I have network analyst set up to find routes. How do I set up a route for a street sweeper to sweep the streets in a logical maner to ensure that all of the streets in the city get cleaned?
While Network Analyst can solve many routing issues, I don't believe it currently includes a way to derive a route that does all the streets.
However, there appears to be a third-party application available customized to this task. I have no idea on its effectiveness, but it may be worth checking out:
Street Sweeping & Snow Removal — Route Optimization Software | Routesmart
Chris Donohue, GISP
Perhaps this article about route optimization software will help you.