IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v55y2007i2p215-225.html
   My bibliography  Save this article

Fast, Fair, and Efficient Flows in Networks

Author

Listed:
  • José R. Correa

    (School of Business, Universidad Adolfo Ibáñez, Av. Presidente Errázuriz 3485, Las Condes, Santiago, Chile)

  • Andreas S. Schulz

    (Sloan School of Management, Massachusetts Institute of Technology, E53-361, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139)

  • Nicolás E. Stier-Moses

    (Graduate School of Business, Columbia University, Uris Hall, Room 418, 3022 Broadway, New York, New York 10027)

Abstract

We study the problem of minimizing the maximum latency of flows in networks with congestion. We show that this problem is NP-hard, even when all arc latency functions are linear and there is a single source and sink. Still, an optimal flow and an equilibrium flow share a desirable property in this situation: All flow-carrying paths have the same length, i.e., these solutions are “fair,” which is in general not true for optimal flows in networks with nonlinear latency functions. In addition, the maximum latency of the Nash equilibrium, which can be computed efficiently, is within a constant factor of that of an optimal solution. That is, the so-called price of anarchy is bounded. In contrast, we present a family of instances with multiple sources and a single sink for which the price of anarchy is unbounded, even in networks with linear latencies. Furthermore, we show that an s - t -flow that is optimal with respect to the average latency objective is near-optimal for the maximum latency objective, and it is close to being fair. Conversely, the average latency of a flow minimizing the maximum latency is also within a constant factor of that of a flow minimizing the average latency.

Suggested Citation

  • José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2007. "Fast, Fair, and Efficient Flows in Networks," Operations Research, INFORMS, vol. 55(2), pages 215-225, April.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:2:p:215-225
    DOI: 10.1287/opre.1070.0383
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1070.0383
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1070.0383?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Olaf Jahn & Rolf H. Möhring & Andreas S. Schulz & Nicolás E. Stier-Moses, 2005. "System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion," Operations Research, INFORMS, vol. 53(4), pages 600-616, August.
    2. L. R. Ford & D. R. Fulkerson, 1958. "Constructing Maximal Dynamic Flows from Static Flows," Operations Research, INFORMS, vol. 6(3), pages 419-433, June.
    3. John J. Jarvis & H. Donald Ratliff, 1982. "Note---Some Equivalent Objectives for Dynamic Network Flow Problems," Management Science, INFORMS, vol. 28(1), pages 106-109, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Georgia Perakis & Wei Sun, 2014. "Efficiency Analysis of Cournot Competition in Service Industries with Congestion," Management Science, INFORMS, vol. 60(11), pages 2684-2700, November.
    2. Feng, Zengzhe & Gao, Ziyou & Sun, Huijun, 2014. "Bounding the inefficiency of atomic splittable selfish traffic equilibria with elastic demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 63(C), pages 31-43.
    3. Sanjiv Kapoor & Junghwan Shin, 2020. "Price of Anarchy in Networks with Heterogeneous Latency Functions," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 755-773, May.
    4. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Post-Print halshs-00983085, HAL.
    5. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Phase transitions of the price-of-anarchy function in multi-commodity routing games," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    6. Yao, Jia & Cheng, Ziyi & Chen, Anthony, 2023. "Bibliometric analysis and systematic literature review of the traffic paradoxes (1968–2022)," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    7. Correa, José R. & Schulz, Andreas S. & Stier-Moses, Nicolás E., 2008. "A geometric approach to the price of anarchy in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 457-469, November.
    8. Werth, T.L. & Holzhauser, M. & Krumke, S.O., 2014. "Atomic routing in a deterministic queuing model," Operations Research Perspectives, Elsevier, vol. 1(1), pages 18-41.
    9. Parilina, Elena & Sedakov, Artem & Zaccour, Georges, 2017. "Price of anarchy in a linear-state stochastic dynamic game," European Journal of Operational Research, Elsevier, vol. 258(2), pages 790-800.
    10. Manxi Wu & Saurabh Amin & Asuman E. Ozdaglar, 2021. "Value of Information in Bayesian Routing Games," Operations Research, INFORMS, vol. 69(1), pages 148-163, January.
    11. Zhu, Feng & Ukkusuri, Satish V., 2017. "Efficient and fair system states in dynamic transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 272-289.
    12. Bo Chen & Xujin Chen & Xiaodong Hu, 2010. "The price of atomic selfish ring routing," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 258-278, April.
    13. Riccardo Colini-Baldeschi & Roberto Cominetti & Panayotis Mertikopoulos & Marco Scarsini, 2020. "When Is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic," Operations Research, INFORMS, vol. 68(2), pages 411-434, March.
    14. Angelelli, E. & Morandi, V. & Savelsbergh, M. & Speranza, M.G., 2021. "System optimal routing of traffic flows with user constraints using linear programming," European Journal of Operational Research, Elsevier, vol. 293(3), pages 863-879.
    15. Bayram, Vedat & Tansel, Barbaros Ç. & Yaman, Hande, 2015. "Compromising system and user interests in shelter location and evacuation planning," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 146-163.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Urmila Pyakurel & Tanka Nath Dhamala, 2017. "Continuous Dynamic Contraflow Approach for Evacuation Planning," Annals of Operations Research, Springer, vol. 253(1), pages 573-598, June.
    2. Hong Zheng & Yi-Chang Chiu, 2011. "A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem," Transportation Science, INFORMS, vol. 45(1), pages 121-137, February.
    3. Bretschneider, S. & Kimms, A., 2011. "A basic mathematical model for evacuation problems in urban areas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 523-539, July.
    4. Jian Li & Kaan Ozbay, 2015. "Evacuation Planning with Endogenous Transportation Network Degradations: A Stochastic Cell-Based Model and Solution Procedure," Networks and Spatial Economics, Springer, vol. 15(3), pages 677-696, September.
    5. Bretschneider, S. & Kimms, A., 2012. "Pattern-based evacuation planning for urban areas," European Journal of Operational Research, Elsevier, vol. 216(1), pages 57-69.
    6. Hong Zheng & Yi-Chang Chiu & Pitu B. Mirchandani, 2015. "On the System Optimum Dynamic Traffic Assignment and Earliest Arrival Flow Problems," Transportation Science, INFORMS, vol. 49(1), pages 13-27, February.
    7. Nadine Baumann & Martin Skutella, 2009. "Earliest Arrival Flows with Multiple Sources," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 499-512, May.
    8. Tanka Nath Dhamala & Urmila Pyakurel & Ram Chandra Dhungana, 2018. "Abstract Contraflow Models and Solution Procedures for Evacuation Planning," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(4), pages 89-100, August.
    9. Natashia Boland & Mike Hewitt & Luke Marshall & Martin Savelsbergh, 2017. "The Continuous-Time Service Network Design Problem," Operations Research, INFORMS, vol. 65(5), pages 1303-1321, October.
    10. Yu-Ting Hsu & Srinivas Peeta, 2015. "Clearance Time Estimation for Incorporating Evacuation Risk in Routing Strategies for Evacuation Operations," Networks and Spatial Economics, Springer, vol. 15(3), pages 743-764, September.
    11. Yuya Higashikawa & Naoki Katoh, 2019. "A Survey on Facility Location Problems in Dynamic Flow Networks," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 163-208, October.
    12. Elisabeth Lübbecke & Marco E. Lübbecke & Rolf H. Möhring, 2019. "Ship Traffic Optimization for the Kiel Canal," Operations Research, INFORMS, vol. 67(3), pages 791-812, May.
    13. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    14. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    15. S. Khodayifar & M. A. Raayatpanah & P. M. Pardalos, 2019. "A polynomial time algorithm for the minimum flow problem in time-varying networks," Annals of Operations Research, Springer, vol. 272(1), pages 29-39, January.
    16. Zhu, Feng & Ukkusuri, Satish V., 2017. "Efficient and fair system states in dynamic transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 272-289.
    17. H. W. Hamacher & S. Tufekci, 1987. "On the use of lexicographic min cost flows in evacuation modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 487-503, August.
    18. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    19. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    20. Anke Stieber & Armin Fügenschuh, 2022. "Dealing with time in the multiple traveling salespersons problem with moving targets," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 991-1017, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:55:y:2007:i:2:p:215-225. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.