A general formalism for the analysis of distributed algorithms

The major contribution of this paper is the presentation of a general unifying description of distributed algorithms allowing to map local, node-based algorithms onto a single global, network-based form. As a first consequence the new description offers to analyze their learning and steady-state behavior by classical methods. A further consequence is the analysis of implementation issues as they appear due to quantization in computing and communication links. Exemplarily, we apply the new method on several different averaging algorithms: the Push-Sum protocol, average consensus as well as its quantized form and furthermore examine the effects of quantization noise which is introduced by the bandwidth limited communication links and finite precision computation ability of every node. Statistical properties of these quantization noises are provided and verified by simulations.