aswp – ad-hoc routing with interference consideration zhanfeng jia, rajarshi gupta, jean walrand,...

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

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

Interference Model

Node

LinkLink

Conflict

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

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

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.

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.

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

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

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

aswp – ad-hoc routing with interference consideration zhanfeng jia, rajarshi gupta, jean walrand,...

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