Blocking in 3-Stage "Folded" Switching Arrays

Following a brief consideration of multistage switching arrays in general, with particular emphasis on the advantages of 3-stage switching systems, this paper discusses the blocking properties of "folded" vs. "nonfolded" 3-stage switching arrays. Conditions under which a "folded" array will be nonblocking are stipulated. A comprehensive series of formulas are given for determining the internal blocking of any "folded" 3-stage array which does not satisfy the conditions for nonblocking. Included also are tables (based on certain of these formulas) for quickly finding the blocking in any "symmetrical" 3-stage "folded" array, and for determining the "dimensions" of symmetrical arrays required to carry any given density of traffic at any given maximum allowable blocking. Additional information and formulas are included, covering the use of "multiple-linkage" in special arrays intended for register access. The derivation of certain of these blocking formulas is given in the Appendix. It should be noted that the formulas given in this paper are all based on the assumption that the distribution of telephone traffic offered to the arrays will conform to the Exponential Binomial Probability Distribution (Bernoulli); this is the usual assumption made in American practice.