Performance evaluation of the random replacement policy for networks of caches

Caching is a key component for Content Distribution Networks and new Information-Centric Network architectures. In this paper, we address performance issues of caching networks running the RND replacement policy. We first prove that when the popularity distribution follows a general power-law with decay exponent α > 1, the miss probability is asymptotic to O( C1-α) for large cache size C. We further evaluate network of caches under RND policy for homogeneous tree networks and extend the analysis to tandem cache networks where caches employ either LRU or RND policies.

[1]  Niklas Carlsson,et al.  Characterizing web-based video sharing workloads , 2009, WWW '09.

[2]  Massimo Gallo,et al.  Modeling data transfer in content-centric networking , 2011, 2011 23rd International Teletraffic Congress (ITC).

[3]  Diego Perino,et al.  A reality check for content centric networking , 2011, ICN '11.

[4]  M. Rao.  Probability theory with applications , 1984 .

[5]  Erol Gelenbe,et al.  A Unified Approach to the Evaluation of a Class of Replacement Algorithms , 1973, IEEE Transactions on Computers.

[6]  Massimo Gallo,et al.  Bandwidth and storage sharing performance in information centric networking , 2011, ICN '11.

[7]  Takayuki Osogami,et al.  A Fluid Limit for Cache Algorithms with General Request Processes , 2009, IEEE INFOCOM 2009.

[8]  Pablo Rodriguez,et al.  I tube, you tube, everybody tubes: analyzing the world's largest user generated content video system , 2007, IMC '07.

[9]  Naoto Miyoshi,et al.  Fluid limit analysis of FIFO and RR caching for independent reference models , 2012, Perform. Evaluation.

[10]  James Allen Fill,et al.  On the distribution of search cost for the move-to-front rule , 1996, Random Struct. Algorithms.

[11]  Asit Dan,et al.  An approximate analysis of the LRU and FIFO buffer replacement schemes , 1990, SIGMETRICS '90.

[12]  Ludmila Cherkasova,et al.  Analysis of Enterprise Media Server Workloads : Access Patterns , Locality , Dynamics , and Rate of Change , 2002 .

[13]  Hao Che,et al.  Hierarchical Web caching systems: modeling, design and experimental results , 2002, IEEE J. Sel. Areas Commun..

[14]  Predrag R. Jelenkovic,et al.  Least-recently-used caching with dependent requests , 2004, Theor. Comput. Sci..

[15]  Nikolaos Laoutaris,et al.  The LCD interconnection of LRU caches and its analysis , 2006, Perform. Evaluation.

[16]  Scott Shenker,et al.  A data-oriented (and beyond) network architecture , 2007, SIGCOMM '07.

[17]  Donald F. Towsley,et al.  Approximate Models for General Cache Networks , 2010, 2010 Proceedings IEEE INFOCOM.

[18]  Ítalo S. Cunha,et al.  Analyzing client interactivity in streaming media , 2004, WWW '04.

[19]  N. R. Chaganty,et al.  Multidimensional large deviation local limit theorems , 1986 .

[20]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[21]  P. J. Burville,et al.  On a model for storage and search , 1973, Journal of Applied Probability.

[22]  John McCabe,et al.  On Serial Files with Relocatable Records , 1965 .

[23]  Massimo Gallo,et al.  Performance evaluation of the random replacement policy for networks of caches , 2014, Perform. Evaluation.

[24]  Van Jacobson,et al.  Networking named content , 2009, CoNEXT '09.

[25]  Azer Bestavros,et al.  Changes in Web client access patterns: Characteristics and caching implications , 1999, World Wide Web.

[26]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[27]  Ludmila Cherkasova,et al.  Analysis of enterprise media server workloads: access patterns, locality, content evolution, and rates of change , 2004, IEEE/ACM Transactions on Networking.

[28]  Arjen K. Lenstra.  Birthday Paradox , 2011, Encyclopedia of Cryptography and Security.

[29]  Donald F. Towsley,et al.  Analysis of TTL-based cache networks , 2012, 6th International ICST Conference on Performance Evaluation Methodologies and Tools.

[30]  ShenkerScott,et al.  A data-oriented (and beyond) network architecture , 2007 .

[31]  Philippe Robert,et al.  A versatile and accurate approximation for LRU cache performance , 2012, 2012 24th International Teletraffic Congress (ITC 24).

[32]  Predrag R. Jelenkovic,et al.  Performance of the move-to-front algorithm with Markov-modulated request sequences , 1999, Oper. Res. Lett..

[33]  Özalp Babaoǧlu,et al.  Hierarchical replacement decisions in hierarchical stores , 1982, SIGMETRICS '82.

[34]  Predrag R. Jelenkovic,et al.  Characterizing the miss sequence of the LRU cache , 2008, PERV.

[35]  Philippe Flajolet,et al.  Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search , 1992, Discret. Appl. Math..

[36]  Predrag R. Jelenkovic,et al.  Optimizing LRU Caching for Variable Document Sizes , 2004, Combinatorics, Probability and Computing.

[37]  MuscarielloLuca,et al.  Performance evaluation of the random replacement policy for networks of caches , 2012 .

[38]  Li Fan,et al.  Web caching and Zipf-like distributions: evidence and implications , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[39]  James Allen Fill,et al.  On the distribution of search cost for the move-to-front rule , 1996 .

[40]  P. Jelenkovic.  Asymptotic approximation of the move-to-front search cost distribution and least-recently used caching fault probabilities , 1999 .

[41]  W. J. Hendricks.  The stationary distribution of an interesting Markov chain , 1972, Journal of Applied Probability.