How are service areas created in ArcGIS Network Analyst?

Question

I want to create a service area map of Burma in order to spot the areas that are within xx kilometers from a set of cities.

The problem is that the generated polygons aren't exactly what I expected.

In order to understand why, I tried to generate service areas on a very simple network where the greens dots are my three facilities :

The first network is a simple triangle. We can see that computing service areas on this shape completely failed.

However, if I complexify a little bit the network by adding edges inside the triangle, it runs smoothly :

In front of these results, I wonder if someone can explain to me how a service area is generated. More precisely, how does ArcMap interpolate the values of the polygons in the areas where there are no streets?

Answer 1

At the bottom of the help page on service area analysis that PolyGeo links to, there is a link to another help page: Algorithms used by the ArcGIS Network Analyst extension. From that help page:

The Service Area solver is also based on Dijkstra's algorithm to traverse the network. Its goal is to return a subset of connected edge features such that they are within the specified network distance or cost cutoff; in addition, it can return the lines categorized by a set of break values that an edge may fall within. The service area solver can generate lines, polygons surrounding these lines, or both.

The polygons are generated by putting the geometry of the lines traversed by the Service Area solver into a triangulated irregular network (TIN) data structure. The network distance along the lines serves as the height of the locations inside the TIN. Locations not traversed by the service area are put in with a much larger height value. A polygon generation routine is used with this TIN to carve out regions encompassing areas in between the specified break values. The polygon generation algorithm has additional logic to produce the generalized or detailed polygons and to deal with the many special cases that can be encountered.

So in part hopefully that provides more information, and the other part is "it's proprietary" as PolyGeo said.

There are also several user options that go into polygon creation - trim or not (does not affect regions completely enclosed by network edges - see my related answer at this question), general or detailed polygons, etc. Some of the issues in your posted images and example may be related to the complexity of the network and how the points are associated with it - without seeing the network creation or analysis settings it is hard to comment.

The short version is that polygons are always going to be an interpretation of some sort, whereas line output will be a more true representation of the analysis results (as stated in the Service Area Analysis help file).

Answer 2

The ArcGIS 10.2 and 10.2.1 Online Help on Service Area Analysis does not seem to provide any information on how Aervice Areas are calculated.

It is possible/likely that proprietary algorithms, which may be of commercial value to Esri, are involved.

Consequently, I think your best chance to find out will be to submit a question to your local Esri Support to ask whether they can explain the discrepancy between what you observe and what would expect to see.