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The aim of this paper is to introduce a macroscopic fluid dynamic model dealing with the flows of information on a telecommunication network encoded in packets. Taking an intermediate time and space scale, we propose a model similar to that introduced recently for car traffic, see [11]. For dynamics at nodes we consider two "routing algorithms" and prove existence of solutions to Cauchy problems. The main difference among the two algorithms is the possibility of redirecting packets of the second, which in turn implies stability, i.e. Lipschitz continuous dependence from initial data, not granted for solutions using the first algorithm.

Abstract.A continuum-discrete model for supply networks is introduced. The model consists of a system of conservation laws: a conservation law for the goods density and an evolution equation for the processing rate. The network is formed by subchains and nodes at which, motivated by real cases, two routing algorithms are considered: the first maximizes fluxes taking into account the goods' final destinations, while the second maximizes fluxes without constraints. We analyze waves produced at nodes and equilibria for both algorithms, relating the latter to production rates in real supply networks. In particular, we show how the model can reproduce the well-known Bullwhip effect.

The paper deals with a fluid dynamic model for supply chains. A mixed continuum-discrete model is proposed and possible choices of solutions at nodes guaranteeing the conservation of fluxes are discussed. Fixing a rule a Riemann solver is defined and existence of solutions to Cauchy problems is proved.

This paper is focused on continuum-discrete models for supply\ud chains. In particular, we consider the model introduced in [10], where a system\ud of conservation laws describe the evolution of the supply chain status on\ud sub-chains, while at some nodes solutions are determined by Riemann solvers.\ud Fixing the rule of flux maximization, two new Riemann Solvers are defined. We\ud study the equilibria of the resulting dynamics, moreover some numerical experiments\ud on sample supply chains are reported. We provide also a comparison,\ud both of equilibria and experiments, with the model of [15]