**6. References**

Bruni, C., Delli Priscoli, F., Koch, G., Marchetti, I. (2009). Resource management in network dynamics: An optimal approach to the admission control problem, Computers & Mathematics with Applications, article in press, available at

www.sciencedirect.com, 8 September 2009,doi:10.1016/j.camwa.2009.01.046


**0**

**18**

*Fisciano (SA)*

<sup>1</sup>*Italy* <sup>2</sup>*USA*

**Simulation and Optimal Routing of Data Flows**

<sup>1</sup>*Department of Electronic and Information Engineering, University of Salerno,*

<sup>2</sup>*Department of Mathematical Sciences, Rutgers University, Camden, New Jersey*

There are various approaches to telecommunication and data networks (see for example Alderson et al. (2007), Baccelli et al. (2006), Baccelli et al. (2001), Kelly et al. (1998), Tanenbaum (1999), Willinger et al. (1998)). A first model for data networks, similar to that used for car traffic, has been proposed in D'Apice et al. (2006), where two algorithms for dynamics at nodes were considered and existence of solutions to Cauchy Problems was proved. Then in D'Apice et al. (2008), following the approach of Garavello et al. (2005) for road networks (see also Coclite et al. (2005); Daganzo (1997); Garavello et al. (2006); Holden et al. (1995); Lighthill et al. (1955); Newell (1980); Richards (1956)), sources and destinations have been

In this Chapter we deal with the fluid-dynamic model for data networks together with optimization problems, reporting some results obtained in Cascone et al. (2010); D'Apice et al.

A telecommunication network consists in a finite collection of transmission lines, modelled by closed intervals of **R** connected by nodes (routers, hubs, switches, etc.). Taking the Internet

1) Each packet seen as a particle travels on the network with a fixed speed and with assigned

2) Nodes receive, process and then forward packets which may be lost with a probability increasing with the number of packets to be processed. Each lost packet is sent again. Since each lost packet is sent again until it reaches next node, looking at macroscopic level, it is assumed that the packets number is conserved. This leads to a conservation law for the

The flux *f*(*ρ*) is given by *v*(*ρ*)· *ρ* where *v* is the average speed of packets among nodes, derived

*ρ<sup>t</sup>* + *f* (*ρ*)*<sup>x</sup>* = 0. (1)

introduced, thus taking care of the packets paths inside the network.

**1. Introduction**

(2006; 2008; 2010).

final destination;

packets density *ρ* on each line:

considering the amount of packets that may be lost.

network as model, we assume that:

**Using a Fluid Dynamic Approach**

Ciro D'Apice1, Rosanna Manzo1 and Benedetto Piccoli2

