Title: Message Ferry Route Design for Sparse Ad hoc Networks with Mobile Nodes
1Message 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.
2Message 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
3Summary
- 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
4Problem 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?
5Route 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
6Route 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)
7Route 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
8Route 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
9Some 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
10Ferry 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
11Ferry 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
12The 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!
13Simulations 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
14Simulation 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
15Simulation 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
16Results 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
17Results
- 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
18Results 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
19Impact 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
20Impact 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
21Summary 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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