Algorithms for flows over time with scheduling costs

Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting whic...

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Veröffentlicht in:Mathematical programming Jg. 192; H. 1-2; S. 177 - 206
Hauptverfasser: Frascaria, Dario, Olver, Neil
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Calculus of Variations and Optimal Control; Optimization
Combinatorial analysis
Combinatorics
Full Length Paper
Game theory
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Scheduling
Theoretical
Flows over time
Secondary: 05C21
90B20
Tolls
Traffic
Primary: 90C27
ISSN:0025-5610, 1436-4646
Online-Zugang:Volltext
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Zusammenfassung:Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01725-z