Power-aware Topology Control in Wireless Ad Hoc Networks
description
Transcript of Power-aware Topology Control in Wireless Ad Hoc Networks
David S. L. Wei
Dept of Computer and Information SciencesFordham University
Bronx, New York
Szu-Chi Wang and Sy-Yen Kuo
Dept of Electrical EngineeringNational Taiwan University
Taipei, Taiwan
Joint work with
Introduction
Wireless ad hoc networks are - Characterized by scarce resources - Prone to topology changes - Lack of physical infrastructure
The flexibility and mobility of wireless ad hoc networks make them suitable for applications such as automated battlefields and disaster rescues
Introduction (cont.)
A wireless ad hoc network can be modeled by an undirected/directed graph G = (V, E)
Power conservation has been widely used as a primary control parameter in the design of protocols for wireless ad hoc networks
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Introduction (cont.)
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Motivations
Each node in a wireless ad hoc network can potentially change the network topology by adjusting its transmission range
The primary goal of topology control is to design power-efficient algorithms that
- Maintain network connectivity - Optimize performance metrics (network lifetime, throughput,…)
Preliminaries
In the most common power-attenuation model
- The transmission power between node u and v is denoted as
- All receivers have the same power threshold for signal detection
We assume that - Each mobile host has a low-power GPS receiver - Initially all the nodes are operated at full transmitter power ─ the resulted graph G is a unit-disk graph (denoted as UDG (V))
t ||uv|| + rp(u,v)
transmitter power
receiver power
Preliminaries (cont.)
Hereinafter we use G to present a wireless ad hoc network - The edge weight is defined as w(u, v) = t||uv|| + rp(u,v) - We also call G the transmission graph
A path from node u to node v is denoted as
The total transmission power of this path is
(u, v) = v0v1…vh-1vh where u = v0 and v = vh
h
iii vvwvup
11 ) ,()),((
Transmission Power Assignment
A transmission power assignment on the vertices is a function f from V into real numbers
Given a graph H = (V’, E’) , the transmission power assignment f is induced by H if for each node v V’,
The total transmission power of f is defined as
A transmission power assignment f is complete if the associated graph Gf is strongly connected
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uvwvfEuv
Vv ii
vf )(
Minimum-Energy Path
Given a communication graph H G, the minimum-energy path between node u and node v, denoted by H
min(u, v), is a path
whose total transmission power is the minimum among all paths that connect (u, v) in H
Let pH(u, v) stand for p(Hmin(u, v)), the power stretch factor of
H with respect to G is defined as
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,, vup
vupGpsf
G
H
vuVvuH
Related Works
Our major work is to develop a localized topology control algorithm where each node makes a decision about its transmission power based on only its local information
The two widely used energy conservation approaches in literature are to - Reduce the total transmission power - Reduce the power stretch factor
However, these two approaches may offset each other
The problem of finding a complete f whose total transmission power is the minimum among all of the complete assignments is called the min-total assignment problem
The min-total assignment problem is NP-hard when the nodes are deployed in a d-dimensional space, d 2
The general structure of the minimum-power topology for rp 0 is still unknown
Related Works (cont.)
Basic Ideas
The proposed algorithm is based on the following ideas - First construct a connected subgraph H = (V, E’) - Assure that the power stretch factor of H is bounded - The total transmission power is then minimized as much as possible
We use the local information of each node to excise some links of G while still keeps the power stretch factor being bounded by a predetermined value cb
Our Localized Topology Control Algorithm
The proposed algorithm consists of two phases - Phase I: Local shortest tree construction - Phase II: Path search replacement
A simple illustrative example is shown below
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Phase I of the Proposed Algorithm
Definition 1 (Local Topology View) The local topology view of node u, LTV (u, k) = (V’, E’)), is a subgraph of G such that (1) vi V’ if the hop distance between vi and u is no more than k (2) (vi, vj) E’ if both vi and vj belong to V’
Suppose that a subgraph of G is associated with a transmission power assignment f
- For each node u, if link (u, v) satisfies w (u, v) = f (u) then (u, v) is called a critical link of u
Phase I of the Proposed Algorithm (cont.)
Each node u individually applies Dijkstra’s algorithm to get the shortest-paths from the source u to the other nodes in LTV (u, 1)
The local shortest path tree of node u (denoted by LSPT (u)) can thus be obtained
DC (u) = {v V’ | h (LSPT (u), v) = 1}, where h (LSPT (u), v) is the height of a child node v in LSPT (u)
Node u then deletes the edges {(u, w) | w DC (u)}
The topology generated is denoted as GI
Phase II of the Proposed Algorithm
For each node u, its transmission power could be further reduced by trying to eliminate the critical links that are replaceable with alternative paths
For each critical link (u, v), node u tries to search another path that reaches node v based on LTV (u, k)
- We call such path the replacing path of (u, v) - The entire replacing paths of node u is denoted as RP (u)
The searching procedure is applying Dijkstra’s algorithm again on LTV (u, k)
Phase II of the Proposed Algorithm (cont.)
If no such path exists or no replacing path has transmission power cb w (u, v)
- The search process is ended - RP (u) is set as an empty list - ps (u) is set to 0
The priority of node u is a pair pri(u) = <ps(u), ID(u)>
- pri(v1) = (ps(v1), ID1), pr (v2) = (ps(v2), ID2) - pri(v1) > pri(v2) if ps(v1) > ps(v2) (ps(v1) = ps(v2) ID1 < ID2)
The above procedure for deciding RP (u) starts if node u has the highest priority in its k-hop neighborhood
Phase II of the Proposed Algorithm (cont.)
After Phase I, each node deletes its uni-directional links and the resulting topology is denoted as GII
The constructed topology after Phase II is denoted as GIII
A simple heuristic for further decreasing the total transmission power is also proposed
Important Properties
The minimum-energy path between any two nodes in G is preserved in GI
The minimum-energy path between the two end nodes of each deleted link in GI is preserved in GII
GII preserves the network connectivity of G
is bounded by cb
GIII preserves the network connectivity of G and has a bounded power stretch factor cb
)(III GpsfG
Dealing with Mobility
We also consider the case of modest movement of the nodes
It would be extremely difficult for a topology control algorithm to even effectively guarantee network connectivity if network topology changes too fast
As mentioned in previous works, node movement can be viewed as two events, namely node addition and node deletion
In our case, however, at the beginning of each beacon interval each node u should check if there is a change in transmission radius after deciding the new logical links
Performance Comparisons
We compared the performance via extensive simulations
We observe the following metrics of each constructed topology H
- Total transmission power (denoted by tpc) - Power stretch mean (denoted by psm)
- The maximum power stretch factor (denoted by max psf) - The variance of transmission power (denoted by var tp) - Average node degree (denoted by avg nd) - The maximum node degree (denoted by max nd)
Simulation ResultsThe Performance Measurements with s = 1 The Performance Measurements with s = 3
The Performance Measurements with s = 5 The Performance Measurements with s = 7
tpc psm
s = 1
max psf avg nd max nd
1.0
0.000328
1.0
1.0
0.000123 1.03482
0.000666 1.0
0.000099 1.1967
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.99171
1.0
9.70118
96.5312
2.6996
2.1356
3.5992
1.98
99
6
5
8
4
0.000178 1.0ESPT1 1.0 2.4252 5
0.000137 1.016ESPT2 , cb=1.5 1.49991 2.2036 4
0.0
1.20E+15
1.27E+14
4.68E+15
9.30E+13
2.43E+14
1.52E+14
var tp
0.000253 1.01491AMST 2.51846 2.3386 58.76E+14
tpc psm
s = 1
max psf avg nd max nd
1.0
0.000328
1.0
1.0
0.000123 1.03482
0.000666 1.0
0.000099 1.1967
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.99171
1.0
9.70118
96.5312
2.6996
2.1356
3.5992
1.98
99
6
5
8
4
0.000178 1.0ESPT1 1.0 2.4252 5
0.000137 1.016ESPT2 , cb=1.5 1.49991 2.2036 4
0.0
1.20E+15
1.27E+14
4.68E+15
9.30E+13
2.43E+14
1.52E+14
var tp
0.000253 1.01491AMST 2.51846 2.3386 58.76E+14
tpc psm
s = 3
max psf avg nd max nd
1.0
0.026874
1.0
1.0
0.010102 1.03485
0.05339 1.0
0.010074 1.08511
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.99906
1.0
6.31301
25.5408
2.7016
2.1372
3.59
2.0258
53
6
5
8
4
0.01495 1.0ESPT1 1.0 2.4284 5
0.011188 1.01516ESPT2 , cb=1.5 1.49855 2.2044 4
0.0
8.10E+18
8.56E+17
2.82E+19
2.01E+18
2.60E+18
9.95E+17
var tp
0.020503 1.01413AMST 2.46733 2.3388 45.71E+18
tpc psm
s = 3
max psf avg nd max nd
1.0
0.026874
1.0
1.0
0.010102 1.03485
0.05339 1.0
0.010074 1.08511
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.99906
1.0
6.31301
25.5408
2.7016
2.1372
3.59
2.0258
53
6
5
8
4
0.01495 1.0ESPT1 1.0 2.4284 5
0.011188 1.01516ESPT2 , cb=1.5 1.49855 2.2044 4
0.0
8.10E+18
8.56E+17
2.82E+19
2.01E+18
2.60E+18
9.95E+17
var tp
0.020503 1.01413AMST 2.46733 2.3388 45.71E+18
tpc psm
s = 5
max psf avg nd max nd
1.0
0.159539
1.0
1.0
0.086227 1.03671
0.245597 1.0
0.10403 1.03698
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.9971
1.0
4.38695
10.4232
2.6596
2.1564
3.4496
2.135
27
5
5
8
4
0.122629 1.0ESPT1 1.0 2.45 5
0.09287 1.01372ESPT2 , cb=1.5 1.49999 2.2236 5
0.0
1.47E+20
6.51E+19
2.29E+20
9.96E+19
1.08E+20
6.87E+19
var tp
0.128633 1.01305AMST 2.49099 2.3204 41.15E+20
tpc psm
s = 5
max psf avg nd max nd
1.0
0.159539
1.0
1.0
0.086227 1.03671
0.245597 1.0
0.10403 1.03698
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.9971
1.0
4.38695
10.4232
2.6596
2.1564
3.4496
2.135
27
5
5
8
4
0.122629 1.0ESPT1 1.0 2.45 5
0.09287 1.01372ESPT2 , cb=1.5 1.49999 2.2236 5
0.0
1.47E+20
6.51E+19
2.29E+20
9.96E+19
1.08E+20
6.87E+19
var tp
0.128633 1.01305AMST 2.49099 2.3204 41.15E+20
tpc psm
s = 7
max psf avg nd max nd
1.0
0.299838
1.0
1.0
0.228194 1.03382
0.380877 1.0
0.254784 1.0228
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.99931
1.0
3.14811
5.6392
2.44
2.1096
2.9548
2.1376
14
6
5
8
4
0.27593 1.0ESPT1 1.0 2.3468 5
0.237019 1.0135ESPT2 , cb=1.5 1.4938 2.158 5
0.0
3.01E+20
2.32E+20
3.46E+20
2.71E+20
2.86E+20
2.40E+20
var tp
0.261474 1.01752AMST 2.8558 2.1856 42.66E+20
tpc psm
s = 7
max psf avg nd max nd
1.0
0.299838
1.0
1.0
0.228194 1.03382
0.380877 1.0
0.254784 1.0228
UDG
SMECN
ESPT2 , cb=2.0
GG
LMST
1.0
1.0
1.99931
1.0
3.14811
5.6392
2.44
2.1096
2.9548
2.1376
14
6
5
8
4
0.27593 1.0ESPT1 1.0 2.3468 5
0.237019 1.0135ESPT2 , cb=1.5 1.4938 2.158 5
0.0
3.01E+20
2.32E+20
3.46E+20
2.71E+20
2.86E+20
2.40E+20
var tp
0.261474 1.01752AMST 2.8558 2.1856 42.66E+20
Network topologies constructed by various algorithms I
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Topology by UDG
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Topology by GG
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Topology by AMST
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Topology by SMECN
Network topologies constructed by various algorithms II
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Topology by ESPT2, cb = 1.5
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Topology by ESPT2, cb = 2.0
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Topology by ESPT1LMST
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Topology by LMST
Conclusions
In this paper we develop a localized algorithm that requires only local information for constructing a logical topology on a given unit disk graph
The topology constructed by our algorithm has several desired features such as bounded power stretch factor, low total power consumption, and small variance of transmission power
The simulation results show that our algorithm outperforms others in terms of various important metrics
Future Research
• Power-aware topology control
• Topology control of ad-hoc networks in three-dimensional space
• Secure topology control algorithm
• Applications in overlay control for P2P communications
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