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The Number of Rearrangements in a 3-stage Clos Network Using an Auxiliary Switch

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Part of the Network Theory and Applications book series (NETA, volume 5)

Abstract

We consider the problem raised by Bassalygo: “What is the maximum number of rearrangements required by a rearrangeable 3-stage Clos network when there is an auxiliary middle switch carrying a light. load?” For a 3-stage Clos network with an auxiliary middle switch carrying s connections, he claimed that the maximum number of rearrangements φ 1(n,n, r; s) is less than \( s + \sqrt {2s} + 1 \). In this paper, we give a lower bound \( 3 \times \left\lfloor {s/2} \right\rfloor \) and an upper bound 2s + 1. where the lower bound shows that the upper bound given by Bassalygo does not hold in general.

Keywords

Network State Complete Bipartite Graph Light Load Adjacent Stage Nection Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    L.A. Bassalygo, On a number of reswitching in a three-stage connecting network, Inter. Teletraffic Cong. 7, pp. 231/1–231/4, 1973.Google Scholar
  2. [2]
    V.E. Benes, Mathematical Theory of Connecting Networks and Telephone Traffic, Academic, New York, 1965.zbMATHGoogle Scholar
  3. [3]
    M.C. Paull, Reswitching of connection networks, Bell Syst. Tech. J. 4, pp. 833–855, 1962.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinChuTaiwan, ROC

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