A navigation device that performs route guidance (or routing assistance) to a destination retrieves the most proper route to the destination to thereby indicate the most proper route to a user when the user sets the destination.  Further, a navigation device is proposed that indicates the shortest traveling-time route for avoiding a congested main road to select a short-traveling-time loophole path or alternative route (refer to JP-H5-216406 A). 
However, from the inventor's viewpoint, the navigation device sometimes indicates the alternative route involving danger in traffic only because of the shorter traveling time to the arrival, even though the user can arrive at the destination by selecting the route including the main roads.  In other words, a known route guidance is not performed based on a desired arrival time point.