By Frank K. Hawang, Frank Hwang

The 1st variation of this publication coated intensive the mathematical conception of nonblocking multistage interconnecting networks, that's appropriate to either communique and laptop networks. This comprehensively up-to-date model places extra emphasis to the multicast and multirate networks that are less than quick improvement lately because of their broad purposes. This comprehensively up-to-date new version not just introduces the classical concept of the basic point-to-point community but additionally has a renewed emphasis at the newest multicast and multirate networks. The e-book can function both a one- or two-semester textbook for graduate scholars of knowledge technology, (electronic) communications, and utilized arithmetic. furthermore, as all of the proper literature is geared up and evaluated below one dependent framework, the amount is a vital reference for researchers in these components.

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**Example text**

Mn+ n/2 . 5 is verified for r = 2. Update M 11 . Then |S3 | = n/2 . Again, let S3 and S3 be two disjoint |S3 |/2 -subsets of S3 . Delete S3 from M 11 , delete S3 from M 33 , and add |S3 |/2 new (I1 , O3 ) connections which must be carried by Mj ’s with j > n + n/2 , say, by Mn+ n/2 +1 , . . , Mn+ n/2 + |S3 |/2 . It is easily verified that n/2 + n/2 /2 = n − n/4 . 5 is verified for r = 3. In general, at the (j − 1)st move, we delete Sj from M 11 , delete Sj from jj M , and add |Sj |/2 = n/2j−2 /2 new M s.

Therefore, we assume y4 (s ) = 0. (i) Since I1 and O1 can each be engaged in at most n − 1 connections, y1 (s ) + y2 (s ) + y5 (s ) + y6 (s ) ≤ n − 1, y1 (s ) + y3 (s ) + y5 (s ) + y6 (s ) ≤ n − 1. 1. 3-stage Clos Network 35 Using the induction hypothesis (iii) y2 (s ) + y3 (s ) + y6 (s ) ≤ n. Adding up, 2 [y1 (s ) + y2 (s ) + y3 (s ) + y5 (s ) + y6 (s )] ≤ 3n − 2, or y(s ) ≤ 3n/2 − 1. Route the new request through an unused middle crossbar. Then y(s) ≤ 3n/2 . (ii) y1 (s) + y4 (s) + y5 (s) = 1 + y1 (s ) + y4 (s ) + y5 (s ) = 1 + y1 (s ) + y5 (s ) ≤ n, since every connection involves I1 .

Extended generalized shuffle networks: sufficient conditions for strictly nonblocking operation. , 33, 269–291. Shannon, C. E. 1950. Memory requirements in a telephone exchange. Bell Syst. Tech. , 29, 343–349. -T. 1991. Log2 (N, m, p) strictly nonblocking networks. IEEE Trans. , 39, 1502–1510. Smith, D. G. 1977. Lower bound on the size of a 3-stage wide-sense nonblocking network. Elec. , 13, 215–216.