A cardinal rule of network diagramming is to avoid intersecting lines wherever possible. Line intersections, particularly many in close proximity, make casual inspection difficult. Of course, sometimes such intersections cannot be avoided.
Microsoft Visio adds line "jumps" to more clearly indicate flow, but these aren't always desirable. To prevent a line from jumping at intersections, select it and navigate to Format -> Behavior and select the Connector tab. Here we have the option to modify the placement of line jumps. We can opt to always add jumps to the selected line, to always add jumps to the lines intersected, or to remove them completely.
After setting line jump addition to "Never" our drawing looks a bit more tidy:
You might have noticed there are several styles of line jump available beside the default arc. Try out some of these and see if any better suite your style (I recommend "gap" for a minimalist feel).