---
title: "ST and TS drawbacks solved by STS"
subject: "Telecommunications"
chapter: 4
key: "semester_8/telecommunications:st-ts-drawbacks-sts"
source: https://www.bctengineer.com/q/semester_8/telecommunications/st-ts-drawbacks-sts
site: BCT Engineering
---

# ST and TS drawbacks solved by STS

Telecommunications · Chapter 4: Digital Switching

- Asked in: 2070 Chaitra, 2+2+4 marks
- Video: [Lecture - 10 Basic Time Division Switching Networks, Space-Time-Space (S-T-S) &Time-Space-Time (TST)](https://www.youtube.com/watch?v=peoFGpGCR34) — Engineering Jnana
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/st-ts-drawbacks-sts
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4

## Question

What are the drawbacks of ST and TS switch and how are they solved by STS switch? Explain.

## Short answer

Two-stage TS and ST networks suffer high blocking because the space stage must use a fixed slot. STS solves this by adding k centre TSIs: input space sends the sample in its original slot to any free TSI, TSI changes the slot, output space connects. Blocking becomes [1-(1-p')^2]^k, and if k≥2N-1 it is non-blocking.

## Answer

#### Drawbacks of ST and TS switches
A **TS switch** has a time stage followed by a space stage; an **ST switch** has a space stage followed by a time stage. Both are two-stage and give only **one possible path** for each connection, so they block heavily.

- **TS drawback:** the input TSI moves the sample from slot $i$ to the wanted output slot $j$ on its own highway, and then the space stage must connect the highway to the output highway in slot $j$. If another input highway already uses slot $j$ to reach the same output highway, the call is **blocked**, even though both A and B are free.
- **ST drawback:** the space stage must connect input highway $a$ to output highway $b$ in the **input slot $i$**. If slot $i$ is already used on output highway $b$ by a call from another input, the call is blocked. The output TSI could change the slot afterwards, but it never receives the sample.

```text
 TS: [T] -> [S]   S must use slot j  (fixed)
 ST: [S] -> [T]   S must use slot i  (fixed)
 => one path only, blocking = P(that slot busy)
```

#### How STS solves this
An **STS** switch has an input space stage, a middle stage of $k$ TSIs and an output space stage.

```text
 HW1 -->+------+  [TSI 1]  +------+--> HW1
 HW2 -->|N x k |->[TSI 2]->|k x N |--> HW2
 HWN -->+------+  [TSI k]  +------+--> HWN
```

1. In input slot $i$, the input S stage can send the sample to **any free centre TSI** $m$ (one with a free link in slot $i$).
2. TSI $m$ changes the slot from $i$ to $j$.
3. In slot $j$, the output S stage connects TSI $m$ to output highway $b$.
4. The call is blocked only if **all $k$ centre TSIs** are busy in slot $i$ or slot $j$.

So there are now $k$ alternative paths instead of one. Using a Lee graph with internal link occupancy $p' = pN/k$:
$$
P_B = \left[1 - (1 - p')^2\right]^{k}
$$
For $p' = 0.3$ and $k = 8$: $P_B = 0.51^8 \approx 4.6 \times 10^{-3}$, compared with about $0.3$ for a single path. With $k \ge 2N - 1$ the STS switch becomes strictly non-blocking.

(TST solves the same problem using $l$ internal time slots as alternative paths, and is usually cheaper.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the main drawback of ST and TS?
   A. Too many TSIs
   B. Only one possible path per connection, so heavy blocking
   C. They cannot change slots
   D. They need no control memory
   Answer: B. A single path means blocking whenever that slot is busy. (Key point: Drawback of two-stage)

2. In TS, why can a call be blocked even though A and B are free?
   A. Slot j is already used on the output highway by another input
   B. Input TSI is full
   C. No memory
   D. Output TSI is missing
   Answer: A. The space stage must use slot j, which may be taken. (Key point: TS blocking)

3. How does STS avoid this?
   A. Sample can go to any free centre TSI, which changes slot i to j
   B. Space stage changes slot
   C. It uses one path
   D. It removes the output stage
   Answer: A. k centre TSIs give k alternative paths. (Key point: STS solution)

4. When is an STS call blocked?
   A. If one centre TSI is busy
   B. If all k centre TSIs are busy in slot i or slot j
   C. If slot i is busy
   D. Never
   Answer: B. Blocking needs every one of the k paths busy. (Key point: STS blocking)

## Related in Telecommunications

- [Time and space switch drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-space-switch-drawbacks) — Telecommunications, chapter 4
- [Short note: ST switch](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ashort-note-st-switch) — Telecommunications, chapter 4
- [Space switch and two-stage S-T drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-switch-two-stage-st) — Telecommunications, chapter 4
- [Time switch and two-stage T-S network](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-switch-two-stage-ts) — Telecommunications, chapter 4
- [Space switch and why TST is used](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-switch-why-tst) — Telecommunications, chapter 4
- [Multistage switching; TST vs STS](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-tst-sts-compare) — Telecommunications, chapter 4

## Related in other subjects

- [IPv4 drawbacks solved by IPv6](https://www.bctengineer.com/question.md?key=semester_7%2Fcomputer_networks_and_security%3Aipv4-drawbacks-ipv6-advantages) — Computer Networks and Security, chapter 7, asked 2×