On the Probability of Unsafe Disagreement in Group Formation Algorithms for Vehicular Ad Hoc Networks

Abstract

We address the problem of group formation inautomotive cooperative applications using wireless vehicle-to-vehiclecommunication. Group formation (GF) is an essential stepin bootstrapping self-organizing distributed applications such asvirtual traffic lights. We propose a synchronous GF algorithm andinvestigate its behaviour in the presence of an unbounded numberof asymmetric communication failures (receive omissions). Giventhat GF is an agreement problem, we know from previousresearch that it is impossible to design a GF algorithm thatcan guarantee agreement on the group membership in thepresence of an unbounded number of messages losses. Thus, under this assumption, disagreement is an unavoidable outcomeof a GF algorithm. We consider two types of disagreement(failure modes): safe and unsafe disagreement. To reduce theprobability of unsafe disagreement, our algorithm uses a localoracle to estimate the number of nodes that are attempting toparticipate in the GF process. (Such estimates can be provided byroadside sensors or local sensors in a vehicle such as cameras.)For the proposed algorithm, we show how the probability ofunsafe and safe disagreement varies for different system settingsas a function of the probability of message loss. We also showhow these probabilities vary depending on the correctness ofthe local oracles. More specifically, our results show that unsafedisagreement occurs only if the local oracles underestimates thenumber of participating nodes.