Victoria Manfredi (UMass)Robert Hancock (Roke)

Jim Kurose (UMass)

Robust Routing in Dynamic MANETsACITA 2008

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Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Outline

3

Problem

network structure changing over time

network protocols

must adapt

Adapt to every change? yes: perform optimally, but more overhead no: perform sub-optimally, but less overhead

robust: solution performs well over many scenarios, solution is not fragile

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src-dest reliability• stochastic graph• probability instantaneous path exists between src and dest

But,• reliability #P-complete to compute exactly• searching over all sub-graphs costly

Robust Routing

Find max reliability subgraph using specified # of nodes

Most robust routing subgraph

Identify structural properties of graph that make it reliable, efficiently find subgraph with those properties

Most robust routing subgraph

Robust routing: routing subgraph has path from src to dest, as links up/down

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Some Intuition

What is effect of graph structure on src-dest reliability?

src-dest reliability dominated by shortest paths

Most robust routing subgraph should contain shortest path and have large min cut

Small p limit

src-dest reliability dominated by smallest cuts

Large p limit

Given graph, src, dest, assume links iid and up with prob p

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Braid

s

d

ss

d d

k-hop braid: routing subgraph containing shortest path + all nodes within k-hops of shortest path

Shortest Path 1-Hop Braid 2-Hop Braid

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Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Outline

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Theoretical Analysis

Is braid max reliability subgraph using specified # of nodes?

s

N

d

Assumptions: links iid, up with prob p

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Theoretical Analysis

Lemma:

Suppose routing subgraph already contains shortest path and 0<n<N 1-hop nodes. Given 1 or 2 extra nodes to use, to max reliability, use all 1-hop nodes before any 2-hop nodes

Add black node rather than blue nodes?

When adding nodes incrementally, 1-hop braid most reliable

N

s d

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Conjecture 1: N extra nodes: 1-hop braid most reliable

From lemma: true for N ≤ 5

Conjectures

Generally: conjecture no “holes” in most reliable graph

N=6 N=6

Conjecture 2: 2N extra nodes: 2-hop braid most reliable

s d s d

Experimentally: for N=6, 2-hop braid more reliable than pyramid

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Adding edges rather than nodes

link up prob at which reliabilities of partial braid and 2-disjoint paths match

As N increases, partial braid more reliable for more values of p

Conjecture 3: N+1 extra edges: partial 1-hop braid most reliable

not true, see counterexamples

N=4 Partial braid less reliable than 2-disjoint paths for 1p√2/3

ds s d

Partial braid less reliable than 2-disjoint paths for 1p0

Partial Braid

N=3

2-Disjoint Paths

s sd d

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Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Outline

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Monte Carlo simulation

Assumptions links iid, 2-state link model random, torus graphs

500 runs, each lasting 100 time-steps

Reliability Experiments

up downp

1-p

1-q

q

Critical parameterT = time between routing updates

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What is Braid Reliability?

full graph

1-hop braid

2-shortest disjoint paths

shortest path

T = routing update interval

Re

liab

ility

Braid reliability: for these parameters, close to that of using full graph

Random, p=0.85, q=0.5

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What is Braid Overhead?

# of Nodes Used in Addition to Shortest Path

Ga

in in

Re

liab

ility

ove

r S

ho

rtes

t Pa

th

Full Graph

2 Shortest Disjoint Paths

1-Hop Braid

Braid overhead: significantly less than overhead of full graph

Random, p=0.85, q=0.5, T=5

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Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Outline

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Every T

Step 1: Identify shortest path in network

Step 2: Build braid around shortest path

Step 3: Perform local forwarding within braid key: each node within braid locally controls forwarding on outgoing links e.g., backpressure routing [Tassiulas&Ephremides,1992]

d

s

Robust Routing Algorithm

Local adaptation every time-step

Global adaptation every T time-steps

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GloMoSim 60 nodes, 250m transmission radius 1.5km x 1.5km area 1 cbr flow: 5 million pkts (~29 days) random waypoint: min 4km/hr, max 10km/hr, no pause

Compare throughput, overhead AODV 1-hop braid

built around AODV path

choose next hop based on last successful use

10 runs, each lasting life of flow

Routing Experiments

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What is Braid Throughput?

Packets delivered: braid delivers up to 5% more packets than AODV

T = routing update interval (seconds)

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What is Braid Overhead?

Braid overhead: ~25% more control overhead than AODV

T = routing update interval (seconds)

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Reliability vs Routing

Reliability gains Throughput gains

don’t use AODV, instead estimate link reliability

Braid construction independent of “best” path algorithm

Reliability experiments iid links shortest path = most reliable path

Routing experiments non-iid links

shortest path ≠ most reliable path

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Reliability vs Routing

Reliability gains Throughput gains

consider link correlations, mobility characteristics

Reliability experiments iid links rate at which down links re-appear is “high”

prob down link reappears = 0.5

broken link likely re-appears during T

Routing experiments non-iid links rate at which down links re-appear is “low”

2 nodes meet on avg once every 22.7 min

broken link likely does not re-appear during T

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Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Outline

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Related Work

2007: Motiwala, Feamster, Vempala Path splicing

2008: Tschopp, Diggavi, Grossglauser Paths within constant factor of length

of best path

Routing subgraph structurally like 1-hop braid … we also consider k-hop braids

1983: Shacham, Craighill, Poggio 2000: Lee, Gerla, 2000 2007: Nicolaou, See, Xie, Cui,

Maggiorini

Non-disjoint paths

Similar goals

2001: Ganesan, Govindan, Shenker, Estrin

For each node n on primary path add best path not using node n

Braided routing

2005: Mosko, Garcia-Luna-Aceves 2007: Ghosh, Ngo, Yoon, Qiao 2007: Su, Chan, Chan

Reliability

Differ in construction and structure of the routing subgraph

But different approaches

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Problem and Approach Theoretical Analysis Reliability Experiments Routing Experiments Related Work Conclusions and Future Work

Outline

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Conclusions

Braided routing increases reliability, throughput when re-computing routes less frequently:

Theoretical analysis validated by simulations but gains depend on network characteristics

Future work How do we incorporate network characteristics such as non-iid

links, rate at which links re-appear, more explicitly into braid and analysis?

Are there better ways to perform routing and rate control within braid? E.g., opportunistic routing, backpressure routing?

Should we build braid around most reliable path? Around path best situated to have a good braid?

How frequently should routes be re-built? What should be braid width (trade-off with interference)?

Can we make braid secure as well as robust?

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The authors would like to thank Majid Ghaderi, Matt Grossglauser, Andy Lam, John Spicer, Patrick Thiran, Don Towsley, and Andy Twigg for their input. This research was supported in part under the International Technology Alliance sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence under Agreement Number W911NF-06-3-0001, and by the National Science Foundation under award number CNS-0519998 and via an International Research in Engineering Education supplement to Engineering Research Centers Program award number EEC-0313747. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of the US Army Research Laboratory, the US National Science Foundation, the US Government, the UK Ministry of Defense, or the UK Government. The U.S. and U.K. Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.

Contact info: Victoria Manfredi vmanfred@cs.umass.edu

Thank You!

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Some Intuition

Given graph G, assume links iid and up with prob p

Pathsets Small p limit:

Reliability dominated by shortest paths

Cutsets Small q=1-p limit:

Un-reliability dominated by smallest cuts

Intuition: Short paths + Large cuts dominate

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Theoretical Analysis

s d

Lemma:

When incrementally adding nodes 1 or 2 at a time, adding all nodes one hop away from the shortest path before adding any nodes that are two hops away maximizes reliability

Add black node rather than grey nodes

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P({q0,q1} | {s0,s1}) P(d | {d0,d1})Product always for

adding black node

Theoretical Analysis

d

Proof:

s

P(d|s) = P(d | s0 s1) P(s0 s1|s) + P(d | s0 s1) P(s0 s1|s) + P(d | s0 s1) P(s0 s1|s)

- -- -

Recursively iterate: get eqn with 27 terms

s0

s1 s1

s0

q1

q0 q0 d0

q1 d1

d0

d1

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Conjectures

p

relia

bilit

y

Conjecture 2: 2N extra nodes: 2-hop braid most reliable

experimentally: for N=6, 2-hop braid more reliable than pyramid

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Derived recurrence relations: used to show adding nodes contiguously is more reliable

Growing 2xN Node Strip

Contiguously

Non-contiguously

ds

s d

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Disjoint Paths vs. Braid

Scaling behaviour as N increases

k disjoint paths NN+1 reliability decreases by roughly p (regardless of k)

k hop braid NN+1 reliability decreases by roughly 1-(1-p)2k+1

(which can be made small by increasing k)

This difference is due to braid’s ability to provide opportunities for local repair