Graphical solution and continuum approximation for the single destination dynamic user equilibrium problem

This paper studies the user optimum dynamic traffic assignment in a network consisting of a congested freeway section connected to a surface street grid via capacitated off-ramps. It is shown that although the network is simple, it is in general complicated to obtain the optimum solution analytically because (i) it has two different alternating diversion patterns and (ii) it can only be obtained sequentially in time. A simplified graphical solution method is proposed to cope with (i) but the method remains sequential. Finally, a continuum approximation is proposed that enables finding closed-form solutions without the above limitations.