Future Plan: Add solvers for DUE and DSO

[toruseo]

There are 3 famous route choice principles for dynamic traffic assignments (the definition varies depending on the terminology).

• Dynamic User Optimal (DUO): Travelers choose the shortest path based on the instantaneous travel time (the current average speed).
• Dynamic User Equilibrium (DUE): Travelers choose the shortest path based on the actual travel time.
• Dynamic System Optimal (DSO): Travelers choose the path so that the total travel time is minimized.

The default routing principle of UXsim is based on DUO, because it is reasonable and very easy to compute.

DUE and DSO are also useful as theoretical benchmarks. It is known that they are difficult to solve, especially when the network is large. But, for small or mid scale networks, they can be solved by UXsim (see example22 and example25). General solvers based on these codes (or more sophisticated version, especially for DSO) could be added.

[toruseo]

TODO list

DUE solver is almost completed.

DSO solver is partially completed, but the following issue must be fixed:

UXsim/uxsim/DTAsolvers/DTAsolvers.py

Line 470 in 3ce811d

game_prob[np.isnan(game_prob)] = 0.5 #TODO: 確率計算を正確にする

Vehicles that did not completed their trip need to be considered in the objective function.

Time-dependent toll need to be incorporated. This requires update of UXsim main module. This can be a future task.

Demo is work in progress.

Related documents need to be reworked.