Energy-efficient initialization protocols for single-hop radio networks with no collision detection

A radio network (RN, for short) is a distributed system consisting of n radio stations. We assume that the stations are small, bulk-produced, hand-held devices running on batteries and cannot be distinguished by serial or manufacturing number. Since recharging batteries may not be possible while on mission, we are interested in designing protocols that are highly energy-efficient. The initialization problem is to assign each of the n stations in the RN a unique ID. The initialization problem is nontrivial since the stations are assumed to be indistinguishable. The problem is fundamental, since practically all communication protocols for RNs proceed under the assumption that the RN has been initialized in advance. The main contribution of this work is to propose energy-efficient randomized initialization protocols for single-hop RNs lacking collision detection capabilities. First. we show that if the number n of stations is known beforehand, the single-channel RN can be initialized by a protocol that terminates, with probability exceeding 1 - 1/n, in O(n) time slots, with no station being awake for more than O(log log n) time slots. We then go on to address the multichannel case and show that if k, (k greater than or equal to 1), channels are available, an n-station RN can be initialized, with probability exceeding 1 - 1/n, in O(n/k + log n) time slots, with no station being awake for more than O(log log n) time slots.