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Dynamic Proportional Sharing: A Game-Theoretic Approach

Published:03 April 2018Publication History
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Abstract

Sharing computational resources amortizes cost and improves utilization and efficiency. When agents pool their resources together, each becomes entitled to a portion of the shared pool. Static allocations in each round can guarantee entitlements and are strategy-proof, but efficiency suffers because allocations do not reflect variations in agents' demands for resources across rounds. Dynamic allocation mechanisms assign resources to agents across multiple rounds while guaranteeing agents their entitlements. Designing dynamic mechanisms is challenging, however, when agents are strategic and can benefit by misreporting their demands for resources.

In this paper, we show that dynamic allocation mechanisms based on max-min fail to guarantee entitlements, strategy-proofness or both. We propose the fbp (FBPA) mechanism and show that it satisfies strategy-proofness and guarantees at least half of the utility from static allocations while providing an asymptotic efficiency guarantee. Our simulations with real and synthetic data show that the performance of the fbp mechanism is comparable to that of state-of-the-art mechanisms, providing agents with at least 0.98x, and on average 15x, of their utility from static allocations. Finally, we propose the T-period mechanism and prove that it satisfies strategy-proofness and guarantees entitlements.

References

  1. Atila Abdulkadirouglu and Kyle Bagwell. 2013. Trust, Reciprocity, and Favors in Cooperative Relationships. American Economic Journal: Microeconomics Vol. 5, 2 (2013), 213--259.Google ScholarGoogle ScholarCross RefCross Ref
  2. Martin Aleksandrov, Haris Aziz, Serge Gaspers, and Toby Walsh. 2015. Online Fair Division: Analysing a Food Bank Problem Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI). 2540--2546. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Martin Aleksandrov and Toby Walsh. 2017. Pure Nash Equilibria in Online Fair Division. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI). 42--48. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Susan Athey and Kyle Bagwell. 2001. Optimal Collusion with Private Information. RAND Journal of Economics Vol. 32, 3 (2001), 428--465.Google ScholarGoogle ScholarCross RefCross Ref
  5. Luiz André Barroso and Urs Hölzle. 2007. The case for energy-proportional computing. Computer, Vol. 40, 12 (2007). Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Garrett Birkhoff. 1946. Tres observaciones sobre el algebra lineal. Univ. Nac. Tucumán Rev. Ser. A Vol. 5 (1946), 147--151.Google ScholarGoogle Scholar
  7. Eric Boutin, Jaliya Ekanayake, Wei Lin, Bing Shi, Jingren Zhou, Zhengping Qian, Ming Wu, and Lidong Zhou. 2014. Apollo: Scalable and coordinated scheduling for cloud-scale computing Proceedings of the 11th USENIX conference on Operating Systems Design and Implementation (OSDI). USENIX Association, 285--300. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Alan Demers, Srinivasan Keshav, and Scott Shenker. 1989. Analysis and simulation of a fair queueing algorithm ACM SIGCOMM Computer Communication Review, Vol. Vol. 19. ACM, 1--12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Eric Friedman, Christos-Alexandros Psomas, and Shai Vardi. 2017. Controlled Dynamic Fair Division. In Proceedings of the 2017 ACM Conference on Economics and Computation (EC). ACM, 461--478. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Ali Ghodsi, Vyas Sekar, Matei Zaharia, and Ion Stoica. 2012. Multi-resource fair queueing for packet processing. ACM SIGCOMM Computer Communication Review, Vol. 42, 4 (2012), 1--12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Ali Ghodsi, Matei Zaharia, Benjamin Hindman, Andy Konwinski, Scott Shenker, and Ion Stoica. 2011. Dominant Resource Fairness: Fair Allocation of Multiple Resource Types Proceedings of the 8th USENIX Symposium on Networked Systems Design and Implementation (NSDI), Vol. Vol. 11. 24--24. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Ali Ghodsi, Matei Zaharia, Scott Shenker, and Ion Stoica. 2013. Choosy: Max-min fair sharing for datacenter jobs with constraints Proceedings of the 8th ACM European Conference on Computer Systems (EuroSys). ACM, 365--378. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Artur Gorokh, Siddhartha Banerjee, and Krishnamurthy Iyer. 2016. Near-Efficient Allocation Using Artificial Currency in Repeated Settings. (2016).Google ScholarGoogle Scholar
  14. Artur Gorokh, Siddhartha Banerjee, and Krishnamurthy Iyer. 2017. From Monetary to Non-Monetary Mechanism Design Via Artificial Currencies. (2017).Google ScholarGoogle Scholar
  15. Ajay Gulati, Ganesha Shanmuganathan, Xuechen Zhang, and Peter J Varman. 2012. Demand Based Hierarchical QoS Using Storage Resource Pools USENIX Annual Technical Conference. 1--13. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Mingyu Guo, Vincent Conitzer, and Daniel M. Reeves. 2009. Competitive Repeated Allocation Without Payments. Proceedings of the Fifth Workshop on Internet and Network Economics (WINE). Rome, Italy, 244--255. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Gary J Henry. 1984. The UNIX system: The fair share scheduler. AT&T Bell Laboratories Technical Journal Vol. 63, 8 (1984), 1845--1857.Google ScholarGoogle ScholarCross RefCross Ref
  18. Ian Kash, Ariel D Procaccia, and Nisarg Shah. 2014. No agent left behind: Dynamic fair division of multiple resources. Journal of Artificial Intelligence Research Vol. 51 (2014), 579--603. Google ScholarGoogle ScholarCross RefCross Ref
  19. J. Kay and P. Lauder. 1988. A Fair Share Scheduler. Communications of the ACM Vol. 31, 1 (1988), 44--55. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Lawrence Berkeley National Laboratory. 2017. National Energy Research Scientific Computing Center. https://www.nersc.gov. (2017).Google ScholarGoogle Scholar
  21. Abhay K Parekh and Robert G Gallager. 1993. A generalized processor sharing approach to flow control in integrated services networks: The single-node case. IEEE/ACM Transactions on Networking Vol. 1, 3 (1993), 344--357. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Charles Reiss, John Wilkes, and Joseph L. Hellerstein. 2011. Google cluster-usage traces: formatGoogle ScholarGoogle Scholar
  23. schema. Technical Report. Google Inc., Mountain View, CA, USA. Revised 2014--11--17 for version 2.1. Posted at https://github.com/google/cluster-dataGoogle ScholarGoogle Scholar
  24. Thomas Sandholm and Kevin Lai. 2010. Dynamic proportional share scheduling in Hadoop. Job scheduling strategies for parallel processing. Springer, 110--131. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Alan Shieh, Srikanth Kandula, Albert G Greenberg, Changhoon Kim, and Bikas Saha. 2011. Sharing the Data Center Network. In Proceedings of the 8th USENIX Symposium on Networked Systems Design and Implementation (NSDI), Vol. Vol. 11. 23--23. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Shanjiang Tang, Bu-Sung Lee, Bingsheng He, and Haikun Liu. 2014. Long-term resource fairness: Towards economic fairness on pay-as-you-use computing systems Proceedings of the 28th ACM International Conference on Supercomputing. ACM, 251--260. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Duke University. 2017. The Duke Compute Cluster. http://rc.duke.edu/the-duke-compute-cluster/. (2017).Google ScholarGoogle Scholar
  28. Abhishek Verma, Luis Pedrosa, Madhukar Korupolu, David Oppenheimer, Eric Tune, and John Wilkes. 2015. Large-scale Cluster Management at Google with Borg Proceedings of the Tenth European Conference on Computer Systems (EuroSys). ACM, 18:1--18:17. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Carl A. Waldspurger and William E. Weihl. 1994. Lottery Scheduling: Flexible Proportional-Share Resource Management Proceedings of the First Symposium on Operating Systems Design and Implementation (OSDI). 1--11. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Toby Walsh. 2011. Online cake cutting Proceedings of the Second International Conference on Algorithmic Decision Theory (ADT). Springer, 292--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Xiaodong Wang and José F Mart'ınez. 2015. XChange: Scalable Dynamic Multi-Resource Allocation in Multicore Architectures Proceedings of the 21st IEEE International Symposium on High Performance Computer Architecture (HPCA).Google ScholarGoogle Scholar
  32. Seyed Majid Zahedi and Benjamin C. Lee. 2014. REF: Resource Elasticity Fairness with Sharing Incentives for Multiprocessors Proceedings of the 19th International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS). ACM, 145--160. Google ScholarGoogle ScholarDigital LibraryDigital Library

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