Short note: TST and STS

TST and STS are three-stage digital switches that combine time switches (TSIs) and time-multiplexed space switches (S) so that every call has many alternative paths. They solve the high blocking of two-stage ST and TS switches.

 TST:  link-->[T]-->[ S ]-->[T]-->link
 STS:  link-->[ S ]-->[T..T]-->[ S ]-->link

TST (Time–Space–Time)

• Input TSI moves the sample from its external slot to a free internal slot $x$; the space stage switches it in slot $x$ to the right output highway; the output TSI moves it to the required output slot.
• Alternative paths = number of internal time slots $l$.
• Blocking: $P_B = [1-(1-p')^2]^l$, $p' = pc/l$; non-blocking if $l \ge 2c - 1$.

STS (Space–Time–Space)

• The input space stage sends the sample to one of $k$ centre TSIs; that TSI changes its slot; the output space stage sends it to the right outgoing link.
• Alternative paths = number of centre TSIs $k$.
• Blocking: $P_B = [1-(1-p')^2]^k$, $p' = pN/k$; non-blocking if $k \ge 2N - 1$.

TST is more widely used because time expansion only needs faster memory, giving lower blocking at lower cost.