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Capacity Scaling in Delay Tolerant Networks with Heterogeneous Mobile Nodes

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Title: On the capacity of ad hoc networks under general node mobility Author: Paolo Giaccone Last modified by: Emilio Leonardi Created Date: 1/3/2007 8:18:03 AM – PowerPoint PPT presentation

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Title: Capacity Scaling in Delay Tolerant Networks with Heterogeneous Mobile Nodes


1
Capacity Scaling in Delay Tolerant Networks with
Heterogeneous Mobile Nodes
  • Michele Garetto Università di Torino
  • Paolo Giaccone - Politecnico di Torino
  • Emilio Leonardi Politecnico di Torino
  • MobiHoc 2007

2
Outline
  • Introduction and motivation
  • Assumptions and notations
  • Main results
  • Some hints on the derivation of results
  • Conclusions

3
Introduction
  • The sad Gupta-Kumar result
  • In static ad hoc wireless networks with n
    nodes, the
  • per-node throughput behaves as

P. Gupta, P.R. Kumar, The capacity of wireless
networks, IEEE Trans. on Information Theory,
March 2000   
4
Introduction
  • The happy Grossglauser-Tse result
  • In mobile ad hoc wireless networks with n nodes,
    the per-node throughput remains constant
  • assumption uniform distribution of each node
    presence over the network area

M. Grossglauser and D. Tse, Mobility Increases
the Capacity of Ad Hoc Wireless Networks,
IEEE/ACM Trans. on Networking, August 2002
5
Introduction
  • Node mobility can be exploited to carry data
    across the network
  • Store-carry-forward communication scheme

S
R
D
  • Drawback large delays (minutes/hours)
  • Delay-tolerant networking

6
Mobile Ad Hoc (Delay Tolerant) Networks
  • Have recently attracted a lot of attention
  • Examples
  • pocket switched networks (e.g., iMotes)
  • vehicular networks (e.g., cars, buses, taxi)
  • sensor networks (e.g., disaster-relief networks,
    wildlife tracking)
  • Internet access to remote villages (e.g., IP over
    usb over motorbike)

7
The general (unanswered) problem
  • Key issue how does network capacity depend on
    the nodes mobility pattern?
  • Are there intermediate cases in between extremes
    of static nodes (Gupta-Kumar00) and fully mobile
    nodes (Grossglauser-Tse01)?

8
Outline
  • Introduction and motivation
  • Assumptions and notations
  • Main results
  • Some hints on the derivation of results
  • Conclusions

9
Assumptions
  • n nodes moving over closed connected region
  • independent, stationary and ergodic mobility
    processes
  • uniform permutation traffic matrix each node is
    origin and destination of a single traffic flow
    with rate l (n) bits/sec
  • all transmissions employ the same nominal range
    or power
  • all transmissions occur at common rate r
  • single channel, omni-directional antennas

destination node
source node
10
Protocol Model
  • Let dij denote the distance between node i and
    node j, and RT the common transmission range
  • A transmission from i to j at rate r is
    successful if

for every other node k simultaneously
transmitting
RT
(1?)RT
k
j
i
11
Realistic mobility models for DTNs
  • characterized by
  • Restricted mobility of individual nodes
  • Non-uniform density due to concentration points

From Sarafijanovic-Djukic, M. Piorkowski, and M.
Grossglauser, Island Hopping Efficient
Mobility-Assisted Forwarding in Partitioned
Networks,, IEEE SECON 2006
From J.H.Kang, W.Welbourne, B. Stewart,
G.Borriello, Extracting Places from Traces of
Locations, ACM Mobile Computing
and Communications Review, July 2005.
12
Home-point based mobility
Each node has a home-point
and a spatial distribution around the
home-point
13
Home-point based mobility
  • The shape of the spatial distribution of each
    node is according to a generic, decreasing
    function s(d) of the distance from the home-point

s(d)
d
14
Anisotropic node density (clustering)
  • Achieved through the distribution of home-points

Clustered model nodes randomly assigned to m
n? clusters uniformly placed over the area.
Home-points within disk of radius r from the
cluster middle point
Uniform model home-points randomly placed over
the area according to uniform distribution
n 10000
15
Scaling the network size
10 nodes100 nodes..1000 nodes
Moreover node mobility process does not depend
on network size
16
Asymptotic capacity
  • We say that the per-node capacity is
    if there exist two constants c and c such that
  • sustainable means that the network backlog
    remains finite
  • Equivalently, we say that the network capacity in
    this case is

17
Outline
  • Introduction and motivation
  • Assumptions and notations
  • Main results
  • Some hints on the derivation of results
  • Conclusions

18
Asymptotic capacity results
logn ?(n)
Uniform Model
0
per-node capacity
-1/2
Independently of the shape of s(d) !
-1
0
1/2
Recall
19
Asymptotic capacity results
logn ?(n)
Clustered Model
0
per-node capacity
-1/2
Super-critical regime mobility helps
Lower bound in case s(d) has finite support
Lower bound in case s(d) has finite support
-1
Sub-critical regime mobility does not help
0
1/2
Recall clusters
20
Outline
  • Introduction and motivation
  • Assumptions and notations
  • Main results
  • Some hints on the derivation of results
  • Conclusions

21
A notational note
  • In the analysis we have fixed the network size,
    L1
  • and let the spatial distribution of nodes s(d)
    to scale with n, i.e., s(f(n)d)

f(n)1
f(n)2
f(n)3
22
Uniformly dense networks
  • We define the local asymptotic node density ?(XO)
    at point XO as

Where is the disk centered
in XO , of radius
  • A network is uniformly dense if

23
Properties of uniformly dense networks
  • Theorem the maximum network capacity is
    achieved by scheduling policies forcing the
    transmission range to be
  • Corollary simple scheduling policies leading to
    link capacities

are asymptotically optimal, i.e., allow to
achieve the maximum network capacity (in order
sense)
24
Super-critical regime
  • Let (m n in the
    Uniform Model)
  • When we are in the
    super-critical regime
  • Theorem in super-critical regime a random
    network realization is uniformely dense w.h.p.
  • Transmission range is
    optimal
  • Scheduling policy S is optimal

25
Mapping over Generalized Random Geometric Graph
(GRGG)
  • Link capacities can be evaluated in terms of
    contact probabilities
  • which depend only on the distance dij between the
    homepoints of i and j
  • We can construct a random geometric graph in
    which
  • vertices stand for homepoints of the nodes
  • edges are weighted by
  • Network capacity is obtained by solving the
    maximum concurrent flow problem over the
    constructed graph

26
Upper bound network cut
1
0
1
1/2
27
Average/random flow through the cut
  • The average flow through the cut is computed as
  • fundamental question

Answer YES !
1
Proofs idea Consider regular tessellation
where squarelets have area ?(n) Take upper and
lower bounds for number of homepoints falling in
each squarelets, combined, respectively, with
lower and upper bounds of distances between
homepoints belonging to different squarelets
0
1
1/2
28
An optimal routing scheme
Routing strategy Consider a regular
tessellation where squarelets have area
s
Create a logical route along sequence of
horizontal/vertical squarelets, choosing any node
whose home-point lie inside traversed squarelet
as relay
d
  • The above routing strategy sustains per-node
    traffic

29
Sub-critical regime
  • Network is not uniformly dense
  • Transmission range may fail even to guarantee
    network connectivity
  • When s(d) has finite support
  • Nodes have to use
  • System behaves as network of m static node

30
Conclusions
  • We analyzed the capacity of mobile ad-hoc
    networks under heterogeneous nodes
  • Our study has shown the existence of two
    different regimes
  • superctritical
  • Subcritical
  • In this paper we have mainly focused on the
    supercritical regime
  • Subcritical behavior must be better explored

31
Questions ?
Comments ?
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