MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

On the delay margin for consensus in directed networks of anticipatory agents

Fatihcan M. Atay and Dina Irofti


We consider a consensus problem involving a time delay that arises from predicting the future states of agents based on their past history. In case the agents are coupled in a connected and undirected network, the exact condition for consensus is that the delay be less than a constant threshold that is independent of the network topology or size. In directed networks, however, the situation is quite different. We show that the allowable maximum delay for consensus depends on the network topology in a nontrivial way. We study this delay margin in several network constellations, including various circulant networks with directed links. We show that the delay margin depends not only on the number of neighbors, but also on the directionality of connections with those neighbors. Furthermore, the delay margin improves as the circulant networks are rewired en route to a small-world configuration.

Feb 26, 2016
Feb 29, 2016
Consensus, prediction, anticipation, delay, Network, stability

Related publications

2016 Journal Open Access
Fatihcan M. Atay and Dina Irofti

On the delay margin for consensus in directed networks of anticipatory agents

In: IFAC-PapersOnLine, 49 (2016) 10, pp. 206-211