A theoretical analysis of multi-hop consensus algorithms for wireless networks: Trade off among reliability, responsiveness and delay tolerance

Recently great attention has been posed on the consensus protocols in networks of agents. A widely studied consensus algorithm allows every agent automatically converge to a common consensus state using only local information received from its one hop neighboring agents. We study the problem of reaching a consensus in network of mesh nodes under m-hop protocols where each node-agent can access to the state of its m-steps neighboring agents. Moreover we consider also the presence of heterogeneous time delays affecting the communication through the different hops. The first aim of the paper in the WMNs research theoretical foundations is to give a sufficient condition for the multi hop network consensus protocol stability in the presence of heterogeneous time delays that explicitly relates the network and algorithm features (e.g. time delay tolerance, topology, the number of hop). The second aim is to point out by the previous analytical condition the interplay between the network performance/features (i.e. reliability, the delay tolerance, the communication topology) and the effectiveness of the distributed consensus algorithms/communication protocols (i.e. in terms of complexity, amount of the information to be managed, responsiveness and steady state error performance). This trade off must be taken into account in the performance evaluation and algorithm design for WMNs. Finally, the theoretical result has been validated by simulation experiments using a realistic evaluation