How do I determine the maximum route distance to create a service area containing a given total number of route miles?

[ErnestCacciaglia1]

I wish to determine the route length from a given location which will create a service area containing a given total distance of routes.  For example, I wish to create a service area containing  20 miles of total road length.  What is the route length from a given location that would create this service area?

[DanPatterson_Retired]

Freddie, that is my reading of the question as well .... partition the total amongst the edges.  This would make it difficult to model anything other than a pure distance solution, although not impossible (weighted edges)

[ErnestCacciaglia1]

"Create a service area where the sum of the lengths of the edges traveled equals one" is precisely what I am interested in resolving with two clarifications. Obviously, "one" should be a variable, and almost equally obvious is that all edges be of equal length. I believe that these two restrictions should produce one unique solution.  One (possible) problem that I anticipate is in the case where two routes (of different lengths) converge on the same edge, because I'm not certain which length is used for the calculation. Your thoughts?

The purpose of this calculation is to determine the "best" location for future fire stations.  Other variables withstanding, a station would service a given length of road miles, and be centrally located. This is not a critical calculation, but more one of an intellectual interest, so please don't feel obliged to pursue this solution if it becomes too time-consuming.

[DanPatterson_Retired]

as is our reading, you need the segments connecting to a location.  The total desired distance is then divided by that to yield the travel distance along each segment.  This is what Freddie's example shows visually.

addendum

given your example, you are more interested in time... ie a response time, hence it would become a standard service area whereby you use travel time as your constraint and the number of roads connecting to the location isn't relevant, but the travel time from that location along any route in the vicinity of that location.

[ModyBuchbinder]

Here is my 5 cent…

The best way is to try. Make service area for 3 minutes, if it is less than the sum roads you need try 5 minutes etc.

The problem with this is that it takes too long.

Doing simple select by circle is a good way to get the first guess very quick.

Select circles until you get the correct number then use the radius of the circle to estimate the driving time to the edge.

Remember you do not drive in a straight line to the end.

If your first try is close you should get your result in 1-3 tries.

Have fun

Mody

[JaySandhu]

As others have mentioned you can iterate with service area lines many times to find the break value that gives you 20 miles. Or you can use another approach: Location-Allocation. Let's say you have a field on your streets with length in miles. Run the GP tool Feature To Point with the Inside option on the streets. This will create a mid point on every street. Make a location-allocation layer. On the advanced settings, choose the problem type to be Maximize Capacitated Coverage. Load your facility location and set its capacity to 20. Load the mid points (or a relevant subset around your facility). Make sure to map the Length in miles as your Demand weight. Solve the location-allocation layer and it will select the points that sum up to 20 miles. There will be some "noise" at the ends as it may pick a further away point to ensure you get 20. But it will be quite close to the answer you are looking for.

Location-allocation analysis—Help | ArcGIS for Desktop

Jay Sandhu