Computation of arc length in the presence of barriers in networks

In the presence of barriers between the pair of nodes, the rectilinear metric in a single step or multiple steps with p = 1 or the Euclidean metric in multiple steps with p = 2 equation LP = [(xi − xj)p + (yi − yj)p]1/p is used to compute the minimum arc length. As a result, the travel path may be a stair case pattern or zigzag pattern and the practical difficulties arise in laying and maintaining the cable. Hence, there is a need to develop a methodology in order to compute the arc length in a single step between the pairs of nodes for which 'p' value is between 1 and 2. This paper presents a mathematical model developed to compute the 'p' values of the curves. The resultant 'p' value is used to compute the arc length (LP) of the curves in the presence of barriers for the problem under consideration.