Energy-efficient routing in the broadcast communication model

The broadcast communication model (BCM, for short) is a distributed system with no central arbiter populated by p stations denoted by S(1),S(2),...,S(p) that communicate by transmitting messages on a communication channel. The stations are assumed to have the computing power of a laptop computer and to be synchronous, in particular, they all run the same program, albeit on different data. We assume that a station is expending power while transmitting or receiving messages. As it turns out, one of the most effective energy-saving strategies is to mandate individual stations to power their transceiver off (i.e., go to sleep) whenever they are not transmitting or receiving messages. Suppose that the p stations of the BCM store collectively n items such that station S(i), (1 ≤ i ≤ p), stores s_i items. Each of the items has a unique destination which is the identity of the station to which the item must be routed. The goal is to route all the items to their destinations, while expending as little energy as possible. Since, in the worst case, each item must be transmitted at least once, every routing protocol must take at least n time slots to terminate. Furthermore, station S(i), (1 ≤ i ≤ p), must be awake for at least s_i + d_i time slots, where d_i denotes the number of items destined for S(i). Since, in the BCM, every station is within transmission range from every other station, the design of energy-efficient protocols is highly nontrivial. An additional complication stems from the inherent asymmetry of the routing problem: no destination knows the identity of the sender, precluding a priori arrangements between senders and receivers. The main contribution of this work is to present an energy-efficient routing protocol for the single-channel, p-station BCM. We show that for every f ≥ 1, the task of routing n items in this model can be completed with probability exceeding 1 - 1/f, in n + O(q + ln f) time slots and that no station S(i), (1 ≤ i ≤ p), has to be awake for more than s_i + d_i + O(q_i + r_i log p + log f) time slots, where q_i is the number of stations that have items destined for S(i), q = q₁ + q₂ +···+ q- _p, and r_i is the number of stations for which S(i) has items. Since q_i ≤ d_i, r_i ≤ s_i and q ≤ n, our protocol is close to optimal both in terms of overall completion time and energy efficiency.