Impact of Interference on Multihop Wireless Network Performance Kamal Jain, Jitu Padhye, Venkat Padm

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Impact of Interference on Multi-hop Wireless
Network Performance --Kamal Jain, Jitu Padhye,
Venkat Padmanabhan and Lili Qiu
IEG 5200 Optimization and control in
Communication Networks

• LIU Jian (IE Dept.) and WU Weijie (CSE Dept.)
• --With acknowledgements to authors slides and
  Leons slides

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Outline

• Problem raising
• Modeling and bound computing
• Overview of framework
• Protocol model
• Single-path model
• Simulation, results and analysis
• Summary

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Problem raising

• Fundamental issue
• What is the maximum throughput that can be
  supported by a given multi-hop wireless network?
• Distinction from previous work
• Establishing a general modeling without specific
  assumptions

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Outline

• Problem Raising
• Modeling and bound computing
• Overview of framework
• Protocol model
• Single-path model
• Simulation, Results and Analysis
• Summary

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Overview of framework

• Goal To find the maximum throughput
• Architecture of framework
• Model a wired network
• Model a wireless network by adding Interference
  constrains
• Adding different constrains by giving different
  models
• Find maximum throughput by solving the
  optimization problems

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Wired network modeling

• Formulation for single source-destination model

• LP formulation, easy to solve

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Wireless Network -- Protocol model

• A transmission is successful if
• Receiver stays within the communication range of
  the sender
• Other nodes that can interfere the receiver are
  not sending

• How to express these constrains into the LP
  formulations?
• Introducing the conception of Conflict Graph

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Conflict graph

• A vertex in a conflict graph F correspond to
  the a link in the connectivity graph G.
• An edge exist if the two links may not be active
  simultaneously.

Conflict Graph (F)
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Definitions about conflict graph

• Independent set
• A set of vertices of which no edge exist between
  any two of them
• Independent vector
• A V-size vector mapping from independent set
• Consider it as a point in a V-dimensional space

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One independent set 2,3,4,6 Corresponding
independent vector (0,1,1,1,0,1)
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Definitions about conflict graph

• Independent set polytope
• Convex combinations of independent vectors
• Given independent vectors a1,a2,,ak
• Independent set polytope is Si?iaiS?i1, ?igt0
• Usage vector
• A V-size vector
• each value denotes the fraction of time for each
  link

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Constrains under protocol model

• Theorem
• A usage vector is schedulable iff it lies within
  the independent set polytope of the conflict
  graph.
• Corresponding constrains

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Methodology to find optimality

• Difficulty on the constrains
• Given network, sources and destinations
• NP-hard to find all independent sets of a graph
• NP-hard to find or approximate the optimal
  throughput
• Methodology
• Try to find the lower and upper bound
• When they converge, the value will be the exact
  one
• When will they converge? Discuss later

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Lower bound

• Equivalent to find a throughput with feasible
  schedule
• Goal To find the maximum polytope
• How to solve?
• Exponentially expensive to find all maximal
  independent sets
• To find as many as possible
• Just try to pick easy points Discuss later
• The more we pick, the tighter the bound will be,
  and eventually converge to optimal

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Upper bound

• How to lower the upper bound?
• To find as many as constrains
• Particularly total usage of links in a clique lt
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• Special cases about odd holes and anti-holes
• Anyway, this upper bound may still not be tight

odd holes and anti-holes
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Wireless Network -- Single-path model

• Difference from Multi-path model
• At any node in the network, at most one out-going
  edge that has a non-zero flow
• Corresponding constrains to add
• Even more difficult to solve integer programs

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Outline

• Problem raising
• Modeling and bound computing
• Overview of framework
• Protocol model
• Single-path model
• Simulation, results and analysis
• Summary

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Simulation, Results Analysis

• Consider a simple 33 Grid as following

9 nodes 24 links
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Simulation, Results Analysis

• We can then present its Conflict Graph like this

1 Conflict 0None
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To get lower bound means

• A simple algorithm to find IS (Independent Set)
• 1. Start with an empty IS
• 2. Add a new vertex to IS iff it doesnt have
  an edge to the existed vertices in IS so far
• 3. Repeat 2 until we consider all the vertices
• 4. Check to see if we have found this IS
  before if not, we add a new constraint to our
  LP Otherwise, ignore it.
• This is called one unit of effort.
• For the upper bound, we make similar effort to
  search for cliques instead of IS.

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Simulation, Results Analysis

• Calculated result of the upper lower bound

Still has a gap
0.5
Converge to optimal value
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Simulation, Results Analysis
Figure1. A Real Neighborhood Map
Figure2. The Connectivity Graph

• Using the basic Single Path Routing, we obtain
  the optimal cumulative throughput is 0.5

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Generalizations

• Multiple Source-Destination Pairs
• Assign a connection identifier to each
  source-destination pair
• Multiple wireless channels
• Easily modeled by introducing M links between
  nodes i and j
• Multiple radios per node
• Similar to above but may be active simultaneously

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Simulation, Results Analysis

• Possible throughput improvement
• I) Multi-path routing
• II) Double radio range
• III) Two non-overlapping channels
• IV) Two radios per node
• Results

(tend to choose similar path)
(Double the interference too !)
(Double the link capacity)
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Simulation, Results Analysis
More nodes, more interference, throughput
decrease?

• Tradeoff Connectivity V.S. Throughput

Figure1. Connectivity Ratio for 77 grid
Figure2. Normalized per-flow throughput
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Simulation, Results Analysis

• Optimal routing in absence of optimal scheduling
• Four scenarios

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Simulation, Results Analysis

• Optimal routing under optimal scheduling

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Value gt 1 1) always better
Table1. Throughput ratios between scenario 1) and
2)
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Simulation, Results Analysis

• Optimal routing in absence of optimal scheduling

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Value vs. 1 3) sometimes worse!
Table2. Throughput ratios between scenario 3) and
4)
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Outline

• Problem raising
• Modeling and bound computing
• Overview of framework
• Protocol model
• Single-path model
• Simulation, results and analysis
• Summary

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Summary

• The paper presented a model and methodology for
  computing bounds on the optimal throughput that
  can be supported by a multi-hop wireless network.
• Key contribution the generality of the
  methodology and the conflict graph framework.
• The optimal route often outperforms shortest path
  route.
• The richer connectivity contributed by new nodes
  more than offset the increase in traffic load
  they cause.

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• Q and A
• Thanks!

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Wireless Network Physical model

• Constrain under the model
• A link exist iff
• Why introduce
• More similar to real network
• Interference gradually increases
• Prospective tighter upper bound
• Weighted conflict graph

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Lower and upper bound

• Lower bound
• Similar to protocol model
• Schedulable set
• Upper bound
• Similar conception of clique
• Additional constrain