Packet flow on telecommunication networks

The aim of this paper is to introduce a macroscopic fluid dynamic model dealing with the flow 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 [G. M. Coclite, M. Garavello, and B. Piccoli, SIAM J. Math. Anal., 36 (2005), pp. 1862-1886). 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 algorithm, which in turn implies stability, i.e., Lipschitz continuous dependence on initial data, not granted for solutions using the first algorithm.