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By: Jagadish Ghimire st ICT/SET Thesis Examination Committee: Dr. Teerapat Sanguankotchakorn (Chairperson) Assoc. Prof. Tapio J. Erke Dr. R. M. A. P. Rajatheva Prof Noel Crespi (External Expert) Dr. Mehdi Mani (External Expert) Asian Institute of Technology 18 th May 2009

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Outline Related Concepts Problem Statement Objectives Mathematical Analysis Results and Discussion Conclusion 2Asian Institute of Technology

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Wireless ad hoc network MANET Mobile ad hoc network WMN Wireless Mesh Network 3Asian Institute of Technology src: [1] Kim src: [2] Higgins et al.

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Peer-to-Peer (P2P) Client/Server vs P2P Centralization Fault Tolerance Scalability 4Asian Institute of Technology src: [3] Androutsellis-Tehotokis and Spinellis (2004) src: [4]

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P2P Overlay Network One peer knows how to reach to one or more peers of the network. Maintains a Routing Table Structured kind of P2P overlay allow one to define a specific type of Overlay Network Overlay Network: Logical network built on application- layer. Versus Physical Network Common Topologies: Ring, Butterfly 5Asian Institute of Technology src: [5] Wang and Li(2003)

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The Lookup Problem A C F D E B G H Wall-E.avi* I need Wall-E How to find? Lookup successful 6Asian Institute of Technology * We assume that the seeker and owner of the movie have required rights for sharing

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Structured P2P A B - Routing table and Greedy Forwarding - Overlay ID space - Node ID - Resource ID 7 Asian Institute of Technology

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Super Node based P2P Overlay Internet (with core routers and network infrastructure) SN: Super Node CN: Client Node 8Asian Institute of Technology

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IP telephony service control overlay Considered Scenario: Physical Network: Wireless ad hoc network Service level network: SN based P2P overlay Network as the service control overlay providing Lookup service Overlay Model: Ring and Chord 9Asian Institute of Technology

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IP telephony (contd..) Typical “Bob calling Alice” scenario example Lookup Query Message: Initiated by Bob Lookup Response Message: Replied by the SN of Alice SN 1 SN 2 SN 3 SN 4 Lookup Query Message Routing Path Lookup Response Message Routing Path Bob Alice 10 Asian Institute of Technology

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Problem Statement Post Dialing Delay (session setup delay) in IP Telephony: ITU-T recommendation: 95 percentile of the calls < 3 sec HOW MUCH IS IT NOW? How does delay relate to the number of SNs? HOW MANY SUPERNODES TO SELECT? 1 ? A pure C/S architecture 2 ? 3 ? How Many? Increasing SNs results in faster call processing per SN in one hand whereas the overall lookup routing path is increased. What is the exact interplay? In P2P based IP telephony services, determining the optimum number of SNs for minimum session setup delay is crucial. 11Asian Institute of Technology

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Problem Statement (2) Capacity of the IP telephony system How many users can a given service control overlay accommodate? How does the number of SNs affect the capacity of such services? What is the exact relationship between the number of SNs and the capacity? Does increasing the number of SN arbitrarily increase the capacity of such systems? 12Asian Institute of Technology

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Objectives Perform analysis to understand and express mathematically the delay characteristics and the lookup processing capacity of a SN-based P2P IP Telephony service control overlay over wireless ad hoc networks. Perform simulations to validate the analytical results 13Asian Institute of Technology

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Limitations The analytical model of Chord is an ideal model and does not account for the asymmetric keyspace partitioning The overlay model excludes any dynamics due to node joins and leaves. 14Asian Institute of Technology

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Contribution of the Thesis Work (summary) Closed-form mathematical expressions were derived for finding the post-dialing delay in the overlay network as a function of number of supernodes. Post Dialing Delay=f(N) For a given load, there exists a number of SNs at which the session setup delay is minimum Optimum number of SNs for minimum post dialing delay can now be determined 15Asian Institute of Technology

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Contribution of the Thesis Work (2) Closed-form expressions for finding the capacity of such networks were derived. Now, we can answer, with the help of these equations, how many maximum number of users a system can support ( given the number of supernodes). Such expressions can also be used for dimensioning such systems A lower bound on the number of physical hops traveled by a lookup message in wireless ad hoc network is proposed. 16Asian Institute of Technology

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Delay and Capacity Analysis System Model Underlay: Homogeneous Wireless ad hoc network Overlay: SN-based Deterministic graph A service control overlay for IP telephony Two cases: Ring and an idealized Chord Assumptions: SNs are uniformly placed in id-space Equal number of CNs are associated with SNs 17Asian Institute of Technology

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System Model (summary) (1) Network Model Summary (Used in Section 4.3 for Underlay Network Delay) DescriptionParameterRemarks Number of nodesn Mode of communicationAd hocShortest Path Routing Link Model Two state (Existent and Non- existent) Two nodes communicate if their Euclidean distance is less than the individual communication range. Communicate Ranger0r0 Homogeneous communication range Area of Deployment a x bRectangular Node DistributionUniformly distributedx-coordinate and y-coordinate are uniform random number in the interval [0,a] and [0,y] respectively. 18Asian Institute of Technology

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System Model (summary) (2) Overlay Model (Used for delay and capacity analysis in Chapter 4) Model 1. (Ring Overlay Structure) Described in section Number of SNsN Number of successor per SN 1 Structure of the overlay Ring Model 2. (Chord Overlay Structure) Described in section Number of SNsN=2 c Number of successor per SN C Structure of the overlay Chord(By Stoica et al. (2001)) 19Asian Institute of Technology

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System Model(4) SN Model: All SNs of the system are supposed to have the same mean lookup message processing rate (µ) Each SN has an infinite lookup buffer Two cases of service time distribution are considered: Constant service time case, Exponential service time case. Traffic Model: Total lookup message arrival process in the system is a poisson process with λ total total mean arrival rate Each CN generates lookup with equal rates Destination CN in each lookup message is selected uniformly among all the participating nodes. 20 Asian Institute of Technology

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Delay Analysis Model The total delay experienced by any lookup message is viewed to be composed of two delays: The Delay in the Overlay Network (D overlay ) The Delay in the Underlay Network (D underlay ) We decouple the two delays for making our analysis tractable 21Asian Institute of Technology

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Results of Ring Topology Overlay Lemma 1 : The distribution of the number of super nodes visited by a lookup in the ring-topology with load-balance is UNIFORM. Theorem 1: The average SNs visited by a lookup in the load-balanced Ring-topology overlay is Absorption Probability: Definition : Absorption Probability of a SN in an SN-based P2P system with N SNs, represented as P(N), is defined as the probability that the given SN absorbs (does not forward) any lookup message that comes to it. A lookup can be a new lookup from its CN or forwarded ones 22Asian Institute of Technology

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Results (2) Lemma 2: P(N) of load-balanced Ring-Topology overlay is given as: Queuing Network Node Model 23Asian Institute of Technology

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Queuing Network Model 24Asian Institute of Technology

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Routing Probabilities Visit Ratio (e i ): Effective arrival per SN i (λ i ) Utilization per SN (ρ i ) Queuing Network Parameters 25 Asian Institute of Technology

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Mean Overlay Lookup Delay (Expression) Theorem 2: The average delay experienced by a lookup message (excluding any underlay delays incurred) in the load-balanced ring- topology overlay model, in two cases of a constant service time and an exponentially distributed service time, are given respectively as follows where and are : 26Asian Institute of Technology

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Lookup Processing Capacity Corollary 1: The maximum rate of external lookup arrivals the load-balanced ring-topology overlay based IP telephony system can support is given as follows: Capacity scaling in terms of number of SNs is thus given as: Proof: Obtained by letting utilization per node( )=1 (For Finite Delay: ) 27Asian Institute of Technology

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Idealized Chord Model Id space of size K=2 k Number of SNs N=2 c Observation 1 Peer out-degree: c c-regular directed graph 28Asian Institute of Technology

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Absorption Probability Lemma 6: In the idealized Chord model, P(N) is given as follows Average SNs visited Per Lookup Theorem 3. The average number of SNs visited by a lookup (E{S}) in the idealized chord overlay routing modeled is given by: 29Asian Institute of Technology

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Queuing Node Model - Chord 30Asian Institute of Technology

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Overlay Lookup Delay Calculation and Capacity Exponential service time case Per SN delay: Total mean overlay lookup delay Max Throughput 31Asian Institute of Technology

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Analysis of Underlay SN selected Randomly CN associate randomly to SN n wireless nodes uniformly distributed in a rectangular deployment area (a x b m 2 ) Communication range of each node r 0 32Asian Institute of Technology

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Analysis of Underlay Number of Logical hops of communication: E{S}+1 Average physical hops between two randomly elected nodes: E{H} Where Ghosh(1951) E{L} is the average number of physical hops traveled by a lookup E{L}=(E{S}+1).E{H}. So, we get 33Asian Institute of Technology

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Analysis of Underlay For square deployment of (a x a m 2 ). : Per underlay-hop Delay 34Asian Institute of Technology

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Average Length of Lookup Path Ring Topology Chord 35Asian Institute of Technology

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Absorption Probability Ring Topology Chord 36Asian Institute of Technology

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Total Overlay lookup delay Ring Topology Chord 37Asian Institute of Technology

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Delay and Utilization Per SN - Ring 38Asian Institute of Technology

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Lookup Capacity Ring Topology Chord 39Asian Institute of Technology

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Average Underlay Hops Result for N=5 for Ring Overlay 40Asian Institute of Technology

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Conclusion Delay and Capacity Analysis of the lookup processing in a SN-based P2P service control overlay for IP telephony over Wireless ad hoc network have been performed. Estimation of mean lookup hop counts, the distributions, mean delay per SN and mean delay of a lookup in overlay has been estimated for a ring-topology and an idealized version of Chord. Lower Bounds on the number of underlay hops per lookup for the above mentioned overlays have been proposed Capacity of such systems for lookup processing has been obtained as a function of N General case of load-imbalance will be another extension of the work 41Asian Institute of Technology

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Graphics References [1] Dongsoo Stephen Kim, Mobile Ad Hoc Networks url: [2] Kathryn Higgins, Ruth Egan, Shonagh Hurley and Marine Lemur, Ad Hoc Networks url: [3] Stephanos Androutsellis-Theotokis and Diomidis Spinellis. A survey of peer-to-peer content distribution technologies. ACM Computing Surveys, 36(4):335–371, December (doi: / ) [4] url: [5] Chonggang Wang and Bo Li (2003),Peer-to-Peer Overlay Networks: A Survey, April 20, url: Asian Institute of Technology42

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Thank you Questions and suggestions are welcome!!! 43Asian Institute of Technology

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