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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
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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 [email protected]
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