## 1 Introduction  
Modeling and simulation methods are essential elements in the design and operation of transportation systems. Congestion problems in cities worldwide have prompted at all levels of government and industry a proliferation of interest in Intelligent Transportation Systems (ITS) that include advanced supply and demand management techniques. Such techniques include real-time traffic control measures and real-time traveler information and guidance systems whose purpose is to assist travelers in making departure time, mode and route choice decisions. Transportation researchers have developed models and simulators for use in the planning, design and operations of such systems (see, e.g.,[1; 2; 3; 4; 5; 6; 7; 8; 9; 10]).  
There is great potential for useful application of microsimulation models to the analysis of complex traffic problems in urban areas, alongside the analytical techniques that are in use. Microsimulation is useful due to increasing levels of system complexity and uncertainty involved in the operation of urban traffic networks. However, concerns are often expressed regarding misuse of microsimulation. Response to a survey of microsimulation model users was summarised as \"microsimulation is useful but dangerous\" [1].  
Several key components of traffic models are discussed in the literature, and various recommendations are made, with a view to improving the practical usefulness of microsimulation models. These include:  
* the use of simulation for capacity analysis, including the dependence of capacity on demand flow rates;
* modelling of queue discharge (saturation) flow rate, queue discharge speed and other queue discharge parameters at signalised intersections, and relating them to the general queuing, acceleration and car-following models used in microsimulation;
* modelling of gap-acceptance situations at all types of traffic facilities, and
* estimation of lane flows at intersection approaches, and relating this to lane changing models used in microsimulation.  
We start from these considerations and in this paper we propose a prototype of a traffic simulation model, based on fluid dynamics models in order to reproduce the macroscopic _within-day_ evolution of heavy traffic flows across a urban network. The software prototype is based on a complete model developed starting from some basic results on the application of _scalar hyperbolic_ conservation laws in order to describe the conservation of car flows on a single road. Such results, known since the 1950s thanks to [PERSON] [11] and [PERSON] [12] contributions, were extended with a complete theory in [13; 14] to the case of traffic networks with a finite number of roads meeting at junctions. Similar approaches were developed independently and related results and extensions can be found in [15; 16; 17; 18; 19; 20]. The model assumes that distribution of traffic flows at nodes (junctions) is known in advance, and that cars behaviour is such that the throughput at nodes is maximized, subject to the constraints imposed by conservation laws at nodes. _Right-of-way_ coefficients are used in this context to break ties among different roads incoming in a junction.  
Such model is particularly effective to deal with different type of data sources, such as coils [21], mobile GPS phones [22] and clear boxes [23].  
The paper is organized as follows. In Section \(2\), the model is described in more detail, together with some sketches on the numerical methods considered in the simulation prototype. In Section \(3\), the scheme of the simulation prototype and implementation details are presented. Finally, in Section \(4\), we provide computational results on networks of different sizes in order to evaluate computational effort needed by the software when some basic parameters are varied.