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On the wide diameter of directed double-loop networks

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Bibliographic Details
Title: On the wide diameter of directed double-loop networks
Authors: Chen, Yebin1 cyb7102@163.com, Li, Ying2, Wang, Jiankun1
Source: Journal of Network & Computer Applications. Mar2011, Vol. 34 Issue 2, p692-696. 5p.
Subjects: Wireless communications, Data transmission systems, Superposition principle (Physics), Diameter, Computer simulation, Computer networks
Abstract: Abstract: 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. [Copyright &y& Elsevier]
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Database: Engineering Source
Description
Abstract:Abstract: 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. [Copyright &y& Elsevier]
ISSN:10848045
DOI:10.1016/j.jnca.2010.10.014