346 BELL SYSTEM TECHNICAL JOURNAL 



figuration of the holding relays is compared with the present configuration 

 and voltages applied to or eUminated from all relays that should be changed. 

 Needless to say, an exchange of this type, although using the minimum 

 memory, has many disadvantages, as often occurs when we minimize a 

 design for one parameter without regard to other important characteristics. 

 In particular in Fig. 2 the following may be noted: (1) Each of the memory 

 relays must carry an enormous number of contacts. (2) At each new call or 

 completion of an old call a large fraction of the memory relays must change 

 position, resulting in short relay life and interfering transients in the con- 

 versations. (3) Failure of one of the memory relays would put the exchange 

 completely out of commission. 



3. The Separate Memory Condition 



The impracticality of an exchange with the absolute minimum memory 

 suggests that we investigate the memory requirements with more realistic 

 assumptions. In particular, let us assume that in operation a separate part 

 of the memory can be assigned to each call in progress. The completion of 

 a current call or the origination of a new call will not disturb the state of the 

 memory elements associated with any call in progress. This assumption is 

 reasonably well satisfied by standard types of exchanges, and is very natural 

 to avoid the difficulties (2) and (3) occurring in an absolute minimal design. 



If the exchange is to accommodate 5 simultaneous conversations there 

 must be at least S separate memories. Furthermore, if there are only this 



number, each^ of these must have a capacity log — To see this, 



suppose all other calls are completed except the one in a particular memory. 

 The state of the entire exchange is then specified by the state of this par- 

 ticular memory. The call registered here can be between any pair of the N' 

 subscribers, giving a total of NiN — l)/2 possibilities. Each of these must 

 correspond to a different state of the particular memory under considera- 

 tion, and hence it has a capacity of least log N{N — l)/2. 

 The total memory required is then 



M ^ Slog -^-^ . (4) 



If the exchange must remember which subscriber of a pair originated the 

 call we obtain 



M = Slog NiN - 1). (5) 



or, very closely when .V is large, 



M = 2S log N. (6) 



1 li. D. Holhrook has pointed out that l)y using more than 5 memories, each can have 

 for certain ratios of ^, a smaller memory, resulting in a net saving. This only occurs, 

 however, with unrealistically high calling rates. 



