Consensus Problem in Wireless Ad hoc Networks: Addressing the Right Issues * Fatemeh Borran Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL) 1015 Lausanne, Switzerland fatemeh.borran-dejnabadi@epfl.ch Ravi Prakash University of Texas at Dallas Department of Computer Science Texas 75080-3021, U.S.A. ravip@utdallas.edu Andr´ e Schiper Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL) 1015 Lausanne, Switzerland andre.schiper@epfl.ch Abstract Solving consensus in wireless ad hoc networks has started to be addressed in several papers. Most of these papers adopt system models developed for wired networks. These models are focused towards node failures while ig- noring link failures, and thus are poorly suited for wireless ad hoc networks. The HO model, which was proposed re- cently, does not have this drawback. The paper shows that an existing algorithm and the HO model can be used for multi-hop wireless ad hoc networks, if extended with an ad- equate “implementation”. The meaning of “implementa- tion” will become clear from the paper. The description of the “implementation” is augmented with simulation results that validate the feasibility of our approach and provide bet- ter understanding of the behavior of realistic wireless envi- ronments. 1. Introduction Ad hoc networks are self-organizing wireless networks that do not rely on a preexisting infrastructure to commu- nicate. Nodes of such networks have limited transmission range, and packets may need to traverse multiple nodes be- fore reaching their destination. Even if the sender and re- ceiver of a packet do not crash, the packet within a wire- less network can be lost due to collisions and channel inter- ference. The problems that were already solved for wired communications many years ago, become new challenges in wireless ad hoc environments. Consensus is one of these problems. The importance of consensus is due to the fact that it is a basic building block for solving several other fault-tolerant distributed problems. * Research funded by the Swiss National Science Foundation under grant number 200021-111701. Consensus has been extensively studied in traditional networks with various system models. It is now well known that solving consensus deterministically requires some syn- chrony assumptions [10]. One option is to assume that the (asynchronous) system eventually becomes synchronous, which is called partial synchrony [9]; another option is to augment the (asynchronous) system with failure detec- tors [5]. Starting from this background, some papers have considered the consensus problem in ad hoc networks. We comment on these papers in Section 2: basically we believe that the approaches suggested are not adequate. The reason is that these papers essentially adopt system models devel- oped for wired and static networks (sometimes with exten- sions), and these models are not adequate for ad hoc net- works. Indeed, the models for wired networks are strongly biased towards node failures to the detriment of link fail- ures. This bias has its root in the FLP paper [10], which as- sumes process crashes and reliable links. The bias was later strengthened by the failure detector model [5], which also assumes process crashes and reliable links. The bias is so commonly accepted that it is easily overlooked. However, overlooking the bias results in attempts to use solutions for environments where the bias is acceptable, to environments where the bias is unacceptable. This is the case with ad hoc networks, where assuming that links are reliable is clearly inadequate. One may argue that if reliable links are required to solve a problem then there is no work-around, and reli- able links need to be implemented on top of lossy links, even if this is expensive in ad hoc networks. But this is not the case for consensus. We know that consensus can be solved in a model in which the distinction between faulty processes and faulty links completely disappears, namely the HO model [7, 12, 6]. This model has no bias, and is, therefore, well suited to handle transient process and link faults. Not only transient link faults (message losses) are frequent in ad hoc networks, but transient process faults can also occur: consider a wireless device that becomes unavail-