NON-BLOCKING SWITCHING SYSTEMS 



407 



etc., switching stages where less than N^ crosspoints are required. It 

 then deals with conditions for obtaining a minimum number of cross- 

 points, cases where the N inputs and N outputs can not be uniformly 

 assigned to the switches, switching arrays where the inputs do not equal 

 the outputs, and arrays where some or all of the inputs are also outputs. 



SQUARE ARRAY 



A simple square array having iV inputs and N outputs is shown in 

 Fig. 1. The number of crosspoints equals N"^ and any combination of N 

 or less simultaneous connections can exist without blocking between 

 the inputs and the outputs. The number of switching stages, s, is equal 

 to 1. The number of crosspoints, C(s), is: 



C(l) = N' 



(1) 



NUMBER OF 

 CROSSPOINTS =N^ 



Fig. 1 — Square Array. 



THREE-STAGE SWITCHING ARRAY 



An array where less than N^ crosspoints are required is shown in 

 Fig. 2. This array has N = 3Q inputs and iV = 36 outputs. There are 

 three switching stages, namely, an input stage (a), an intermediary stage 

 (b), and an output stage (c). In stage (a) there are six 6 x 11 switches; 

 in stage (b) there are eleven 6x6 switches; and in stage (c) there are 

 six 6 X 11 switches. In total, there are 1188 crosspoints which are less than 

 the 1296 crosspoints required by equation (1). 



Of interest are the derivations of the various quantities and sizes of 

 switches. In stage (a) the number, n, of inputs per switch was assumed 

 to be equal to N^^^, thus giving six switches and six inputs per switch. 

 In a similar manner stage (c) was assigned six switches and six outputs 

 per switch. The number of switches required in stage (b) must be suf- 

 ficient to avoid blocking under the worst set of conditions. The worst 

 case occurs when between a given switch in stage (a) and a given switch 

 in stage (c) : (1) five links from the switch in stage (a) to five correspond- 



