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On Resource Pooling and Separation for LRU Caching

Published:03 April 2018Publication History
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Abstract

Caching systems using the Least Recently Used (LRU) principle have now become ubiquitous. A fundamental question for these systems is whether the cache space should be pooled together or divided to serve multiple flows of data item requests in order to minimize the miss probabilities. In this paper, we show that there is no straight yes or no answer to this question, depending on complex combinations of critical factors, including, e.g., request rates, overlapped data items across different request flows, data item popularities and their sizes. To this end, we characterize the performance of multiple flows of data item requests under resource pooling and separation for LRU caching when the cache size is large.

Analytically, we show that it is asymptotically optimal to jointly serve multiple flows if their data item sizes and popularity distributions are similar and their arrival rates do not differ significantly; the self-organizing property of LRU caching automatically optimizes the resource allocation among them asymptotically. Otherwise, separating these flows could be better, e.g., when data sizes vary significantly. We also quantify critical points beyond which resource pooling is better than separation for each of the flows when the overlapped data items exceed certain levels. Technically, for a broad class of heavy-tailed distributions we derive the asymptotic miss probabilities of multiple flows of requests with varying data item sizes in a shared LRU cache space. It also validates the characteristic time approximation under certain conditions. These results provide new insights on improving the performance of caching systems.

References

  1. Susanne Albers and Jeffery Westbrook. 1998. Self-organizing data structures. Online Algorithms: The state of the art Vol. 1442 (1998), 13--41. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Brian Allen and Ian Munro. 1978. Self-organizing binary search trees. J. ACM Vol. 25 (1978), 526--535. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Noga Alon and Joel H. Spencer. 2000. The probabilistic method (2nd ed.). John Wiley.Google ScholarGoogle Scholar
  4. Sigal Ar, Bernard Chazelle, and Ayellet Tal. 2000. Self-customized BSP trees for collision detection. Computational Geometry: Theory and Applications Vol. 10 (2000), 23--29. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Martin Arlitt, Rich Friedrich, and Tai Jin. 1999. Workload characterization of a Web proxy in a cable modem environment. SIGMETRICS Performance Evalation Review Vol. 27, 2 (Sept. 1999), 25--36.. 2010. A fluid limit for a cache algorithm with general request processes. Advances in Applied Probability Vol. 42, 3 (2010), 816--833. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Stefan Podlipnig and Laszlo Böszörmenyi. 2003. A survey of web cache replacement strategies. ACM Computing Surveys (CSUR) Vol. 35, 4 (Dec.. 2003), 374--398. ISSN0360-0300 Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Guocong Quan, Kaiyi Ji, and Jian Tan. 2018. LRU caching with dependent competing requests. IEEE INFOCOM 2018 - IEEE Conference on Computer Communications (INFOCOM 2018). Honolulu, USA.Google ScholarGoogle ScholarCross RefCross Ref
  8. Ronald Rivest. 1976. On self-organizing sequential search heuristics. Commun. ACM Vol. 19 (1976), 63--67. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. James Roberts and Nada Sbihi. 2013. Exploring the memory-bandwidth tradeoff in an information-centric network Teletraffic Congress (ITC), 2013 25th International. IEEE, 1--9.Google ScholarGoogle Scholar
  10. Liam Roditty and Uri Zwick. 2004. A fully dynamic reachability algorithm for directed graphs with an almost linear update time Proceedings of the 36th STOC. 184--191. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Elisha J. Rosensweig, Jim Kurose, and Don Towsley. 2010. Approximate models for general cache networks. In Proceedings of the 29th Conference on Information Communications (INFOCOM'10). IEEE Press, San Diego, California, USA, 1100--1108. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Albers S. and M. Mitzenmacher. 1998. Average case analyses of list update algorithms. Algorithmica Vol. 21 (1998), 312--329.Google ScholarGoogle ScholarCross RefCross Ref
  13. Daniel D. Sleator and Robert E. Tarjan. 1985 a. Amortized efficiency of list update and paging rules. Commun. ACM Vol. 28 (1985), 202--208. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Daniel D. Sleator and Robert E. Tarjan. 1985 b. Self-adjusting binary search trees. J. ACM Vol. 32 (1985), 652--686. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Alexander L. Stolyar. 2004. MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. The Annals of Applied Probability Vol. 14, 1 (02. 2004), 1--53.Google ScholarGoogle ScholarCross RefCross Ref
  16. Toyoaki Sugimoto and Naoto Miyoshi. 2006. On the asymptotics of fault probability in least-recently-used caching with Zipf-type request distribution. Random Structures & Algorithms Vol. 29, 3 (2006), 296--323. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Jian Tan, Li Zhang, and Yandong Wang. 2015. Miss behavior for caching with lease. SIGMETRICS Performance Evaluation Review, MAMA workshop, Vol. 43, 2 (2015), 60--62. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Andrew S. Tanenbaum. 2001. Modern Operating Systems (2rd ed.). Prentice Hall Press, Upper Saddle River, NJ, USA. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Naoki Tsukada, Ryo Hirade, and Naoto Miyoshi. 2012. Fluid limit analysis of FIFO and RR caching for independent reference models. Performance Evaluation Vol. 69, 9 (2012), 403--412. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Jia Wang. 1999. A survey of Web caching schemes for the Internet. SIGCOMM Computer Communication Review Vol. 29, 5 (Oct.. 1999), 36--46. ISSN 0146-4833 Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Xingbo Wu, Li Zhang, Yandong Wang, Yufei Ren, Michel Hack, and Song Jiang. 2016. zExpander: a key-value cache with both high performance and fewer misses Proceedings of the Eleventh European Conference on Computer Systems (EuroSys '16). ACM, New York, NY, USA, Article 14, 15 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Yuehai Xu, Eitan Frachtenberg, Song Jiang, and Mike Paleczny. 2014. Characterizing Facebook's Memcached workload. IEEE Internet Computing Vol. 18, 2 (2014), 41--49.Google ScholarGoogle ScholarCross RefCross Ref
  23. Yuehai Xua, Eitan Frachtenbergb, and Song Jiang. 2014. Building a high-performance key-value cache as an energy-efficient appliance. Performance Evaluation Vol. 79 (September. 2014), 24--37.Google ScholarGoogle Scholar
  24. Yue Yang and Jianwen Zhu. 2016. Write skew and Zipf distribution: Evidence and implications. ACM Transactions on Storage (TOS) Vol. 12, 4, Article 21 (June. 2016), pages 19 pages. ISSN1553-3077 Google ScholarGoogle ScholarDigital LibraryDigital Library

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