Deterministic Collision-Free
Communication Despite Continuous
Motion
ALGOSENSORS 2009
Saira Viqar
Jennifer L. Welch
Parasol Lab, Department of CS&E
TEXAS A&M UNIVERSITY
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Outline
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Problem Definition
Contributions
Applications
Related Work
System Model and Definitions
Solution
Examples
Simulation results
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Problem Definition
• Deterministic solution for nodes to
communicate reliably.
• Every node gets infinitely many
opportunities to broadcast.
• Medium Access Control (MAC) Layer for
mobile ad hoc networks.
• Nodes may be in continuous motion on
the plane.
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Why this is difficult
• Shared communication medium.
• Collisions in a wireless network cannot
be detected reliably.
• Continuous mobility of nodes.
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Contribution
1. Collision-free communication scheme for
continuously mobile nodes.
2. Deterministic technique for maintenance of
neighborhood knowledge.
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The two parts above are interleaved and interdependent.
Assume that initially nodes possess local neighborhood
knowledge
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Applications
• Deterministic guarantees: real time,
mission critical applications:
– VANETs (Vehicular ad hoc networks)
• Driver safety.
• Adverse traffic conditions, severe weather.
– Robotic Sensor Networks.
• Rescue.
• Reconnaissance.
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Related Work
• Much of the previous work assumes static nodes
[Gandhi et al.], [Prabh et al.] .
• Some protocols handle node mobility but rely on
centralized infrastructure [Arumugam et al.].
• [Ellen et al.] present deterministic collision-free
schedule for nodes on a one-dimensional line.
• No previous deterministic solution for continuously
mobile nodes in two dimensions.
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Definitions
• There are n nodes which move on a 2 dimensional plane.
• The mobile nodes may fail at any time. We only consider
crash failures.
• Unique ids from set I which is bounded in size.
• Each node has a trajectory function which gives the
location of the node at any time.
• Maximum speed of each node is σ
• Each node has access to the current time (through GPS
etc.)
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Definitions cont.
• Broadcast radius R
R
• Interference radius R’
p
R’
q
r
• Broadcast slot: time it takes for a node to complete
its transmission.
• Assumption: upper bound on the number of nodes per
unit area.
• Assumption: node’s trajectory function does not
change for a certain fixed interval of time.
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Solution
• Use a combination of space division multiplexing
(SDM) and time division multiplexing (TDM).
• Tile the plane with hexagons.
– Regular tiling.
– Approximation of circular broadcast range.
• Mobile nodes are dynamically allocated broadcast
slots depending on the tile they occupy at specific
times.
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Space Division Multiplexing
– Partition hexagons into m
colors.
– m contiguous hexagonal
tiles of different colors
form a supertile.
– Nodes in two same colored
hexagons broadcast
simultaneously.
– These nodes are too far
apart to cause
interference.
• Size (m) and shape of
supertile is carefully
chosen to ensure this.
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Time Division Multiplexing
• Fixed number of broadcast slots (u) form a round: this
corresponds to one hexagon
– maximum number of nodes that can occupy a tile at any
instant is v <u
• m rounds = 1 phase: this corresponds to a supertile.
• A node is allocated a slot in a phase depending on its
location at the beginning of the phase.
1 round=
u broadcast
slots
Color: 0
1
2
…
m-1
0
1
2
…
1 phase
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Collision Avoidance
• m depends on value of R, R’ and σ
• Supertile should be large enough:
– Nodes in tiles of same color at the beginning of a phase
should remain far enough apart even if they move straight
towards each other
– (C1) λ- 2muσ ≥R+R’
– Lemma 1: If (C1) holds then every broadcast that arrives at a
node is received
mu
σ
R+R’
mu
σ
λ
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Maintenance of Neighborhood Knowledge
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(A1) Assumption: Initially every node knows about every other node
within R of itself.
Size of tiles depends on R.
R spans more than two tiles.
(C2) ρ+2muσ ≤ R
• Lemma 2:
If assumption (A1) and
constraints (C1) and (C2) hold,
then at the beginning of each
phase П (П> 0) every node
knows about every node that
is in its own or an adjacent
hexagon.
muσ
R
ρ
muσ
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Example Tiling
• Use
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R=250 meters
R’=550 meters
σ =200 km/hour
1 phase=100 millisec
• The tiling shown
satisfies these
parameters
• It consists of 5
concentric rings of
hexagons in one
supertile.
• m=91
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Schedules
• A schedule defines the order in which rounds are
allocated to colors in a supertile.
– Tailoring it to mobility pattern of the nodes (e.g.
on a highway) vs. a general purpose schedule.
– Prerequisite for propagation of information: lower
bound on density of the nodes.
• For example for information to get from A to B requires
connected path of neighbors for a specific interval.
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Schedules
• May span multiple phases.
• Liveness: every color is allocated at least one
round in the schedule
• Fairness: each color is allocated the same
number of rounds in the schedule.
• Directional bias: favors the propagation of
information in one particular direction.
– Should be avoided in a general purpose schedule.
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Schedules
• Left to Right schedule.
• Suffers from
directional bias.
• Favors left to right
information
propagation but not
right to left.
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Schedules
• Spiral schedule.
• 4 Phases
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Clockwise outwards
Anticlockwise inwards
Anticlockwise outwards
Clockwise inwards
• Helps information
propagation in all
directions (inwards,
outwards, left, right,
up, down).
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Simulation Results
Comparison of number of rounds on different paths between
points on the boundary tiles of a supertile.
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Assume lower bound on density: one node per tile.
Assume static nodes.
Shows how fast info traverses Schedules
a supertile.
Spiral
Consider all pairs of tiles on
a supertile boundary.
Left to Right
Random
Average number of
rounds
87.64828
293.16553
275.25516
250
200
150
100
50
0
Spiral schedule
Left to Right schedule
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
525
550
575
600
625
650
675
700
725
750
775
800
825
850
No. of Paths
How many paths can be traversed in a certain
Number of Rounds
Random schedule
rounds
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Conclusions
1. Collision-free communication scheme for
continuously mobile nodes.
2. Deterministic technique for maintenance of
neighborhood knowledge.
3. General purpose schedule.
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Open Problems
•
Relax assumption about initial knowledge
• possibly related lower bound of (N − n)A [Krishnamurthy et
al.].
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Tailor schedules to applications
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Quantify constraints on motion and density for ensuring information
propagations.
– Analyze the rate of information propagation.
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Explore limitations of deterministic solutions
– Lower bounds on performance.
– Impossibility results.
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Questions
viqar@cse.tamu.edu
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