aswp – ad-hoc routing with interference consideration
DESCRIPTION
ASWP – Ad-hoc Routing with Interference Consideration. Zhanfeng Jia, Rajarshi Gupta, Jean Walrand , Pravin Varaiya Department of EECS University of California, Berkeley ISCC, June 28, 2005. Scenarios. Deploy troops into field Goals QoS Traffic classes, flow requirements Scalable - PowerPoint PPT PresentationTRANSCRIPT
ASWP – Ad-hoc Routing with Interference Consideration
Zhanfeng Jia, Rajarshi Gupta, Jean Walrand, Pravin Varaiya
Department of EECSUniversity of California, Berkeley
ISCC, June 28, 2005
Scenarios Deploy troops into field Goals
QoS Traffic classes, flow requirements
Scalable Difficulty
Interference
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Interference Wired networks
Independent links Ad-hoc networks
Neighbor links interfere Interference range >
Transmission range For simulations
Tx range = 500 m Ix range = 1 km
InterferenceRange
TransmissionRange
Node A
Node D
Node C
Node B
Link 2
Link 1
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Interference Model
Node
LinkLink
Conflict
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Non-Local Constraints Examples:
Local constraints would indicate 50% Ratio between global and local is bounded by the (chromatic) degree of imperfection
Square: 100%, Pentagon: 80%, Hexagon: 100%
50%50% 40%
Non-Local Constraints
Is new request feasible?
35
40
35 35
40
Links with current load (Mbps)Channel = 100Mbps
10Mbps
Request for new flow
Non-Local Constraints
With new flow: 45
40
45 45
40
Local constraints satisfied: Sum of locally conflicting links < 100
However, new flow is not possible
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Failure of Principle of Optimality Principle states: If optimal path from S
to D goes through A, then it follows optimal path from A to D. (Bellman)
S AD
Failure of Principle of Optimality
• Widest Path (31): path A (Capacity = 1)• Widest Path (51): path EDCB (Capacity = 1/2)
Path EDA has capacity only 1/3
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
NP-Completeness
Fact:Finding the widest path in conflict
graph is NP-Complete
Essentially, one has to try all the paths; there is no know polynomial algorithm.
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Approach: Approximation Clique Approximation: We assume that
scaled local constraints are sufficient. Fact: Known to be correct for
Unit disk graphs (scaling = 0.46) Graph with conflict radius in [x, 1]
(e.g., scaling = 0.40 if x = 0.8) Unfortunately, many graphs are not of
this type. E.g., unit disk graph with arbitrary
obstructions: Scaling can be arbitrarily close to 0.
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
K-Best Paths Recall Problem: Find widest path
between s and d. Width = available bandwidth measured by scaled clique constraints.
Since this problem is NP-Complete, we adopt the following heuristic:Each node maintains the list of the k-best paths; extensions by neighbors.Best: widest; ties resolved in favor of shorter.
K-Best Paths
Bellman approach Key step
Compute path width for one-hop extension
Bottleneck clique Unchanged A maximal clique that the extending link
belongs to Can be done locally
K-Best Paths – Example (1 5)
1: [- , 1]2: [B, 1]3: [A, 1], [BC, ½]4: [AD, ½], [BCD, ½]5: [ADE, 1/3], [BCDE, ½]
Path
Capacity
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Simulations – path width
50-node network Distant s/d pair
7 hops away X axis: load =
average clique utilization
Y axis: path width
Simulations – path width
50-node network Load = 0.32 All pairs performance X axis: distance
between s/d pair Y axis (upper): ratio
of improved s/d pair Y axis (lower):
average improvement
Simulations – admission ratio
50-node network Dynamic simulation 5 s/d pairs
Randomly chosen Given distance
Traffic model Flow requests: 4Kb/s, 10,000 flow requests Incoming rate: 0.32 flows per second Duration: uniform distribution between 400 and 2800
seconds Load = 0.32(400+2800)/24 = 2048 Kb/s = 2 Mb/s
Results: admission ratio (%) Note: Larger k is not necessarily better
distance
SP ASWP 2ASWP
4ASWP
2 hops 99.4 100 100 100
4 hops 47.9 54.8 54.8 54.7
7 hops 31.8 44.1 43.4 43.9
Mixed 66.5 71.4 71.0 70.9
More on ASWP Optimal path = shortest widest path Complexity
Polynomial, but … Running time (sec):
Optimal SWP necessary? Wide path = long path Long term behavior: bad
SP ASWP 2ASWP
4ASWP
5.3 27.9 50.4 80.0
50 nodes; MATLAB 6.0; 700MHz Pentium
Outline QoS Routing in Ad-Hoc Network
Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness
Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths
Simulations Conclusions
Conclusions Overall goals
Bandwidth guaranteed path Long-term admission ratio
Interference model Conflict constraints
ASWP solution Find shortest widest path Distributed algorithm
Bellman-Ford architecture + k-best-paths approach
A small k value is a good trade-off
Thank You!
www.eecs.berkeley.edu/~wlr
Google: jean walrand