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

Outline Problem Definition Contributions Applications Related Work System Model and Definitions Solution Examples Simulation results 2

3 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.

4 Why this is difficult Shared communication medium. Collisions in a wireless network cannot be detected reliably. Continuous mobility of nodes.

5 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

6 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.

7 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.

8 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.)

9 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. pq RR’ r

10 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.

11 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.

12 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:012m-1012 …… 1 phase

13 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 mu σ λ R+R’

14 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+2mu σ ≤ 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. mu σ R ρ

15 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. 16

17 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

18 Schedules Left to Right schedule. Suffers from directional bias. Favors left to right information propagation but not right to left.

19 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).

20 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. SchedulesAverage number of rounds Spiral Left to Right Random

Conclusions 1.Collision-free communication scheme for continuously mobile nodes. 2.Deterministic technique for maintenance of neighborhood knowledge. 3.General purpose schedule. 21

22 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.

23 Questions