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 doubleloop network yields an L-shaped tile, an L-shaped tile can be described by four geometric parameters: a, b, p and q, let m1⁄4a–p, n1⁄4b 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 amethod 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 doubleloop networks, but the directed double-loop network must be tight optimal one when its wide diameter obtainsminimumvalue. The simulation results indicate that there aremanydouble tight optimal directed double-loop networks. & 2010 Elsevier Ltd. All rights reserved.