1410 IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 8, AUGUST 2015 Randomized Gossip With Power of Two Choices for Energy Aware Distributed Averaging Valerio Freschi, Emanuele Lattanzi, and Alessandro Bogliolo Abstract—Distributed computation of average values held by nodes belonging to a self-organized network is a key task in many application areas, ranging from sensor and ad-hoc net- works to networked control systems. Severe computational, com- munication, and energy constraints typical of these environments prompt for the design of specific solutions addressing these issues. In this context, gossip algorithms represent valuable approaches because of their simple local communication patterns, resulting into robustness to dynamic topology changes. Several variants of gossip-based techniques have been proposed, mainly focused on improvements of the convergence time, which directly impacts energy expenditure. Energy efficiency remains however a chal- lenging issue to be addressed. In this letter, we introduce a novel energy aware distributed averaging algorithm which combines the standard randomized gossip protocol with a probabilistic load bal- ancing technique, the power of two choices. Experimental results show that the proposed solution achieves better load balancing with respect to standard pairwise averaging, enabling consid- erable improvements in the network lifetime without impairing convergence time. Index Terms—Distributed averaging, power of two choices, networks. I. I NTRODUCTION R ECENT technological advancements in the field of wire- less embedded systems have paved the way for the de- velopment of novel architectures, protocols and applications. Sensor and actuator networks play a key role as distributed infrastructures in many scientific, environmental, and industrial applicative contexts. These networks are designed to flexibly operate according to a wide spectrum of paradigms, from struc- tured to self-organizing systems. On the other hand, embedded devices acting as nodes are typically constrained in terms of energy, computational, and communication resources. In order to meet these requirements, several research challenges have to be tackled. Computing the average of the values sensed and stored by nodes of a sensor network is a common task in various applicative settings. In particular, the capability of driving in a distributed fashion all nodes of the network toward the average of their values represents a useful primitive in many protocols related to distributed signal processing, multi-agents system coordination, sensor fusion, networked control systems [1]–[6]. Manuscript received April 22, 2015; revised June 3, 2015; accepted June 15, 2015. Date of publication June 18, 2015; date of current version August 10, 2015. The associate editor coordinating the review of this paper and approving it for publication was H. Otrok. The authors are with the Dipartimento di Scienze di Base e Fondamenti (DiSBeF), University of Urbino, 61029 Urbino, Italy (e-mail: valerio.freschi@ uniurb.it; emanuele.lattanzi@uniurb.it; alessandro.bogliolo@uniurb.it). Digital Object Identifier 10.1109/LCOMM.2015.2446987 Distributed averaging is also central to load balancing with divisible tasks in parallel and distributed systems [7]. Algo- rithmic approaches to distributed averaging based on rounds of information exchange between neighbor nodes (also known as gossip algorithms) have received considerable attention be- cause of their inherent robustness to noise and adaptability to network topology changes [1], [3]. Gossip algorithms are usually compared by evaluating their speed of convergence, often measured as the number of transmissions (i.e. the com- munication complexity) required to achieve a given accuracy in estimating the average. Needless to say, higher number of transmissions negatively affect the network lifetime. Therefore, significant efforts have been devoted to mitigate the energy waste of gossip algorithms, mainly through acceleration of the rate of convergence [1], [3], [4]. In this work we take a different perspective, which doesn’t target the reduction of convergence rate, rather it focuses on reducing the imbalance of energy consumption of the various nodes of the target network. Indeed, information regarding the state of energy buffers at neighbor nodes can be exploited to apply load balancing strategies which could result in a more uniform network loading and, in turn, into lifetime increase. We introduce in this letter a novel approach to distributed averaging which makes use of a randomized load balancing technique known as the power of two choices [8], [9] in combination with the randomized gossip algorithm proposed by Boyd et al. in 2006 [1]. The selection of neighbor nodes according to the power of two choices scheme enables to effectively balance the energy levels of nodes taking part into a computation round of randomized gossip, leading to more uniform energy expenditure across the network. Simulation results show that the proposed algorithm im- proves the randomized gossip algorithm in terms of energy balancing without impairing the convergence rate, thus substan- tially prolonging network lifetime while guaranteeing the same latency to perform the averaging task. The remainder of the letter is organized according to the fol- lowing outline: in Section II we recapitulate some contributions of recent scientific literature regarding distributed averaging algorithms and randomized load balancing; in Section III we describe the proposed algorithm and prove its convergence; in Section IV we introduce simulation setup and illustrate numerical results; in Section V we provide some conclusive considerations. II. RELATED WORK In this section we recall some state of the art works related to, respectively, distributed averaging algorithms and load bal- ancing based on the power of two choices paradigm. 1558-2558 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.