ON DEGENERATE DOUBLE-LOOP L-SHAPES

Abstract

Most of the results about the L-shapes of double-loop networks are given in terms of the four parameters ℓ, h, p, n. But these parameters are not well defined in the degenerate case. Recently, Cheng and Hwang proposed an efficient algorithm to compute the four parameters ℓ, h, p, n of an L-shape which works for both the regular and the degenerate cases. On the other hand, Chen and Hwang gave a set of rules to determine the four parameters ℓ, h, p, n of a degenerate L-shape. Unfortunately, the solutions given by the above two methods do not always coincide. In this paper, we investigate their respective meanings and their relations. We also prove that, in the degenerate case, the set of rules given by Chen and Hwang is the most reasonable one among all known methods.