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Optimizing Throughput and Makespan of Queuing Systems by Information Design

Authors Svenja M. Griesbach , Max Klimm , Philipp Warode , Theresa Ziemke

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Author Details

Svenja M. Griesbach
  • Institute of Mathematics, Technische Universität Berlin, Germany
Max Klimm
  • Institute of Mathematics, Technische Universität Berlin, Germany
Philipp Warode
  • School of Business and Economics, Humboldt-Universität zu Berlin, Germany
Theresa Ziemke
  • Institute of Mathematics, Technische Universität Berlin, Germany

Funding

Supported by Deutsche Forschungsgemeinschaft(DFG, German Research Foundation) under Germany’s Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project IDs: 390685689).

Acknowledgements

We thank Martin Hoefer and the other participants of Dagstuhl seminar 22192 "Dynamic Traffic Models in Transportation Science" for inspiration and discussions.

Cite AsGet BibTex

Svenja M. Griesbach, Max Klimm, Philipp Warode, and Theresa Ziemke. Optimizing Throughput and Makespan of Queuing Systems by Information Design. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 62:1-62:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.62

Abstract

We study the optimal provision of information for two natural performance measures of queuing systems: throughput and makespan. A set of parallel links (queues) is equipped with deterministic capacities and stochastic offsets where the latter depend on a realized state, and the number of states is assumed to be constant. A continuum of flow particles (agents) arrives at the system at a constant rate. A system operator knows the realization of the state and may (partially) reveal this information via a public signaling scheme to the flow particles. Upon arrival, the flow particles observe the signal issued by the system operator, form an updated belief about the realized state, and decide on which link they use. Inflow into a link exceeding the link’s capacity builds up in a queue that increases the cost (total travel time) on the link. Dynamic inflow rates are in a Bayesian dynamic equilibrium when the expected cost along all links with positive inflow is equal at every point in time and not larger than the expected cost of any unused link. For a given time horizon T, the throughput induced by a signaling scheme is the total volume of flow that leaves the links in the interval [0,T]. The public signaling scheme maximizing the throughput may involve irrational numbers. We provide an additive polynomial time approximation scheme (PTAS) that approximates the optimal throughput by an arbitrary additive constant ε > 0. The algorithm solves a Lagrangian dual of the signaling problem with the Ellipsoid method whose separation oracle is implemented by a cell decomposition technique. We also provide a multiplicative fully polynomial time approximation scheme (FPTAS) that does not rely on strong duality and, thus, allows to compute the optimal signals. It uses a different cell decomposition technique together with a piecewise convex under-estimator of the optimal value function. Finally, we consider the makespan of a Bayesian dynamic equilibrium which is defined as the last point in time when a total given value of flow leaves the system. Using a variational inequality argument, we show that full information revelation is a public signaling scheme that minimizes the makespan.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Theory of computation → Nonconvex optimization
  • Applied computing → Transportation
Keywords
  • Information Design
  • Dynamic Flows
  • Public Signals
  • Convex Envelope

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References

  1. Daron Acemoglu, Ali Makhdoumi, Azarakhsh Malekian, and Asuman Ozdaglar. Informational Braess' paradox: The effect of information on traffic congestion. Oper. Res., 66(4):893-917, 2018. Google Scholar
  2. David Avis and Komei Fukuda. Reverse search for enumeration. Discret. Appl. Math., 65:21-46, 1996. Google Scholar
  3. Dirk Bergemann and Stephen Morris. Information design: A unified perspective. J. Econ. Lit., 57:44-59, 2019. Google Scholar
  4. Umang Bhaskar, Yu Cheng, Young Kun Ko, and Chaitanya Swamy. Hardness results for signaling in Bayesian zero-sum and network routing games. In Proc. 17th Conf. Econ. Comput. (EC), pages 479-496, 2016. Google Scholar
  5. Umang Bhaskar, Lisa Fleischer, and Elliot Anshelevich. A Stackelberg strategy for routing flow over time. Games Econ. Behav., 92:232-247, 2015. Google Scholar
  6. Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004. Google Scholar
  7. Robert C. Buck. Partition of space. Amer. Math. Monthly, 50(9):541-544, 1943. Google Scholar
  8. Matteo Castiglioni, Andrea Celli, Alberto Marchesi, and Nicola Gatti. Signaling in Bayesian network congestion games: the subtle power of symmetry. In Proc. 35th Conf. Artif. Intell. (AAAI), pages 5252-5259, 2021. Google Scholar
  9. Yu Cheng, Ho Yee Cheung, Shaddin Dughmi, Ehsan Emamjomeh-Zadeh, Li Han, and Shang-Hua Teng. Mixture selection, mechanism design, and signaling. In Venkatesan Guruswami, editor, Proc. 56th Symp. Found. Comput. Sci. (FOCS), pages 1426-1445, 2015. Google Scholar
  10. Roberto Cominetti, José R. Correa, and Omar Larré. Dynamic equilibria in fluid queueing networks. Oper. Res., 63(1):21-34, 2015. Google Scholar
  11. Roberto Cominetti, José R. Correa, and Neil Olver. Long-term behavior of dynamic equilibria in fluid queuing networks. Oper. Res., 70(1):516-526, 2022. Google Scholar
  12. José R. Correa, Andrés Cristi, and Tim Oosterwijk. On the price of anarchy for flows over time. Math. Oper. Res., 47(2):1394-1411, 2022. Google Scholar
  13. Sanmay Das, Emir Kamenica, and Renee Mirka. Reducing congestion through information design. In Proc. 55th Annual Allerton Conference on Communication, Control, and Computing, 2017. Google Scholar
  14. Shaddin Dughmi. On the hardness of signaling. In Proc. 55th Symp. Found. Comput. Sci. (FOCS), pages 354-363, 2014. Google Scholar
  15. Lukas Graf, Tobias Harks, Kostas Kollias, and Michael Markl. Machine-learned prediction equilibrium for dynamic traffic assignment. In Proc. 36th Conf. Artif. Intell. (AAAI), pages 5059-5067, 2022. Google Scholar
  16. Lukas Graf, Tobias Harks, and Leon Sering. Dynamic flows with adaptive route choice. Math. Program., 183(1):309-335, 2020. Google Scholar
  17. Svenja M. Griesbach, Martin Hoefer, Max Klimm, and Tim Koglin. Public signals in network congestion games. In David M. Pennock, Ilya Segal, and Sven Seuken, editors, Proc. 23rd Conf. Econ. Comput. (EC), page 736, 2022. Google Scholar
  18. Martin Grötschel, László Lovász, and Alexander Schrijver. Geometric Algorithms and Combinatorial Optimization. Springer, Berlin, Heidelberg, Germany, 1988. Google Scholar
  19. Jonas Israel and Leon Sering. The impact of spillback on the price of anarchy for flows over time. In Tobias Harks and Max Klimm, editors, Proc. 13th Symp. Algorithmic Game Theory (SAGT), pages 114-129. Springer, 2020. Google Scholar
  20. Emir Kamenica and Matthew Gentzkow. Bayesian persuasion. Amer. Econ. Rev., 101(6):2590-2615, 2011. Google Scholar
  21. Ronald Koch and Martin Skutella. Nash equilibria and the price of anarchy for flows over time. Theory Comput. Syst., 49(1):71-97, 2011. Google Scholar
  22. Olivier Massicot and Cedric Langbort. Public signals and persuasion for road network congestion games under vagaries. IFAC-PapersOnLine, 51(34):124-130, 2019. Google Scholar
  23. James Nachbar and Haifeng Xu. The power of signaling and its intrinsic connection to the price of anarchy. In Proc. 3rd Intl. Conf. Distrib. Artif. Intell. (DAI), pages 1-20, 2021. Google Scholar
  24. Neil Olver, Leon Sering, and Laura Vargas Koch. Continuity, uniqueness and long-term behavior of Nash flows over time. In Proc. 62nd Symp. Found. Comput. Sci. (FOCS), pages 851-860, 2021. Google Scholar
  25. Tim Oosterwijk, Daniel Schmand, and Marc Schröder. Bicriteria Nash flows over time. In Kristoffer Arnsfelt Hansen, Tracy Xiao Liu, and Azarakhsh Malekian, editors, Proc. 18th Conf. Web and Internet Econ. (WINE), page 368, 2022. Google Scholar
  26. Leon Sering and Martin Skutella. Multi-source multi-sink Nash flows over time. In Ralf Borndörfer and Sabine Storandt, editors, Proc. 18th Workshop on Algorithmic Approaches for Transportation Modelling (ATMOS), volume 65, pages 12:1-12:20, 2018. Google Scholar
  27. Leon Sering and Laura Vargas Koch. Nash flows over time with spillback. In Timothy M. Chan, editor, Proc. 30th Symp. Discret. Algorithms (SODA), pages 935-945, 2019. Google Scholar
  28. Shoshana Vasserman, Michal Feldman, and Avinatan Hassidim. Implementing the wisdom of Waze. In Proc. 24th Int. Joint Conf. Artif. Intell. (IJCAI), pages 660-660, 2015. Google Scholar
  29. William S. Vickrey. Congestion theory and transport investment. Am. Econ. Rev., 59(2):161-179, 1969. Google Scholar
  30. Manxi Wu, Saurabh Amin, and Asuman Ozdaglar. Value of information in Bayesian routing games. Oper. Res., 69(1):148-163, 2021. Google Scholar
  31. Haifeng Xu. On the tractability of public persuasion with no externalities. In Proc. 31st Symp. Discret. Algorithms (SODA), pages 2708-2727, 2020. Google Scholar
  32. Chenghan Zhou, Thanh H. Nguyen, and Haifeng Xu. Algorithmic information design in multi-player games: Possibility and limits in singleton congestion. In Proc. 23rd Conf. Econ. Comput. (EC), page 869, 2022. Google Scholar
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