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

  • Frank K. Hwang
  • Wen-Dar Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)

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 ϕ1 (n,n,r;s) 1 is less than \( s + \sqrt {2s } + 1 \) . In this paper, we give a lower bound 3×⌊s/2⌋ and an upper bound 2s + 1, where the lower bound shows that the upper bound given by Bassalygo does not hold in general.

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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

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Frank K. Hwang
    • 1
  • Wen-Dar Lin
    • 1
  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinChuTaiwan, Republic of China

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