Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective

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Delay and Capacity Trade-offs in Mobile Ad Hoc
Networks A Global Perspective

Gaurav Sharma,Ravi Mazumdar,Ness Shroff IEEE/ACM
Transaction on Networking, Vol 15,No 5. 2007,
pp981-991
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• Is node mobility a liability or an asset in
  ad hoc networks?

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• Liability
• Hand-off protocols for cellular networks Toh
  Akyol
• Adverse effect on the performance of traditional
  ad hoc routing protocols Bai, Sadagopan and
  Helmy
• Asset
• Grossglauser and Tse showed node mobility can
  increase the capacity of an ad hoc network, if
  properly exploited.
• The delay related issues were not considered.

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• To Provide better understanding of
• the delay and capacity trade-offs
• in mobile ad hoc networks (MANET)
• from a global perspective

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Outlines

• Introduction
• Capacity scaling of ad hoc networks
• Mobility can increase capacity
• Main contributions
• Main Results
• Overview
• The Models
• Hybrid random walk model
• i.i.d mobility model
• Random walk model
• Hybrid random direction model
• Discrete random direction model
• Brownian motion mobility
• Critical Delay and 2-hops Delay
• Critical Delay and 2-hops Delay Under Various
  Mobility Models
• Lower bound on critical delay for hybrid random
  walk models
• Upper bound on critical delay for hybrid random
  walk models
• Lower bound on critical delay for discrete random
  direction models
• Upper bound on critical delay for discrete random
  direction models

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Introduction
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Capacity scaling of ad hoc networks

• Study fundamental properties of large wireless
  networks Gupta Kumar
• Derive asymptotic bounds for throughput capacity
• To derive upper bounds, use
• Interference penaltynodes within range need to
  be silenced for successful communication
• Multi-hop relaying penalty a node that traverses
  a distance of d needs to use order of d hops.
• To derive constructive lower bounds, use
• Geographic routing strategic along great circles
• Greedy coloring schedules.

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Capacity scaling of ad hoc networks
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Mobility can increase capacity

• Grossglauser Tse achieve constant capacity
  scaling by two-hop relaying
• Gupta Kumar allow for constant capacity
  scaling if the traffic pattern is purely local.
• Source uses one of all possible mobile nodes as a
  relay.
• Source splits stream uniformly across all relays.
• When a mobile forwarder nears the destination, it
  hands off packet.

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Mobility can increase capacity

• Why does mobility increase capacity?
• By choosing a random intermediate relay, the
  traffic is diffused uniformly throughout the
  network.
• Thus, on average, every mobile node has a packet
  for every other destination and can schedule a
  packet to a nearby destination in every slot.
• (For those who took randomized algorithms, this
  is akin to permutation routing algorithms)
• Catch forwarding strategy improves capacity at
  the expense of introducing delay.
• Need to study the delay-capacity tradeoff!!

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Main contributions

• Delay-capacity tradeoff increasing the maximum
  allowable average delay increases the capacity.
• Delay-capacity tradeoff depends on network
  setting, mobility patterns.
• Different mobility models have been studied in
  the literature
• i.i.d
• Brownian motion
• Random way-point
• Random walk
• Difficult to compare results across paper because
  network setting are quite different.
• How does the mobility model affect the delay
  capacity trade-off?

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Main Results Notion of critical delay to compare
mobility modes

• For each mobility model, there is a critical
  delay below which node mobility cannot be
  exploited for improving capacity.
• Critical delay depends mainly on mobility
  pattern, not on network setting

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Overview

• Mobility can increase capacity.
• Delay-capacity tradeoff depends on network
  setting, mobility models.
• Some questions arises
• How representative are these mobility models in
  this study?
• Can the delay-capacity relationship be
  significantly different under the mobility
  models?
• What sort of delay-capacity trade-off are we
  likely to see in real world scenario?

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Main Results A new hybrid random walk model

• Propose and study a new family on hybrid random
  walk models, indexed by a parameter in 0,
  .
• For the hybrid random walk model with parameter
  ,critical delay is
• As approaches 0, the hybrid random walk
  model approaches an i.i.d mobility model.
• As approaches , the hybrid random walk
  model approaches a random walk mobility model.

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Main Results A new hybrid random walk model
1
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Main Results A new hybrid random direction model

• Propose and study a new family on hybrid random
  direction models, indexed by a parameter in
  0, .
• For the hybrid random direction model with
  parameter , the critical delay is
• As approaches 0, this hybrid random
  direction model approaches a random way-point
  model.
• As approaches , this hybrid random
  direction model approaches a Brownian mobility
  model.

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Main Results A new hybrid random direction model
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The Models
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Hybrid random walk model

• Divide the unit square into cells of area
  
• Divide each cell into sub cells of area
  
• In each time slot, a node is in one of sub cells
  in a cell.
• At the beginning of a slot, node jumps uniformly
  to one of the sub cells of an Adjacent cell

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i.i.d mobility model

• As approaches 0, we get i.i.d mobility.
• One big cell with n sub-cells.
• In each slot, a node is in one of the sub-cells.
• At the beginning of a time slot, a node jumps
  uniformly to one of the n subcells.

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Random walk model

• As approaches , we get the random walk.
• n cells, one sub-cell in each cell.
• In any slot, a node is in particular cell.
• At the beginning of a slot, node jumps uniformly
  to one of the adjacent cells.

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Hybrid random direction model

• Motion of a node is divided into trips.
• In a trip, node chooses a direction in 0,360
  and moves a distance
• Speed of movement (for scaling
  reasons).

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Discrete random direction model.

• Divide the square into cells of area
  tours of size
• Time divided into equal duration slots
• At the beginning of a slot, a node jumps
  uniformly to an adjacent cell.
• During a slot, the node chooses a start and end
  point uniformly inside the cell, and moves from
  start to end.
• Velocity of motion is made inversely proportional
  to distance.

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Brownian motion mobility

• For , the discretized random direction
  model degenerates to the random walk discrete
  equivalent of a Brownian motion with variance

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Critical delay and 2-hop delay
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Definition of critical delay

• We know that in the static node case, per node
  capacity is . Capacity achieving scheme
  is the multi-hop relaying scheme of Gupta
  Kumar.
• If mobility is allowed, the two-hop relaying
  strategy achieves per node capacity of
  Grossglauser Tse
• The two hop relaying strategy has an average
  delay of , under most mobility models.
• Mobility increase capacity at the expense of
  delay.

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Definition of critical delay (conti)

• Suppose we impose the constraint that the average
  delay can not exceed .
• Under this constraint, relaying strategy that use
  mobility will achieve a capacity ,
  somewhere between and
• For some critical delay bound , this
  capacity will be equal to capacity of
  static node networks.
• Below this critical delay , there is no benefit
  from using mobility based relaying.

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An illustration of critical delay
Capacity
Maximum average delay
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More on the critical delay

• It depends on the mobility mode.
• It provides a basic to compare mobility model.
• If mobility model A has lower critical delay than
  mobility model B , then A provides more leeway to
  achieve capacity gains from mobility than B.
• Critical delay also depends on what scheduling
  strategies are allowed.

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Critical Delay and 2-hops Delay Under Various
Mobility Models
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Lower bound on critical delay for hybrid random
walk models

• Obtain a value such that if average delay is
  below this value than (on average) packets travel
  a constant distance using wireless transmissions
  before reaching their destinations. For the
  hybrid random walk model , this value is
• Show that if packets are on average relayed over
  constant distance using wireless transmission,
  this results in a throughput of ,with
  the protocol model of the interference.
• Thus, the critical delay can not be any lower
  than this value.

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Lower bound on critical delay for hybrid random
walk models (cont)

• Step1 Establish a lower bound on the first exit
  time from a disc of radius
• Step2 If average delay is smaller than
  , than packets must on average be
  relayed over a distance no smaller than
• Pigeonhole argument
• Exit lemma
• Union Bound
• Motion arguments for successful relaying.

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Upper bound on critical delay for hybrid random
walk models

• Develop a scheduling and relaying scheme that
  provides a throughput of while
  incurring a delay of
• Consider a scheme where relay node transfer the
  packet to destination when it is in the same cell
  as destination
• Delay(approx) time for delay node to move into
  destination nodes cell.
• Packet arrivals are independent of mobility?
  delay is the same as mean first hitting time on a
  torus of size
• This first hitting time

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Upper bound on critical delay for hybrid random
walk models (conti)

• With this strategy, multi-hop relaying is only
  used once we reach the destinations cell, ie.,
  at most distance
• Each hop travels a distance
• Throughput loss from multihop relaying
• Since each wireless transmission travels
  ,nodes within this range must stay silent.
• An additional throughput loss of
• Combining the two, throughput

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Discussion on hybrid random walk models

• As increases, the critical delay increases,
  thereby shrinking the delay-capacity trade-off
  region.
• Two extreme cases
• i.i.d model when the static node capacity can be
  achieved even with a constant delay constraint.
• Random walk model where delay on the order of
  is required to achieve the static
  node capacity.

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Lower bound on critical delay for hybrid
discretized random direction models

• Same approach as before to obtain lower bound on
  critical delay as
• Step1 derive a lower bound on exit time from a
  disc of radius 8 under the random direction model
• Step2 If average delay is smaller than
  packets must on average be relayed over a
  distance on smaller than

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Upper bound on critical delay for hybrid
discretized random direction models

• Same strategy as before
• Replicate and give to relay node
• Relay node hands off to destination when it is in
  the cell of the destination
• Can obtain a throughput of with a
  delay of
• Provides an upper bound on critical delay for
  discreted random direction model.

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Discussion
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Discussion Characteristic path length

• Critical delay seems to be inversely proportion
  to characteristic path length of a mobility
  model.
• Characteristic path length is the average
  distance traveled before changing direction under
  the model.
• For example, with hybrid discretized random
  ditection model, characteristic path length is
  and the critical delay is

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Discussion Characteristic path length(cont)

• Thus, a scenario with nodes moving long distance
  before changing direction provides more
  opportunities to harness delay-capacity
  trade-off, e.g., random way point model vs.
  Brownian model.

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Conclusion
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Conclusion

• Motivate capacity-delay tradeoff in MANET(Mobile
  Ad-hoc NETworks ).
• Define critical delay to compare capacity-delay
  tradeoff region across mobility models.
• Define a parameterized set of hybrid random walk
  models and hybrid random direction models that
  exhibit continuous critical delay behavior from
  minimum possible to maximum possible.

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QA??????Thanks for your Listening