Traffic Flow on a Road Network Using the Aw–Rascle Model

Phase Transition Model for Traffic at a Junction

“…We provide below a solution to the resulting Riemann problem. As in [3,7,8], this solution is PSfrag replacements a necessary preliminary step to the solution of the general Cauchy problem on a net.…”

“…We refer in particular to [3], where the LWR model is considered, and to [8] which is related to the Aw-Rascle model [1]. In these papers, junctions are modeled so that the presence of a single fully congested outgoing road immediately saturates the junction and no vehicle may pass through it.…”

Numerical Discretization of Coupling Conditions by High-Order Schemes

“…Among the many examples where such systems arise are traffic flow [24,25,29,31], production networks [21,23,30], telecommunication networks [22], gas flow in pipe networks [3, 11-13, 15, 16] or water flow in canals [4,5,28,35]. Mathematically, flow problems on networks are boundary value problems where the boundary value is implicitly defined by a coupling condition.…”

Existence of Solutions for the Aw–rascle Traffic Flow Model With Vacuum

“…In [2] Aw and Rascle solve the Riemann problem for this model and they include the vacuum state. For a discussion of the model, see also [1], [5], [6], [8], [9], [10], [11], [12] and [15]. The model is of Temple class, i.e., the shock and rarefaction curves coincide.…”

“…When including the vacuum state, the available invariant domains are given by (4) requiring w(u) ≥ v(u) instead of w − > v + . All these regions are subdomains of (5) D V = {u ∈ U : 0 ≤ v(u) ≤ w(u) ≤ v + } .…”