NON-BLOCKING SWITCHING SYSTEMS 



417 



J. Riordan has found a more efficient arrangement for cases where 

 N = kn -{- r. In place of using k switches of size n and one switch of 

 size r, he proposes that {k -\- 1 - n + r) switches of size n and {n - r) 

 switches of size n — 1 be used. For this case the number of crosspoints 



is: 



C = 2(2n - l){k + 1 - n + r)n + 2{2n - 2) (n - r){n - 1) 



+ (2/z - 3)(/c + 1)^ + 2(k + l){k + 1 - n + r) 



(17) 



INPUT 



SWITCHES 



o o o o o 



INTERMEDIARY 

 SWITCHES 



QpQOQQOQO 



oooooooon 



OppOOQOOQ 



oooooono 



OOOOQOpp 



OUTPUT 

 SWITCHES 



Q O O O O 







I 



Fig. 7 — Three-stage array. 25 ^ 1 (mod 3). An equivalent arrangement is to 

 provide two 8x8 and three 9x9 intermediary switches. Two of the 9x9 switches 

 need only 80 crosspoints. 



