On the wide diameter of directed double-loop networks

In parallel transmission system, the wide diameter has become an important factor to measure transmission efficiency instead of the diameter. The minimum distance diagram of a directed double-loop network yields an L-shaped tile, an L-shaped tile can be described by four geometric parameters: a, b, p and q, let m=a–p, n=b−q, the L-shaped tiles can be classified into 4 types according to the value of m and n. In this paper, through classification and superposition to L-shaped tiles, we give a method to search the equivalent node, and provide the formulas for the wide diameter of directed double-loop networks. We also prove that for any directed double-loop networks, the lower and the upper bounds of the wide diameter are ceil (sqrt(3×N))−1 and N−1, respectively. Next, we use simulation results to demonstrate the relationship between the wide diameter and tight optimal directed double-loop networks. It is obvious that the wide diameter doesn’t always obtain minimum value in tight optimal directed double-loop networks, but the directed double-loop network must be tight optimal one when its wide diameter obtains minimum value. The simulation results indicate that there are many double tight optimal directed double-loop networks.