Time and space switch drawbacks

Time switch (T)

A time switch or Time Slot Interchanger (TSI) changes the time slot of PCM samples on a TDM highway.

 in ---->[ Speech memory (c x 8 bits) ]----> out
           ^ write addr      read addr ^
     [slot counter]          [Control memory]

• Speech memory (SM): $c$ words of 8 bits, one per slot. Control memory (CM): $c$ words of $\log_2 c$ bits.
• Sequential write, random read: sample in slot $i$ is written to SM($i$); in output slot $j$, CM($j$) = $i$ gives the read address. So input slot $i$ appears in output slot $j$.
• Random write, sequential read: CM($i$) = $j$ gives the write address; SM is read in order.
• Example: CM(7) = 3 connects TS3 to TS7 with a delay of 4 slots.

Space switch (S)

A time-multiplexed space switch connects $N$ input highways to $M$ output highways through a gate matrix. Each output column has a control memory with $c$ words; in slot $t$ the word selects which input is connected to that output. The slot stays the same; only the highway changes.

        O1  O2  ..  OM
  I1 ---x---x-------x
  I2 ---x---x-------x
  IN ---x---x-------x
        |   |       |
      [CM1][CM2]..[CMM]

Example: CM$_2$(5) = 3 connects I3 to O2 during slot 5.

Drawbacks

Time switch

1. Size limited by memory speed: two accesses per slot, so $t_{access} \le 125\ \mu s/2c$. A 50 ns memory allows at most $125\ \mu s/(2 \times 50\ ns) = 1250$ channels, not enough for a large exchange.
2. Works on one highway only; it cannot connect different highways.
3. Adds a delay of up to one frame (125 µs).

Space switch

1. Cannot change time slots: a caller in slot 3 cannot reach a called party in slot 17.
2. Crosspoints grow as $N \times M$; a big single matrix is costly.
3. Gate speed limits the number of slots.

Two-stage TS or ST combination

• Only one path per connection; the S stage must use a fixed slot ($j$ in TS, $i$ in ST). If that slot is already busy into the output highway, the call is blocked, so blocking is high (about $p$).

How the drawbacks are solved

1. Combine T and S: time stages change slots; space stages change highways. Together they connect any slot on any highway to any slot on any other highway.
2. Use three stages (TST or STS) to give many alternative paths:
   • TST: $l$ internal slots as paths, $P_B = [1-(1-p')^2]^l$, non-blocking for $l \ge 2c - 1$.
   • STS: $k$ centre TSIs as paths, $P_B = [1-(1-p')^2]^k$, non-blocking for $k \ge 2N - 1$.
3. Time expansion in TST (more internal slots than external) reduces blocking cheaply.
4. Multistage space networks (Clos, $k \ge 2n - 1$) reduce crosspoints while staying non-blocking.
5. Larger structures such as TSST or TSSST for very large exchanges.
6. Faster memory and parallel (wider) highways (serial-to-parallel conversion) allow more channels per TSI.

Example: with $c = l = 32$ and $p = 0.5$, a TST switch has $P_B = 0.75^{32} \approx 1.0 \times 10^{-4}$, compared with about 0.5 for a two-stage TS switch.