Gossip based Asynchronous and Randomized Distributed Task Assignment with Guaranteed Performance on Heterogeneous Networks

The main contribution of this paper is a novel distributed algorithm based on asynchronous and randomized local interactions, i.e., gossip based, for task assignment on heterogeneous networks. We consider a set of tasks with heterogeneous cost to be assigned to a set of nodes with heterogeneous execution speed and interconnected by a network with unknown topology represented by an undirected graph. Our objective is to minimize the execution time of the set of tasks by the networked system. We propose a local interaction rule which allows the nodes of a network to cooperatively assign tasks among themselves with a guaranteed performance with respect to the optimal assignment exploiting a gossip based randomized interaction scheme. We first characterize the convergence properties of the proposed approach, then we propose an edge selection process and a distributed embedded stop criterion to terminate communications, not only task exchanges, while keeping the performance guarantee. Numerical simulations are finally presented to corroborate the theoretical results. Draft version, published as: M. Franceschelli, A. Giua, C. Seatzu, ”Gossip based asynchronous and randomized distributed task assignment with guaranteed performance on heterogeneous networks, Nonlinear Analysis: Hybrid Systems, Vol. 26, pp. 292306, November 2017. The research leading to these results was partially supported by the Italian grant SIR ”Scientific Independence of young Researchers” with project CoNetDomeSys, code RBSI14OF6H, funded by the Italian Ministry of Research and Education (MIUR)