Weights

Conduit tracing is similar to the Esri Find Path trace task in that if no weights are assigned, the results are the smallest number of edges through which a path can be traced. While it seems intuitive that the find path trace task would find the shortest path based upon distance, it does not. To trace an available path through the shortest distance, a weight must be assigned to the field of the Conduit feature class that stores the distance value, such as the default Shape.Len (Shape_Length in Access) field.

You could also use a cost factor as a weight. A cost weight field might have a monetary value that is managed based on the ease of running cable through particular sizes of ducts or the cost of digging up existing trenches. Then, in addition to various duct query criteria, a cost range representing the compromise between saving money and providing a quality installation could be used as a weight for the trace. Other examples include:

Diameter of a pipe	Solvers that calculate pressure or head in a network
Impedance (electrical resistance)	Calculating voltage drop in an electrical network
Time to traverse an edge	Shortest path solvers

Weights are assigned during the process of creating a geometric network. For tracing conduit availability:

If you create a distance weight, choose a single or double data type.
Assign it to the Shape.Len (Shape_Length) field of the Conduit System feature class.