On the Connectivity of Finite Wireless Networks with Multiple Base Stations

TRUST, Autumn Conference, November 11-12, 2008

On the Connectivity of Finite Wireless Networks with Multiple Base Stations

Sergio Bermudez and Prof. Stephen WickerSchool of ECE, Cornell UniversityInternational Conference on Computer Communications and Networks, August 3-7, 2008

TRUST, November 11-12, 2008

Agenda

Introduction– Wireless Networks Connectivity– Approaches to Analyze Connectivity

Model and Results– Assumptions– Main Result– Simulation Results

Conclusions

"Connected Sub-networks," Sergio Bermudez 2


Introduction

Connectivity is a fundamental quality of a wireless network.

Any two nodes are able to communicate between them, either single- or multi-hop.



Previous Work on Connectivity

Focus on the connectivity of wireless networks having a single connected component.

Approaches on the number of nodes for random deployments:– Asymptotic– Finite



Asymptotic Connectivity Analysis

Gupta and Kumar: n uniformly distributed nodes, letting n → ∞, finite area. Percolation theory.

Bettstetter: Infinite network, constant node density, analyzing finite area. Geometric random graphs theory.



Finite Connectivity Analysis

Desai and Manjunath: network over a line segment, nodes distributed uniformly, geometrical argument.

Godehardt and Jaworski: random interval graphs in the unit interval, combinatorial theory.



Multiple Base Stations Scenario

Envisioned application of sensor networks is monitoring Physical Infrastructure– It is feasible that those networks have base

stations.– Example in systems like water quality monitoring,

electricity generation plants.

In general, due to factors like:– Increase network capacity– Manage large deployment area– Enhance network reliability



Considering multiple base stations

It is intuitive that having more than one base station provide less stringent requirements on the numbers of nodes needed to have a connected network.



Model for Analysis

We will focus on:– analysis of connectivity with sub-networks– one-dimensional deployments

Connected Sub-network– connected components of the network realization

that are able to communicate with at least one BS.



General Assumptions

Uniformly random deployment of n nodes over a line segment [0,S]

m base stations at given location yi Fix communication radius r Boolean communication link model



Problem Statement

Given n nodes with communication radius r , and m base stations and their locations, what is the probability that the network realization is connected?

– We consider a network as connected if its composing sub-networks are connected.



Problem Decomposition

Conditioning on the number of nodes in a sub-segment, nodes are uniformly distributed.

Independence on the probability of sub-network connectivity.



Probability of Connectivity

C: all nodes in the network reach at least one base station.

Ci : all nodes inside segment wi reach at least one base station.

There are two general cases:– border and inner connectivity



Main Formula

By the Law of Total Probability


border and inner connectivity term


Simulation Setup

Segment [0,1] Deployment with n nodes Use different locations for the base stations Monte Carlo method with 105 random

replications



One Base Station Network



Two Base Stations Network



Summary

Used the concept of connected sub-networks.

Presented a formula to calculate the probability of connectivity for wireless networks with infrastructure.



Further Reading

“On the Connectivity of a Random Interval Graph,” E. Godehardt and J. Jaworski, Random Structures and Algorithms, 137–161, 1996.

“On the connectivity in finite ad hoc networks,” M. Desai and D. Manjunath, IEEE Commun. Lett., 425–436, 2005.



Border and Inner Connectivity

Border-Connectivity Formula

Inner-Connectivity Formula


On the Connectivity of Finite Wireless Networks with Multiple Base Stations

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