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 %s,FModeling and Analysis of Random Walk Search Algorithms in P2P NetworksGG0LNabhendra Bisnik, Alhussein Abouzeid ECSE, Rensselaer Polytechnic Institute 2M%&H  ) Contributions# Analytical expressions for performance metrics of random walk search in decentralized P2P networks An algorithm, called equation based adaptive search (EBAS), that uses analytical results to set the parameters of random walk Feedback based mechanism for maintaining popularity estimates0$qZOutlinet Search mechanisms and trade-offs involved Analytical results EBAS Simulation results Conclusion and future workuqu t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future Work<+Jq,ISearch Algorithmsg Stateless search algorithms No state information about network or links maintained e.g. Flooding, Iterative Deepening, Random Walk, k-Random Walk State-full search algorithms Improvement in performance by maintaining state information (goodness of neighbors, resource indices) Better performance but more complex e.g. Directed BFS, Local Indices, APS qxqqqx Search Algorithms (cont.){ Desired performance Low overhead Low delay High success rate Trade-offs Overhead and success rate Overhead and delayq, q/   / The k-Random Walk0    The k-Random Walk0    The k-Random Walk0    The k-Random Walk0   The k-Random Walk0  The k-Random Walk (cont.)0X Popular alternative to flooding [3] So far focus is on adaptively forwarding queries to   good  neighbors Performance depends on parameters k and T and popularity of resource (p) low k and T => high delay and low success rate high k and T => high overhead Problem: Number of nodes queried are either more or less than what is required Solution: Adaptively set parameters of random walk according to popularity of resource qZMZqZZ$ G #L G P t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future Work\+q6q+5 Analytical results Random walk has statistical properties similar to sampling from uniform distribution [1] Using above we found analytical expressions of success rate, overhead and delay in terms of number of random walkers (k), TTL (T) and popularity (p)q "Verification of Analytical Results## t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future Workd?q0q>/EBAS Objective: Set parameters (k,T) of random walk such that EBAS consists of two components: Popularity estimation module Parameter selection moduleF_q:^$: Popularity Estimator Module Popularity estimator is based on exponentially weighted moving average Uses the fraction of successful searches in an update interval ( ) to obtain current estimate according to Popularity estimate for next update interval is updated according to :q G Parameter selection module Uses in order to set and such that (1), (2) and (3) are satisfied Inequality (1) is satisfied if Inequalities (2) and (3) may be solved numerically in order to obtain a the range of feasible k and T The parameter selection module may be implemented by means of a parameter selection table in which feasible values of k and T corresponding to various range of popularitiesRqATG!  " An Example (r Consider a case where and Inequality (1) is satisfied if 0qqqs/ t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future WorkdEqqD1Simulation Scenario Extensive simulations done for Evaluating performance of popularity estimator Comparing performance EBAS with non-adaptive random walk Network for simulation 104 nodes px104 nodes randomly chosen and marked to have resource Network grown according to [2] qhqa gR0`Simulation Results  Popularity Estimator Module11( Simulation Results - EBAS4Simulation Results - EBAS5 t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future WorkDYqX3Conclusion & Future Work EBAS effectively maintains popularity estimates and performs better than random walk EBAS performs best in scenarios where same or  similar  item is searched several times Modeling problem of choosing optimal parameters as control theoretic problem Model performance of other state-full search mechanisms such as APS &CqB 7  References D[1] C. Gkantsidis, M. Mihail, and A. Saberi. Random walks in peer-to-peer networks. In Proc. of IEEE INFOCOM, Mar. 2004. [2] P. Holme and B. J. Kim. Growing Scale-free Networks with Tunable Clustering. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 65, 2002 [3] Q. Lv, P. Cao, E. Cohen, K. Li, and S. Shenker. Search and Replication in Unstructured Peer-to-Peer Networks. In Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, pages 258 259. ACM Press, 2002. Z#ZY^Co%  W6  Thank You.  P/H9:;<=>?@AB C D E F HIJKLMNOPQRSTUVW  ` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> $(    6ܣ  `}  T Click to edit Master title style! !  0d  `  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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