Maxplus Function

WardropN - Wardrop equilibrium ( Newton hybrid method )

Calling Sequence

bench=WardropN(a,k,eps,niter)

Parameters

Description

Compute the Wardrop equilibrium of a transport assignment problem by solving the following nodes-links variational formulation of the problem:

Min_q Sum_l C(f_l)

f_l=Sum_i q_li

Hq_i=d_i

O<=q_li

where :

- C(f) is a cost in the classes defined by the lpf function, - H is is the incidence nodes-arcs matrix of the network, - q_li is the flow of the commodity i on the link l,

%net is the netlist containing all the information relative to the network and the cost function used.

The method used is a decomposed newton method in the space (q_i,v_i) i=1,p, where the v_i denote the dual variables associated to the constraints Hq_i=d_i .

The variable a regularizes the matrices giving the potentials. At each iteration a is reduced by a factor k. We can try first a small a and k=1.

This method is useful mainly in the case of a small number of commodities.

EXAMPLES

See Also