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EE 4720 Lecture Notes Generated from file lsli18.dvi. This page was generated using an imperfect translator. Text may be poorly positioned and mathematics will be barely readable. Illustrations will not show at all. If possible, view the PostScript versions of these notes. 12-1 * * 12-1 Classes of Circuit-Switched Networks Circuit-switched networks are classified based upon: - the connection assignments they can realize and - how they can change from satisfying one CA to satisfying an- other. Types of Connection Assignments Permutation CA: a set of requests in which each input and output appears exactly once. The symbol N will denote the set of all permutation connection assignments for N -input, N -output networks. Note: jN j = N ! A network is called a permutation network if it can satisfy all permu- tation connection assignments. d-limited generalized CA: a set of requests in which no input appears more than d times and no output appears more than once. A network is called a d-limited generalized connector if it can satisfy all d-limited generalized connection assignments. Generalized CA: a set of requests in which no output appears more than once. A network is called a generalized connector if it can satisfy all gener- alized connection assignments.

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12-1 EE 7725 Lecture Transparency. Formatted 11:16, 12 November 1997 from lsli1* *8. 12-1 12-2 * * 12-2 Ways in Which Networks Change Connection Assignments Consider two CAs, A and B. Suppose a network is to satisfy A and then B. The following might occur: - Paths are set up for A. - Data for A is transmitted. - Paths for A are torn down. - Paths are set up for B. - Data for B is transmitted. - Paths for B are torn down. In most cases this would be fine, but suppose: A = C [ f(a; ff)g and B = C [ f(b; fi)g and jCj = 99; 999. In this case, 99; 999 paths are being torn down and then being immediately rebuilt. Imagine the waste! Q: Would it be possible to only tear down the paths that change? A: It depends upon the type of network. For banyans the answer is yes. But these aren't permutation networks.
For inexpensive permutation networks the answer is no. 12-2 EE 7725 Lecture Transparency. Formatted 11:16, 12 November 1997 from lsli1* *8. 12-2 12-3 * * 12-3 Network Types A network is non-blocking if it can change from satisfying A to satis- fying B without tearing down paths in A " B, where A and B are any two connection assignments the network can realize. A network is rearrangeably non-blocking if when changing from satis- fying A to satisfying B it may tear down and rebuild some paths in A"B, where A and B are any two connection assignments the network can realize. These networks are called rearrangeable for short. A network is strictly non-blocking if it can change from satisfying A to

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## This note was uploaded on 07/18/2011 for the course EE 4770 taught by Professor Staff during the Fall '99 term at LSU.

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notes - EE 4720 Lecture Notes Generated from file...

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