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)
By:
Jagadish Ghimire
st105636
ICT/SET
Asian Institute of Technology
18th May 2009
Outline
 Related Concepts
 Problem Statement
 Objectives
 Mathematical Analysis
 Results and Discussion
 Conclusion
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Wireless ad hoc network
src: [1] Kim
 MANET
 Mobile ad hoc network
 WMN
 Wireless Mesh Network
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src: [2] Higgins et al.
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Peer-to-Peer (P2P)
 Client/Server vs P2P
 Centralization
 Fault Tolerance
 Scalability
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 applicationlayer .

Versus Physical Network
 Common Topologies: Ring,
Butterfly
src: [5] Wang and Li(2003)
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The Lookup Problem
Lookup
successful
H
B
Wall-E.avi*
I need
Wall-E
A
How to
find?
C
G
E
D
F
* We assume that the seeker and owner of the movie have required rights for sharing
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Structured P2P
- Routing table and Greedy Forwarding
- Overlay ID space
- Node ID
- Resource ID
B
A
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Super Node based P2P Overlay
Internet (with core
routers and
network
infrastructure)
SN: Super Node
CN: Client Node
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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
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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
Bob
SN
2
SN
3
SN
4
Lookup Query Message Routing Path
Lookup Response Message Routing Path
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Alice
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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.
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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?
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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
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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.
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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
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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.
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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
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System Model (summary) (1)
Network Model Summary (Used in Section 4.3 for Underlay Network Delay)
Description
Parameter
Number of nodes
n
Mode of communication
Ad hoc
Shortest Path Routing
Link Model
Two state (Existent and Nonexistent)
Two nodes communicate if their
Euclidean distance is less than the
individual communication range.
Communicate Range
r0
Homogeneous communication range
Area of Deployment
axb
Rectangular
Node Distribution
Uniformly distributed
x-coordinate and y-coordinate are
uniform random number in the
interval [0,a] and [0,y] respectively.
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Remarks
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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 4.1.1
Number of SNs
N
Number of successor per 1
SN
Structure of the overlay
Ring
Model 2. (Chord Overlay Structure) Described in section 4.2.1
Number of SNs
N=2c
Number of successor per C
SN
Structure of the overlay
Chord
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(By Stoica et al. (2001))
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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 λtotal 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.
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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 (Doverlay)
 The Delay in the Underlay Network (Dunderlay)
Dtotal  Doverlay  Dunderlay
 We decouple the two delays for making our analysis
tractable
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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
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Results (2)
 Lemma 2: P(N) of load-balanced Ring-Topology overlay is
given as:
Queuing Network Node Model
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Queuing Network Model
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Routing Probabilities
Queuing Network Parameters
Visit Ratio (ei):
Effective arrival per SN i (λi)
Utilization per SN (ρi)
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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 ringtopology overlay model, in two cases of a constant service time and an
exponentially distributed service time, are given respectively as follows
where
and
are :
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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:
2N
max 
N 1

Proof: Obtained by letting utilization per node( i)=1
(For Finite Delay:
)
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Idealized Chord Model
 Id space of size K=2k
 Number of SNs N=2c
 Observation 1
 Peer out-degree: c

c-regular directed graph
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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:
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Queuing Node Model - Chord
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Overlay Lookup Delay Calculation and Capacity
 Exponential service time case
 Per SN delay:
 Total mean overlay lookup delay
 Max Throughput
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1
 c
D
1  
 (1  i )  2 
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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 m2)
 Communication range of each node r0
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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
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Analysis of Underlay
 For square deployment of (a x a m2 ).

X
: Per underlay-hop Delay
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Average Length of Lookup Path
Ring Topology
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Chord
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Absorption Probability
Ring Topology
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Chord
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Total Overlay lookup delay
Ring Topology
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Chord
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Delay and Utilization Per SN - Ring
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Lookup Capacity
Ring Topology
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Chord
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Average Underlay Hops Result for N=5 for
Ring Overlay
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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
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Graphics References





[1] Dongsoo Stephen Kim, Mobile Ad Hoc Networks
url: http://www.ece.iupui.edu/~dskim/manet/
[2] Kathryn Higgins, Ruth Egan, Shonagh Hurley and Marine Lemur, Ad Hoc Networks
url: http://ntrg.cs.tcd.ie/undergrad/4ba2.05/group11/index.html
[3] Stephanos Androutsellis-Theotokis and Diomidis Spinellis. A survey of peer-to-peer content
distribution technologies. ACM Computing Surveys, 36(4):335–371, December 2004.
(doi:10.1145/1041680.1041681)
[4] url: http://www.cs.virginia.edu/~mngroup/hypercast/
[5] Chonggang Wang and Bo Li (2003),Peer-to-Peer Overlay Networks: A Survey, April 20, 2003.
url: http://ww.cse.ust.hk/~gabriel/Group/P2Psurvey/TR-P2P.pdf
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Thank you
Questions and suggestions are
welcome!!!
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