Blocking and non-blocking switching

Blocking and non-blocking switching

• A blocking switch is one in which a call between a free input and a free output may still fail because no free internal path exists (internal links are busy with other calls). Multistage networks with too few middle-stage paths are blocking. Blocking probability is the chance that such a call is lost.
• A non-blocking switch is one in which any free input can always be connected to any free output, whatever other calls are in progress. A single-stage $N \times N$ crossbar is non-blocking but needs $N^2$ crosspoints.

Condition for a digital switch to be non-blocking

(a) Space-division three-stage (Clos) network. With $n$ inputs per first-stage array and $k$ middle arrays, the worst case is: the calling input's array already has $n-1$ busy inputs using $n-1$ different middle arrays, and the called output's array has $n-1$ busy outputs using $n-1$ other middle arrays. One more middle array is needed:

$$k \ge 2n - 1$$

(b) TST digital switch. Each incoming link has $c$ time slots, and the time-multiplexed space stage has $l$ internal time slots. By the same reasoning (with time slots in place of middle arrays):

$$l \ge 2c - 1$$

So a TST switch is non-blocking when the space stage runs at about twice the slot rate of the external links (time expansion).

(c) STS digital switch. With $N$ incoming TDM links and $k$ centre-stage TSIs: $k \ge 2N - 1$.

(d) Single time switch (TSI). It is always non-blocking provided the memory is fast enough: $t_{access} \le 125\ \mu s / 2c$.

Example

A TST switch has E1 links with $c = 32$ slots. For non-blocking operation, $l = 2(32) - 1 = 63$, so practical designs use 64 internal slots. With $l = 32$ only (no expansion), and link occupancy 0.9 E, blocking probability is

$$P_B = \left[1 - (1 - 0.9)^2\right]^{32} = 0.99^{32} \approx 0.725$$

Hence the time expansion to $l \ge 63$ is what makes the switch non-blocking.

For a space switch example: $N = 200$, $n = 10$ needs $k \ge 19$ middle arrays for non-blocking operation.