On the Connectivity of Finite Wireless Networks with Multiple Base Stations

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On the Connectivity of Finite Wireless Networks with Multiple Base Stations. Sergio Bermudez and Prof. Stephen Wicker School of ECE, Cornell University International Conference on Computer Communications and Networks, August 3-7, 2008. Agenda. Introduction Wireless Networks Connectivity

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### On the Connectivity of Finite Wireless Networks with Multiple Base Stations

Sergio Bermudez and Prof. Stephen Wicker

School of ECE, Cornell University

International Conference on Computer Communications and Networks, August 3-7, 2008

Agenda
• Introduction
• Wireless Networks Connectivity
• Approaches to Analyze Connectivity
• Model and Results
• Assumptions
• Main Result
• Simulation Results
• Conclusions

"Connected Sub-networks," Sergio Bermudez

Introduction

Connectivity is a fundamental quality of a wireless network.

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

"Connected Sub-networks," Sergio Bermudez

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

"Connected Sub-networks," Sergio Bermudez

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.

"Connected Sub-networks," Sergio Bermudez

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.

"Connected Sub-networks," Sergio Bermudez

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

"Connected Sub-networks," Sergio Bermudez

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.

"Connected Sub-networks," Sergio Bermudez

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.

"Connected Sub-networks," Sergio Bermudez

General Assumptions

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

m base stations at given location yi

"Connected Sub-networks," Sergio Bermudez

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.

"Connected Sub-networks," Sergio Bermudez

Problem Decomposition

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

Independence on the probability of sub-network connectivity.

"Connected Sub-networks," Sergio Bermudez

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

"Connected Sub-networks," Sergio Bermudez

Main Formula
• border and inner connectivity term

By the Law of Total Probability

"Connected Sub-networks," Sergio Bermudez

Simulation Setup

Segment [0,1]

Deployment with n nodes

Use different locations for the base stations

Monte Carlo method with 105 random replications

"Connected Sub-networks," Sergio Bermudez

One Base Station Network

"Connected Sub-networks," Sergio Bermudez

Two Base Stations Network

"Connected Sub-networks," Sergio Bermudez

Summary

Used the concept of connected sub-networks.

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

"Connected Sub-networks," Sergio Bermudez