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On the Connectivity of Finite Wireless Networks with Multiple Base Stations

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

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  1. 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

  2. Agenda • Introduction • Wireless Networks Connectivity • Approaches to Analyze Connectivity • Model and Results • Assumptions • Main Result • Simulation Results • Conclusions "Connected Sub-networks," Sergio Bermudez

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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 "Connected Sub-networks," Sergio Bermudez

  11. 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

  12. 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

  13. 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

  14. Main Formula • border and inner connectivity term By the Law of Total Probability "Connected Sub-networks," Sergio Bermudez

  15. 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

  16. One Base Station Network "Connected Sub-networks," Sergio Bermudez

  17. Two Base Stations Network "Connected Sub-networks," Sergio Bermudez

  18. 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

  19. 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. "Connected Sub-networks," Sergio Bermudez

  20. Border and Inner Connectivity Border-Connectivity Formula Inner-Connectivity Formula "Connected Sub-networks," Sergio Bermudez

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