Message Ferry Route Design for Sparse Ad hoc Networks with Mobile Nodes

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Message Ferry Route Design for Sparse Ad hoc
Networks with Mobile Nodes

• Muhammad Mukarram Bin Tariq, Mostafa Ammar, Ellen
  Zegura
• mtariq, ammar, ezw_at_cc.gatech.edu
• College of Computing,
• Georgia Institute of Technology

ACM Mobihoc 2006May 22-25, Florence, Italy.
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Message Ferrying Model

• Sparse Mobile Ad hoc Network
• Very infrequent contacts among nodes
• A special node Message Ferry facilitates
  connectivity
• Visits nodes
• Delivers messages among them
• Ferry route
• A predetermined path that ferry follows
  repeatedly
• Each traversal is called a tour
• Service Model
• Nodes have a send and receive buffer
• Messages lost if send buffer overflows
• Service is Time-limited
• Upload Service Send Buffer Emptied or Upload
  Timer Expires
• Residue messages Messages left over in send
  buffer after timer
• Download Service Receive Buffer full, or
  Download Timer Expires, or Ferry does not have
  more messages for the node
• Constraints
• Ferry has unlimited resources
• Buffer, Communication, Movement
• Speed of the ferry is limited

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Summary

• Problem How to design route for Message Ferry,
  when the nodes in the network have arbitrary
  movement?
• Cant be certain of nodes location at any time
• Where to place the ferry to make contacts with
  the nodes
• Solution Optimized Waypoints Ferry Route
  Carefully chosen waypoints and waiting times at
  the waypoints
• Lets not try meet nodes with certainty repeated
  and calculated attempts node-ferry contact
  occur with certain controlled probability in each
  attempt
• Waypoints and waiting times are chosen using the
  nodes mobility model information
• Significantly improved performance in terms of
  node-ferry contact frequency, fairness of
  service, and message delay and loss

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Problem Statement

• Problem Formulate Ferry Route when the nodes
  have arbitrary movement, such that
• Node Movement is not disrupted
• No online collaboration between the nodes and the
  ferry
• E.g., due to limited communication range of the
  nodes
• Goal Good Performance
• frequent contacts with all the nodes
• Challenge
• Cant be certain of node location
• How to position the ferry so that the two meet?

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Route Design Key Idea

• If the ferry waits sufficiently long at a point
  that has non-zero node presence probability, then
  a contact would occur
• Contact with certainty ? infinitely long wait for
  many mobility patterns
• Cant wait infinitely long have to serve other
  nodes too
• So lets not try to make contacts with certainty
• In many cases a modest desired contact
  probability can be achieved with moderately small
  amount of waiting
• Key Idea Device route such that the contact
  occurs with certain probability in each tour
• Tours for contact Geometric Random Variable
• Expected tours between contacts 1/p (p
  probability of contact in a tour)
• Expected time between contacts T/p (T is
  expected duration of the tour)
• Goal
• Increase contact frequency
• Decrease time between contacts, i.e., reduce T/p

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Route Design The finer points

• Route Waypoints Wait Times _at_ Waypoints
• Chosen carefully to achieve desired contact
  probability
• Requires understanding the mobility pattern
• What kind of information can be used to choose
  waypoints and waiting times?
• To reduce T/p
• Reduce T, Increase p, or both
• Tour duration T, includes
• Wait Time
• Journey Time
• Service Time
• p only increases with increasing Wait time (for
  many mobility patterns)
• Results in increased T
• Is there a sweet spot? (T/p trade-off)
• What is the right target contact probability p?
• The scheme is called Optimized Waypoints (OPWP)

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Route Design

• Ferry Route O (R, W, vf, r)
• R set of waypoints, chosen from a set of
  candidate waypoints, C.
• Wws s \in R ws is the waiting time at
  way-point s
• vf ferry speed
• r radius of communication
• a(s,r) circular region of radius r around point
  s
• Two types of contact possibilities
• Instantaneous Contact Probability
• Node is in the vicinity when the ferry arrives at
  a waypoints
• gi(a(s, r)) probability of presence of node i
  in region a(s,r)
• Time Cumulative Contact Probability
• Node arrives in the vicinity while the ferry is
  waiting at a waypoint
• hi(a(s, r)), ws) probability of arrival of node
  i in a(s,r) during ws

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Route Design (2.)

• Gi(O)Total instantaneous contact probability in
  route O
• Gi(O) maxs in R gi(a(s, r))
• Hi(O)Total time-cumulative contactprobability
  in route O
• Hi(O) maxs in R hi(a(s, r),ws)
• Goal Find O such that
• Gi(O) Hi(O) pi for all nodes i in the
  network
• We will see how to choose a pi little later

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Some Mobility Examples

• Stationary Node
• Exists some location, s, for which g(a(s,r)) is 1
• For such s, h(a(s,r), ws) 1, for all ws
• Periodic Movement with constant speed
• g(a(s,r)) depends on the intercept of a(s,r) with
  the path of node
• h(a(s,r), ws) min ?s/a, 1 a is the
  period
• for when a(s,r) intercepts, 0 otherwise(we see
  later that periodicity is not a problem as
  optimal p is 1 )
• Random Waypoint
• g(a(s,r)) follows a dome like shape with s
  Jardosh02, Helmy05
• h(a(s,r), ws) 1 exp(-ws/?s,r)
• ?s,r follows bowl like shape with s
• Larger s yields smaller ?s,r

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Ferry Route Design

• Ferry route design has two components
• Select appropriate way-points and wait time for
  each waypoint
• to minimize over all waiting time
• subject to ensuring minimum target contact
  probability for each node
• 2. Stitch the waypoints to form a route
• Order the way-points to form a minimum journey
  time route
• Planar TSP problem (in metric space)
• Caveat Can we pick way-points that yield good
  routes in terms of journey time?
• Save journey time reducing overall route time
• Heuristic weigh the distance of points from
  center of the region
• Minimize total waiting time total distance from
  center

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Ferry Route Design (2)

• Components of Tour Duration
• Tw Wait Time at Waypoints
• Tj Journey Time between Waypoints
• Ts Service Time
• Service Time
• Depends on the service discipline, service timers
  and the amount of messaging traffic
• Recall that we use a time-limited service model
• Expected Maximum Service Time Si1n pi(Ui Di)
• Sensible choice for service timers
• Ui gt ?iT/piB
• Di gt ?iT/piB

Ui Upload Timer Di Download Timer ?i Msg
Arrival Rate ?i Msg Consumption Rate T Tour
Duration B Channel BW msg/sec
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The T/p Tradeoff

• Goal Frequent Contacts
• Minimize T/p
• Reduce T, Increase p, or both
• Increasing p causes T to increase
• Is there a optimal p
• Yes depends on the mobility model
• Exponential h(a,w)
• CDF of exp rv. is concave, giving rise to a
  convex T/p
• Linear h(a,w)
• Suggests that ferry must meet the node in every
  tour!

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Simulations and Results

• Goal Evaluate Effectiveness of our scheme
• Performance
• Susceptibility to system parameters and node
  mobility models
• Simulation Setup
• Sparse Deployment n10 nodes
• 4km x 4km area S
• Node Mobility Models
• Random Waypoint (RWP) Nodes follow RWP in S
• Random Speed 9, 11 m/s
• Exponential Pause Time 1s
• Area Based RWP (AB-RWP) RWP but localized to1km
  x 1km area. Location chosen randomly from S
• Circular (CIRC) Move in along a circle of radius
  500m with randomly chosen center in S
• Random Speed 9, 11 m/s for each round.
  Exponential Pause Time of 1s at beginning of each
  round

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Simulation Setup (2.)

• System Parameters
• Uniform Traffic each message for one of (n-1)
  other nodes at random
• Messages arrive/consumed at 0.1 message/sec
• Send Buffer, Receive Buffer 1000 messages each
• B Channel between Node and Ferry 100 message/sec
• Communication Range 100 m
• Ferry beacons every 2 seconds
• Node and Ferry fail to meet if the node transits
  the vicinity, but does not get a beacon
• Single Ferry
• Uses one of the waypoint based routes
• Speed randomly from 9,11 m/s for each leg
• Ferry Route Models described next

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Simulation Ferry Route Models

• We compare between the following ferry route
  models
• Random Waypoint (RWP)
• Ferry moves according to RWP in S
• Restricted RWP (RWP-res)
• Ferry visits a random point in region of a
  randomly chosen node
• Space Filling Waypoint
• Ferry tries to cover the entire space
• Discretized space points joined using TSP
• Step 4r
• Regions Center Waypoint (RCWP)
• Ferry visits the center of the regions of nodes
• Locations ordered using TSP
• Optimized Waypoints (OPWP)
• The scheme we described
• Optimal p turned out to be around 0.6 for AB-RWP

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Results Evaluation Criteria

• Frequency of Contact
• Average Number of Contacts per unit time
• Fairness
• Higher average contact freq is achievable by
  targeting a subset of nodes, but not fair.
• Measured using Raj Jain Fairness Index
• Delay and Message Loss
• End-to-End Delay Message Generation to Delivery
• Messages lost at source due to buffer overflow
• Performance Under Different System Parameters
• Buffer Size
• Service Timers
• Sparseness of Deployment
• Ferry Movement Speed

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Results

• Contact Frequency
• Relates to Delay and Loss
• Lower Freq means messages must wait longer in
  send buffer and at the ferry
• Fairness
• Fair in approximately min-max sense
• No explicit effort to divide the excess contacts
  evenly

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Results Delay and Loss

• Delay E2E Delay (origination to delivery)
• Loss
• Fraction of Messages Lost due to buffer overflow
  at the source
• Relates to contact frequency as well as buffer
  sizes

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Impact of Buffer Size and Service Timers

• Buffer Size and Service Timers
• Critical parameters for loss
• Expected number of messages between successive
  contacts ?T/p
• Assume Buffer size k?T/p msgs
• Prob. of loss no contact in k successive tours ?
  decreases with k (simplified)
• In reality, residue makes analysis more
  complicated (ref time and buffer limited service
  models)
• Residue is function of service timers
• Larger service timer ? lesser residue ? lesser
  loss probability

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Impact of Sparseness, Ferry Speed

• Sparseness
• Results in larger journey time, as the nodes are
  deployed farther away
• Mostly larger T/p, despite increased optimal p
• Ferry Speed
• Reduces the journey time
• Reduces optimal p somewhat, but generally results
  in better T/p

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Summary and Conclusions

• Optimized Waypoints (OPWP) ferry route design
• Ferry routes for sparse networks with arbitrarily
  moving nodes without online collaboration or
  disruption of node mobility
• Use nodes mobility model information to choose
  waypoints and waiting times to optimize the
  contact frequency
• Adaptable to varying node mobility models and
  network parameters
• Demonstrates the utility of mobility models
• Random movement can be harnessed for better
  performance
• Future Work
• We use pretty loose lower bounds in this work
  these can probably be improved
• How to extend to mobility models such as BM
• Extend to multiple ferries when deployment is
  too sparse, or load too high
• Adaptability
• Hybrid schemes Node-node Node-ferry
  communication

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