1 Deterministic Collision-Free Communication Despite Continuous Motion ALGOSENSORS 2009 Saira Viqar Jennifer L. Welch Parasol Lab, Department of CS&E TEXAS.

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Deterministic Collision-Free Communication Despite Continuous

Motion

ALGOSENSORS 2009

Saira Viqar Jennifer L. Welch

Parasol Lab, Department of CS&ETEXAS A&M UNIVERSITY

Outline

• 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.

– 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

• Interference radius 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.

p q

R R’

r

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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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• 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

Collision Avoidance

muσ

muσ

λ

R+R’

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Maintenance of Neighborhood Knowledge

• (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

muσ

R

ρ

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Example Tiling

• Use – 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

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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• 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.

Schedules

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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– 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. • Assume lower bound on density: one node per tile. • Assume static nodes.• Shows how fast info traverses

a supertile.• Consider all pairs of tiles on

a supertile boundary.

Schedules Average number of rounds

Spiral 87.64828

Left to Right 293.16553

Random 275.25516

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.].

• Tailor schedules to applications

• Quantify constraints on motion and density for ensuring information propagations.– Analyze the rate of information propagation.

• Explore limitations of deterministic solutions– Lower bounds on performance.– Impossibility results.

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Questions

[email protected]