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Coverage Density as a Dominant Property of

Large-Scale Sensor Networks

Osher Yadgar & Sarit Kraus

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Growing needs of Large-scale Sensor Networks

i. Measure the hardness of a given large-scale sensor network problem,

ii. Compare a given system to other large-scale sensor networks in order to extract a suitable solution,

iii. Predict the performance of the solution, and

iv. Derive the value of each system property from the desired performance of the solution, the problem constraints, and the user's preferences.

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Large-scale Agent Systems ?

i. Thousands of agents ? (Ogston 03, Turner & Jennings 00, …) ii. Hundreds of agents ? (Ortiz 04, Scerri 04, …) iii. Dozens of agents ? (Bult 04, …) iv. Sensor coverage ? (Gage 92, Batalin 02, …)

Coverage Density:What is the context ? What is the problem space ?Tradeoffs: time, money, accuracy, survivorability, etc.

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Coverage Density intuition

Coverage Density defines the time needed to cover the problem space.

There may be an overlap of agent coverage such that, for example, a value of 100% Coverage Density does not reflect coverage of all the controlled area.

Given a limited budget, the system designer should consider whether to use many cheap sensors or a small number of expensive sensors.

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i. Let A be a set of n agents such that whereasii. Let be the area covered by the sensor of agent at a given time t. The

agent may detect objects in this area at time t.iii. Let agent coverage be the average area covered by the

sensor of agent such that .iv. Let total coverage be the average area covered by the sensors of all the

agents such that .v. Let Z be the size of the controlled area.vi. Coverage Density is the total coverage divided by the size of the controlled area

such that .

Definition of the Coverage Density

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Using the Coverage Density

Environment: a large number of real-time tasks/objects and a large number of mobile agents in a given geographical area.

Main issues: Resource management in a large scale environment. How the agents should be distributed over the area? How agents should process local information, derived from

possibly noisy sensors, to provide a partial solution? How partial solutions should be integrated into global

solution?

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ANTS (Autonomous Negotiating Teams) related challenge

Environment: Targets and Doppler sensors. Goal: Form an information map of targets in a

controlled area as a function of time. Large scale environment Mobility

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Challenges

Large scale environment; Mobile sensor Dopplers; Real time response; No clock synchronization; No close cooperation between the sensors; Limit the information exchange; Fault tolerant;

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Doppler sensors’ properties

A radar is based on the Doppler effect with a wide beam of 120 degrees.

Provides information only about an arc that the detected target may be located on and the velocity towards the sensor (radial velocity)

A single Doppler measurement cannot be used to establish the exact velocity

Intersection method

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Organizational Structure

Hierarchic structure of groups based on geographical areas; the base level consists of the sensor Dopplers.

Each level controls the level below it. It processes the information obtained from the level

below it forms an estimation of the information map of its zone reports to it group leader.

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Entities Sampler agent Group Leader agent

Data Structures Capsule InfoMap

GoalGenerate a map of targets as a function of time.

Hierarchy Example

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Hierarchy of Group Leaders

Level 4: 1 Zone Group Leader

Level 3: 4 Zone Group Leaders

Level 2: 16 Zone Group Leaders

Level 1: 64 Sampler Group Leaders

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Simulation environment

150 computers X 4 months = 50 years of CPU Z= 400,000,000 square meters. There are 5,000 Sampling and 85 Group Leader agents. Each Doppler sensor has initial random location and

velocity that is up to 50 kilometers per hour. Range of interaction: 50 meters. Sensing time: 10 seconds. Moving time: 5 seconds. %64.1

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Simulation environment

At any given time, there are 1,000 targets in the area. Each target had an initial random location on the border and an initial random velocity, with a speed limit of 50 kilometers per hour (13.9 meters per second).

Targets leave the area when reaching the boundaries of the zone. Each target that leaves the area causes a new target to appear at a new location on the border.

A target stays a random time period in the area.

For 7 simulated days total of 13,635 targets.

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Conclusions

Coverage Density defines the time needed to cover an area equal to the size of the controlled zone.

We have shown that there is a strong correlation between the Coverage Density of a system and its behavior.

We introduced a way to achieve the same system results with different preferences.

As a result, a system designer may find it easier to achieve a certain level of system performance under given specific constraints, such as budget limits.