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On The Latency of BFS Interval

Cooperation Web Caching

Arwa Zabian

Maurizio Bonuccelli

Department of Computer Science

University of Pisa / Italy

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Talk overviewTalk overview

• Give a brief introduction of the problem

• The presentation of our algorithm

• Our results

• Conclusion and future works

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Client Client

Web caching

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Problems of Web CachingProblems of Web Caching

• Limited cache size• Cosistency problem

• Caching dynamic content

Solutions • Prefetching• Cooperative Web Caching

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Cooperative web caching

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Problems in cooperative web cachingProblems in cooperative web caching

• Where the request must be forwarded?

• How it can be retrieved?

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GoalGoal

• The goal is the reduction of the latency perceived by the web client .

• Delay analysis in a cooperative web caching:

- Network factors- System factors

Delay

Searching Routing

Finding the proxy

Findin R

Routing decision

FaultTolerance

System factors

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Delay motivationsDelay motivations: : SearchingSearchingDefining the topologyDefining the topology

• Finding the proxy that have the request, it depends on the topology of the system.

• The proxy cache in our system are organized in a tree.

• The tree construction is done using NDA (Neighbour Discovering Algorithm).

• NDA is based on BFS, it visits the tree by levels.

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Defining the topology Defining the topology NDA (Neighbours Discovering Algorithm)NDA (Neighbours Discovering Algorithm)

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Delay motivation: SeachingDelay motivation: SeachingFinding the requestFinding the request

• When NDA runs in a given graph it constructs a tree called Child-Tree, in which each node reports its parent label.

• The maximum length of label assigned to n nodes is 2logn+1 bits.

• Based on the information collected each node constructs a routing table that is a data structure in which is inserted the node labels and their Interval of documents.

• The documents are organized in intervals of their URL based on the interval routing scheme proposed by Santoro and Khatib[82].

N. Santoro, R. Khatib: Routing Without Routing Table. Tech. Rep, SCS-TR-6School of Computer Science, Carleton University. Ottawa 1982

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Searching : Complexity analysisSearching : Complexity analysis

• NDA is asymptotically optimum as search graph algorithm.

• Time complexity is O(|E|+|V|).

• Message complexity in construction Child-Tree is O(|E|+|V|).

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NDA contribues in the routing process in two factors they are:

• Routing decision.

• Address solution at each hop.

• Fault tolerance: it maintains a backup links used in the case of nodes and links faulty.

Delay motivation Routing and fault tolerance

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Routing : Complexity analysisRouting : Complexity analysis

• The size of data structure constructed by the information collected during the NDA discovering process is logarithmic with the number of nodes of the graph.

• The number of nodes travelled by each message, in Child-Tree is O(log n).

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Simulation ResultsSimulation Results

• All our simulation were run on top of NS2.• The goal was the reduction of the searching and routing

time.• Our simulation results confirm that the searching time is

fixed in all the conditions studied and varied only in the case of miss.

• The routing time is strictely related to the size of the document and to the number of hops between proxy and server

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Simulation Results: factors influenced in the Simulation Results: factors influenced in the latencylatency

• Type of the document: static or dynamic.

• Page popularity.

• Number of request.

• Number of hops.

• Page size

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Type of the document : static or dynamicType of the document : static or dynamic

Static Dynamic

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Page PopularityPage Popularity

Static and popular page Static and less popular page

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Number of requestNumber of request

• The latency is decreased when the number of requests is increased between two modification.

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Simulation Results: Number of hopsSimulation Results: Number of hops

• The retrieving process

R

R

R

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Simulation Results: Number of hopsSimulation Results: Number of hops

The latency is increased linearly with the number of hops

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Simulation Results : Page sizeSimulation Results : Page size

• The simulation results show that the most important factor that influences in the latency variation is the page size.

• The latency is increased linearly with the page size.

Hierarchical

Randomized

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Simulation Results: Page sizeSimulation Results: Page size

• The hit ratio is influenced by the page size.

100%

18%

82%

82%

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Simulation Results: Page sizeSimulation Results: Page size

• The transmission time is strictly related to the page size that affect the latency.

• The transmission time is increased linearly with the page size.

Page size (bytes)

1024 4096 10240 40960 102400 409600

T.T (ms) 3.091 7.179 9.389 15.59 27.64 85.630

Latency (ms)

Randomised

6.534 12.16 15.08 23.43 39.70 126.502

Latency(ms)

Hierarchical

7.528 13.36 15.01 25.51 38.61 101.613

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Simulation Results : Transmission TimeSimulation Results : Transmission Time

T.T

hierarchicalrandomise

d

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ResultsResults::

• Scalability: the latency is independent on the network size.

Number of

nodes 40 60 80 100 120 130

Average of

Latency (ms)

Randomised

6.844 7.26 6.64 6.53 ---------- 16.13

Average of

Latency (ms)

Hierarchical

6.955 9.90 9.77 7.52 6.60 -----

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Results : ScalabilityResults : Scalability

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ResultsResults::

• Reliability : the system ensures that the client receives the request in the presence of some links faults with some additional delay penalty.

Without fault With fault

Average of latency

(ms) for 2 hops 12.209 16.370

Average of latency

(ms) for 6 hops 42.646 48.751

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Related worksRelated works

• Riptide is a peer-to-peer web caching system built on top of OceanStore that uses a routing mechanism called Tapestry.

• The comparison of our system with that for Riptide show that : our system perform well for small documents . Both systems give a similar results for medium document. When Riptide performs better than our system for large documents

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Related worksRelated works

• Comparison results in term of latency

Page size(bytes)

Latency (ms)

Randomised NDA

Latenc(ms)

Hierarchical NDA

Latency(ms)

Riptide

1024 6.534 7.528 23.30

4096 12.167 13.360 24.07

10240 15.080 15.010 24.40

40960 23.437 25.514 25.35

102400 39.704 38.613 38.81

409600 126.502 101.613 63.35

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Related workRelated work

• Comparison results in term of hit

100%

RiptideNDA

100%

82%

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ConclusionConclusion

• We proposed an algorithm based on BFS that reduces the searching time by reducing the size of the data structure used rapresenting the documents in intervals based on their URL’s.

• Our algorithm was proposed to reduce the routing time by reducing the address resolution in each node.

• We obtained a reliable system that allow the client to receive the request with the presence of some faulty link in the system. It is scalable in which the latency perceived by the client is independent on the system size.

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Future workFuture work

• Utilizing the document division method in developing a technique for the request prefetching between proxy and proxy.

• Modelling the system to include the dynamic case ( insertion and deletion of nodes).

• Performs some additional simulations to include the cases not covered in our previous work.

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Questions?

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ReferencesReferences

[1] A. Zabian, M. Bonuccelli ``BFS Based Algorithm for Routing and Fault Tolerance in a Cluster of Web Caching''. Technical Report,

``http:\\www.di.unipi.it\ ~ bonucce''. [2] B. Zaho, A.Joseph and J. Kubiatowicz, ''Tapestry: Infrastructure For Fault-tolerance

Wide Area Location and Routing''. Technical Report UCB//CSD-01-1141, U.C. Berckley 2001.

[3] C. Wells. ``The Oceanstore Archive: Goal, Structure and self Repair'', Master thesis, University of California, Berkeley.May2001

[4] Duane Wessels.``Internet Cache Protocol(ICP)'', version 2. RFC 2186 .[5] E. Zegura, K. Calvert and S. Bhattacharjee. ''How to model an Internetwork''. In Proc. of

INFOCOM, 1999.[6] L.Fan, P. Cao, J. Almedia, A.Z. Border,``Summary-Cache a scalable Wide Area Web

Cache sharing Protocol'', IEEE/ACM Transactions on Networking. Vol 8. No 3,pp: 281-293. June 2000.

[7] Martin Hamilton, Alex Rousskov, Duane Wessels, ``Cache Digest'', National Laboratory for Applied Network Research, Aprile1998.

“http:\\Squid.nlanr.net\Squid\cachedigest''[8] Patrick R .Eaton ``Caching the web with OceanStore'‘ .Technique report UCB/CSD/021212.U.C.Berkely. November 2002.