Critical node lifetimes in random networks via the Chen-Stein method

• Published in: IEEE transactions on information theory Vol. 52; no. 6; pp. 2831 - 2837
• Main Authors: Franceschetti, M., Meester, R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ad hoc networks; Applied sciences; Approximation; Batteries; Battery; Blinds; Communication networks; Communications networks; Delay; Derivation; Exact sciences and technology; H infinity control; Information theory; Intelligent networks; Joining processes; Mathematical analysis; Network topologies; Networks; percolation theory; Poisson approximation; Poisson distribution; Probability; random networks; Reliability theory; Scalability; Scaling laws; sensor networks; Spots; Studies; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Valuation and optimization of characteristics. Simulation; Lifetime; Approximation; percolation theory; random networks; Ad-hoc networks; Poisson approximation; Percolation; sensor networks; Ad hoc network; Sensor array; Poisson process; Nodes
• ISSN: 0018-9448; 1063-6692; 1558-2566
• DOI: 10.1109/TIT.2006.874545

This correspondence considers networks where nodes are connected randomly and can fail at random times. It provides scaling laws that allow to find the critical time at which isolated nodes begin to appear in the system as its size tends to infinity. Applications are in the areas of sensor and ad-hoc networks where nodes are subject to battery drainage and 'blind spots' formation becomes a primary concern. The techniques adopted are based on the Chen-Stein method of Poisson approximation, which allows to obtain elegant derivations that are shown to improve upon and simplify previous related results that appeared in the literature. Since blind spots are strongly related to full connectivity, we also obtain some scaling results about the latter.