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An Urn Occupancy Approach for Modeling the Energy Consumption of Distributed Beaconing

In past years, ultra wideband technology has attracted great attention from academia and industry for wireless personal area networks and wireless sensor networks. Maintenance of connectivity and exchange of data require an efficient way to manage the devices. Distributed beaconing defined by ECMA-368 is used to manage the network in fully distributed fashion. Distributed beaconing requires that all devices acquire a unique beacon slot, with the beacon period accessed using a slotted Aloha scheme. In this paper, we study the efficiency of distributed beaconing in the presence of k newcomer devices forming a closed system. Efficiency is measured in terms of energy consumption and network set-up delay. ECMA-368 defines two distinct phases: extension and contraction. Both phases are analyzed with particular emphasis on the extension phase by means of an absorbing Markov chain model. The main contributions of this paper are: 1) a systematic approach to model distributed beaconing by formulating two equivalent urn occupancy problems of the extension and contraction phases; 2) the use of exponential generating functions to obtain closed form expressions of the transition probabilities of the absorbing Markov chain; and 3) comparison with computer simulations based on Opnet modeling and with the preexisting literature.