Tokyo 112-0012 Japan Management Science and Engineering Stanford University Terman Engineering Center 700-327 CA 94305-4026 USA

In this paper, we propose a numerical option pricing method based on an arbitrarily given stock distribution. We first formulate a European call option pricing problem as an optimal hedging problem by using a lattice based incomplete market model. A dynamic programming technique is then applied to solve the mean square optimal hedging problem for the discrete time multi-period case by assigning suitable probabilities on the lattice, where the underlying stock price distribution is derived directly from empirical stock price data which may possess "heavy tails". We show that these probabilities are obtained from a network flow optimization which can be solved efficiently by quadratic programming. A computational complexity analysis demonstrates that the number of iterations for dynamic programming and the number of parameters in the network flow optimization are both of square order with respect to the number of periods. Numerical experiments illustrate that our methodology generates the implied volatility smile.

关键词： Incomplete markets Lattice models Minimum mean square hedges Dynamic programming network flow optimization

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Scalable node-disjoint and edge-disjoint multiwavelength routing

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Physical Review E 2022年第4期105卷 044316-044316页

作者： Yi-Zhi Xu Ho Fai Po Chi Ho Yeung David Saad The Nonlinearity and Complexity Research Group Aston University Birmingham B4 7ET United Kingdom Department of Science and Environmental Studies The Education University of Hong Kong 10 Lo Ping Road Taipo Hong Kong

Probabilistic message-passing algorithms are developed for routing transmissions in multiwavelength optical communication networks, under node- and edge-disjoint routing constraints and for various objective functions. Global routing optimization is a hard computational task on its own but is made much more difficult under the node- and edge-disjoint constraints and in the presence of multiple wavelengths, a problem which dominates routing efficiency in real optical communication networks that carry most of the world's internet traffic. The scalable principled method we have developed is exact on trees but provides good approximate solutions on locally treelike graphs. It accommodates a variety of objective functions that correspond to low latency, load balancing, and consolidation of routes and can be easily extended to include heterogeneous signal-to-noise values on edges and a restriction on the available wavelengths per edge. It can be used for routing and managing transmissions on existing topologies as well as for designing and modifying optical communication networks. Additionally, it provides the tool for settling an open and much-debated question on the merit of wavelength-switching nodes and the added capabilities they provide. The methods have been tested on generated networks such as random-regular, Erdős Rényi, and power-law graphs, as well as on optical communication networks in the United Kingdom and United States. They show excellent performance with respect to existing methodology on small networks and have been scaled up to network sizes that are beyond the reach of most existing algorithms.

关键词： Computational complexity NP-hard problems network flow network flow optimization

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Cracking urban mobility

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Physical Review Research 2020年第4期2卷 043132-043132页

作者： H. A. Carmona A. W. T. de Noronha A. A. Moreira N. A. M. Araújo J. S. Andrade, Jr. Departamento de Física Universidade Federal do Ceará 60451-970 Fortaleza Ceará Brazil Instituto de Ciências Exatas e da Natureza Universidade da Integracão Internacional da Lusofonia Afro-Brasileira 62785-000 Acarape Ceará Brazil Departamento de Física Faculdade de Ciências Universidade de Lisboa 1749-016 Lisboa Portugal Centro de Física Teórica e Computacional Universidade de Lisboa 1749-016 Lisboa Portugal

Assessing the resilience of a road network is instrumental to improve existing infrastructures and design new ones. Here, we apply the optimal path crack model (OPC) to investigate the mobility of road networks and propose a new proxy for resilience of urban mobility. In contrast to static approaches, the OPC accounts for the dynamics of rerouting as a response to traffic jams. Precisely, one simulates a sequence of failures (cracks) at the most vulnerable segments of the optimal origin-destination paths that are capable to collapse the system. Our results with synthetic and real road networks reveal that their levels of disorder, fractions of unidirectional segments and spatial correlations can drastically affect the vulnerability to traffic congestion. By applying the OPC to downtown Boston and Manhattan, we found that Boston is significantly more vulnerable than Manhattan. This is compatible with the fact that Boston heads the list of American metropolitan areas with the highest average time waste in traffic. Moreover, our analysis discloses that the origin of this difference comes from the intrinsic spatial correlations of each road network. Finally, we argue that, due to their global influence, the most important cracks identified with OPC can be used to pinpoint potential small rerouting and structural changes in road networks that are capable to substantially improve urban mobility.

关键词： network flow optimization network resilience Traffic Transportation research Road networks Data analysis Finite-size scaling

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Revealing structure-function relationships in functional flow networks via persistent homology

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Physical Review Research 2020年第3期2卷 033234-033234页

作者： Jason W. Rocks Andrea J. Liu Eleni Katifori Department of Physics and Astronomy University of Pennsylvania Philadelphia Pennsylvania 19104 USA

Complex networks encountered in biology are often characterized by significant structural diversity. Whether due to differences in the three-dimensional structure of allosteric proteins, or the variation among the microscale structures of organisms' cerebral vasculature systems, identifying relationships between structure and function often poses a difficult challenge. Here we showcase an approach to characterizing structure-function relationships in complex networks applied in the context of flow networks tuned to perform specific functions. Using persistent homology, we analyze flow networks tuned to perform complex multifunctional tasks, answering the question of how local changes in the network structure coordinate to create functionality at the scale of the entire network. We find that the response of such networks encodes hidden topological features—sectors of uniform pressure—that are not apparent in the underlying network architectures. Regardless of differences in local connectivity, these features provide a universal topological description for all networks that perform these types of functions. We show that these features correlate strongly with the tuned response, providing a clear topological relationship between structure and function and structural insight into the limits of multifunctionality.

关键词： network flow network flow optimization network structure Biological networks Functional materials Vascular system Topological tools Topology

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