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001476627 019__ $$a1393137718
001476627 020__ $$a9783031255649
001476627 020__ $$a303125564X
001476627 020__ $$z3031255623
001476627 020__ $$z9783031255625
001476627 0247_ $$a10.1007/978-3-031-25564-9$$2doi
001476627 035__ $$aSP(OCoLC)1393309204
001476627 040__ $$aEBLCP$$beng$$cEBLCP$$dYDX$$dGW5XE$$dOCLCO
001476627 049__ $$aISEA
001476627 050_4 $$aHE336.T68
001476627 08204 $$a388.3/1$$223/eng/20230815
001476627 1001_ $$aFriesz, Terry L.,$$d1949-$$eauthor.
001476627 24510 $$aDynamic network user equilibrium /$$cTerry L. Friesz, Ke Han.
001476627 260__ $$aCham, Switzerland :$$bSpringer,$$c[2022]
001476627 300__ $$a1 online resource (401 p.).
001476627 4901_ $$aComplex Networks and Dynamic Systems ;$$vvolume 5
001476627 500__ $$aDescription based upon print version of record.
001476627 500__ $$a3.3.2 Variational Inequality Problem Equivalent to DUE with Elastic Demand
001476627 504__ $$aIncludes bibliographical references and index.
001476627 5050_ $$aIntro -- Preface -- Contents -- 1 Introduction -- 1.1 Introduction -- 1.2 Some DTA and DUE Literature -- 1.3 Vocabulary of DUE Modeling -- 1.4 Alternative Formulations of DUE -- 1.5 The Structure of DUE Models -- 1.6 Dynamic Network Loading Models -- 1.6.1 Vickrey's Model of a Traffic Bottleneck and Its Extension -- 1.6.2 Network Loading Based on Link Dynamics -- 1.6.3 Network Loading as a LWR-Based PDAE System -- 1.6.3.1 The Perakis-Kachani DNL Models -- 1.6.3.2 The Han-Friesz Within-Link Dynamicsfor DNL -- 1.6.4 Network Loading Based on the CTM
001476627 5058_ $$a1.6.5 Network Loading Based on the Variational Approach -- 1.6.6 LWR Network Loading Based on Closed-Form Operators -- 1.6.7 Dynamic User Equilibrium in Continuous Time -- 1.6.8 Dynamic User Equilibrium in Discrete Time -- 1.7 Other Considerations in Classifying DUE Models -- 1.8 Unresolved/Partially Resolved Fundamental Challenges -- References and Suggested Reading -- 2 Mathematical Preliminaries -- 2.1 Selected Topics in Functional Analysis -- 2.1.1 Hilbert Spaces -- 2.1.2 Topological Vector Spaces -- 2.1.3 Compactness -- 2.1.4 The Contraction Mapping Theorem -- 2.2 Nonlinear Programming
001476627 5058_ $$a2.2.1 Nonlinear Program Defined -- 2.2.2 The Fritz John Conditions -- 2.2.3 The Kuhn-Tucker Conditions -- 2.2.4 Kuhn-Tucker Conditions Sufficient -- 2.2.5 Kuhn-Tucker Conditions for Variational Inequalities -- 2.3 Calculus of Variations -- 2.3.1 The Space C1[t0,tf] -- 2.3.2 The Concept of a Variation -- 2.4 Optimal Control -- 2.4.1 The State Operator -- 2.4.2 Necessary Conditions for Continuous-TimeOptimal Control -- 2.4.3 Sufficiency in Optimal Control -- 2.4.3.1 The Mangasarian Theorem -- 2.4.3.2 The Arrow Theorem -- 2.5 Differential Variational Inequalities -- 2.5.1 Problem Definition
001476627 5058_ $$a2.5.2 Regularity Conditions for DIV -- 2.5.3 Necessary Conditions -- 2.6 Nash Games and Differential Nash Games -- 2.6.1 Nash Equilibria and Normal Form Games -- 2.6.2 Differential Nash Games and Differential Nash Equilibria -- 2.6.3 Generalized Differential Nash Equilibria -- 2.7 The Scalar Conservation Law -- 2.7.1 Definition and Examples of the Scalar Conservation Law -- 2.7.2 Characteristics, Shock Waves, and Weak Solutions -- 2.7.3 Non-uniqueness of Integral Solutions, EntropyConditions -- 2.8 The Hamilton-Jacobi Equations and the Variational Principle -- 2.8.1 The Hamilton-Jacobi Equation
001476627 5058_ $$a2.8.2 The Variational Theory -- 2.8.2.1 The Classical Lax-Hopf Formula -- 2.8.2.2 The Generalized Lax-Hopf Formula -- References and Suggested Reading -- 3 The Variational Inequality Formulation of Dynamic User Equilibria -- 3.1 Notation and Essential Background -- 3.2 The VI Formulation of DUE with Fixed Demand -- 3.2.1 Definition of DUE with Fixed Demand -- 3.2.2 Variational Inequality Problem Equivalent to DUE with Fixed Demand -- 3.3 The VI Formulation of DUE with Elastic Demand -- 3.3.1 Definition of DUE with Elastic Demand
001476627 506__ $$aAccess limited to authorized users.
001476627 520__ $$aThis book presents advanced research in a relatively new field of scholarly inquiry that is usually referred to as dynamic network user equilibrium, now almost universally abbreviated as DUE. It provides the first synthesis of results obtained over the last decade from applying the differential variational inequality (DVI) formalism to study the DUE problem. In particular, it explores the intimately related problem of dynamic network loading, which determines the arc flows and effective travel delays (or generalized travel costs) arising from the expression of departure rates at the origins of commuter trips between the workplace and home. In particular, the authors show that dynamic network loading with spillback of queues into upstream arcs may be formulated as a differential algebraic equation system. They demonstrate how the dynamic network loading problem and the dynamic traffic user equilibrium problem may be solved simultaneously rather than sequentially, as well as how the first-in-first-out queue discipline may be maintained for each when Lighthill-Whitham-Richardson traffic flow theory is used. A number of recent and new extensions of the DVI-based theory of DUE and corresponding examples are presented and discussed. Relevant mathematical background material is provided to make the book as accessible as possible.
001476627 650_0 $$aTraffic assignment$$xMathematical models.
001476627 650_0 $$aTraffic flow$$xMathematical models.
001476627 650_0 $$aTraffic estimation$$xMathematical models.
001476627 650_6 $$aCirculation$$xAffectation$$xModèles mathématiques.
001476627 650_6 $$aCirculation$$xModèles mathématiques.
001476627 650_6 $$aCirculation$$xEstimation$$xModèles mathématiques.
001476627 655_0 $$aElectronic books.
001476627 7001_ $$aHan, Ke,$$eauthor.
001476627 77608 $$iPrint version:$$aFriesz, Terry L.$$tDynamic Network User Equilibrium$$dCham : Springer International Publishing AG,c2023$$z9783031255625
001476627 830_0 $$aComplex networks and dynamic systems ;$$vv. 5.
001476627 852__ $$bebk
001476627 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-25564-9$$zOnline Access$$91397441.1
001476627 909CO $$ooai:library.usi.edu:1476627$$pGLOBAL_SET
001476627 980__ $$aBIB
001476627 980__ $$aEBOOK
001476627 982__ $$aEbook
001476627 983__ $$aOnline
001476627 994__ $$a92$$bISE