LogitB - Logit equilibrium ( Bell Method )
Compute the logit traffic assignment by the Bell method where all the routes are considered not only the efficient ones (see LogitD).
To each route r on the graph defined by the matrix A is associated a weight exp(-theta*l) where l denotes the the total travel time on the route r. The flow for each demand defined by the matrix D is assigned on a route proportionnaly to its wheight.
The graph must be strongly connected. If it is not the case we can add artificial arcs with large travel time in such a way that the new graph becomes strongly connected.
theta must be large enough to insure that the weight of routes with an infinite number of links are finite.
// Graph generation (the graph must be stongly connected), // n is the number of nodes, m the number of arcs. n=10; m=40; c1=m/(n*n); A=sprand(n,n,c1)+diag(sparse(ones(n-1,1)),1); A(n,1)=1;A=A-diag(diag(A)); // Demand generation, p is the number of demand. p=30; c2=p/(n*n);D=sprand(n,n,c2);D=D-diag(diag(D)); //theta definition (almost determinsitic) theta=10; // Flow calculation FD=LogitB(A,D,theta)