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Evolving Random Geometric Graph Models for Mobile Wireless Networks

Karamchandani, Nikhil and Manjunath, D and Yogeshwaran, D and Iyer, Srikanth K (2006) Evolving Random Geometric Graph Models for Mobile Wireless Networks. In: 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, 03-06 April 2006, Boston.

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We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Item Type: Conference Paper
Publisher: IEEE
Additional Information: Copyright 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 24 Nov 2011 06:58
Last Modified: 24 Nov 2011 06:58
URI: http://eprints.iisc.ac.in/id/eprint/42143

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