This paper analyzes the dynamic traffic assignment problem on a three-alternative network with day-based incentive routing strategies by using graphical solution method. It is assumed that the cumulative count curve of vehicles is known and that the arrival rate is unimodal. The dynamic system optimum (DSO) allocation lines are first drawn based on calculus of variations. Three possible optimal allocation lines are analyzed. A day-based incentive routing strategy is designed and conditions that when and how to implement the incentive scheme to realize DSO are then derived. Extension to general parallel networks is also given. Examples are presented to demonstrate the effectiveness of the scheme.