Ciro D'Apice

On the Validity of Fluid-dynamic Models for Data Networks

Simulators have been acknowledged as one of the most flexible tool in studying and evaluating network performance. Variuous approaches have been followed in data networks modeling. The present paper explores the range of applicability of a fluid-dynamic model, proposed in [5], able to describe the load evolution of a data network. Looking at intermediate time scale, it is assumed that packets are conserved, and hence the packets density obey to a conservation law. The assumption underlying the model is the behaviour of the information loss probability from which the flux is derived. Here the validity of the above hypothesis and the rules introduced to solve dynamics at nodes are discussed. In particular packet loss estimations using queueing models have been compared with the assumed loss probability. Moreover a TCP throughput simulation is proposed to evaluate the feasibility of the “tent” flux.

Regulation Of The Input Flow Of Supply Chains To Optimize The Production.

The optimal control problem of adjusting the inflow, of piecewise constant type, to a supply chain in order to minimize the queue size and the quadratic difference between the outflow and the expected one is considered. The controls are represented by the duration of injections of different amounts of goods. The supply chain is modelled by a PDE-ODE: the conservation law describes the density of processed parts and the ODE the queue buffer occupancy. The numerical technique is based on the extensive use of generalized tangent vectors to a piecewise constant control, which represent time shifts of discontinuity points.

Simulation and Optimal Routing of Data Flows Using a Fluid Dynamic Approach

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