Monotonic Random Walks and Clusters Flows on Networks

One approach to modeling flows in the socio-technical systems, for example road traffic, reduces to decompose the movement of the collective and the individual components. A collective component is described by a system of differential equations, and an individual component corresponds to stochastic movement within the cell decomposition defined by the collective modes. This monograph discusses both components with varying degrees of detail including the regular networks. Moreover we study the cluster model as a simplified analogue of structures, following from hydrodynamic approaches, and can be applied for investigation of multi-lane flows on networks. Basic characteristics of the models are researched.