Dear Kevin,
The issue with parallel lines for the “same” street is a problem for all kinds of network analysis. The only way to deal with it is to clean the data before the analysis (=merge the two street center lines). Also, the roundabouts in your map could distort your analysis if they consist of many small line segments (=many origins and destinations). There are tools for simplifying street networks (in QGIS, ArcGIS, and not that advanced in the DeCodingSpaces-Toolbox), or you do it manually.
Best regards
Reinhard