You can use the Target Market Share option of Location-Allocation to solve this problem. Set the Impedance cutoff to 10 minutes, Use the default Linear Impedance Transformation and in the Target market share set it 80 percent.
Now load in your demand locations as demand and make sure the weigth is 1 (default). That is each demand is equally weighted and thus 80 percent market share will mean 80 percent of the demand locations.
You need to load in candidate facilities. If you do not have any, you will need to "manufacture" some. For example you could load a random sample of the junctions. Or use the Create Random Points tool and constrain it with the street line feature class. You can specify some distance they need to be apart, say 200 meters and you could generate a couple of hundred points to serve as your candidates.
Solve and you will have the minimum set of facilities that will be needed to serve 80 percent of the demand in 10 minutes.
Note that if some demand locations are in disconnected portions of the network (due to bad data or restrictions) you may get facilities located next to them just to serve them. So do anaylyze the results and adjust the inputs as necessary.