---
title: "Blocking and non-blocking switching"
subject: "Telecommunications"
chapter: 4
key: "semester_8/telecommunications:blocking-nonblocking-switching"
source: https://www.bctengineer.com/q/semester_8/telecommunications/blocking-nonblocking-switching
site: BCT Engineering
---

# Blocking and non-blocking switching

Telecommunications · Chapter 4: Digital Switching

- Asked in: 2080 Bhadra, 3+5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/blocking-nonblocking-switching
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4

## Question

What is blocking and non-blocking switching system? At which condition digital switch work as no blocking? Explain with example.

## Short answer

A blocking switch may deny a call between free ports when no internal path is available; a non-blocking switch never does. A three‑stage space switch becomes non‑blocking with k ≥ 2n−1 middle arrays; a TST digital switch is non‑blocking when internal time slots l ≥ 2c−1. E.g., with E1 links (c=32), l ≥ 63 slots ensures non‑blocking operation.

## Answer

#### 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.

| Point | Blocking | Non-blocking |
|---|---|---|
| Internal path | May not be free | Always free |
| Crosspoints / hardware | Fewer | More |
| Cost | Lower | Higher |
| Grade of service | Small loss allowed | Zero internal loss |
| Typical use | Local exchanges with light traffic | Trunk/transit switches |

#### 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.

## Check yourself

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

1. What is a blocking switch?
   A. One where a call between a free input and a free output can fail because no free internal path exists
   B. One that has no outputs
   C. One that blocks all calls
   D. One with a single stage
   Answer: A. Internal links may be busy with other calls, so a free input and free output may not be connectable. (Key point: Blocking definition)

2. Why is k >= 2n - 1 needed for a strictly non-blocking three-stage network?
   A. n-1 middle arrays can be used by the input array's other calls, n-1 others by the output array's calls, plus one more must be free
   B. Each input needs two middle arrays
   C. The middle stage must be twice as large as the outer stages
   D. Only the output array matters
   Answer: A. Worst case (n-1) + (n-1) middle arrays are unusable, so one extra is required. (Key point: Clos worst case)

3. A TST switch with c slots per link is non-blocking when
   A. l >= c
   B. l >= 2c - 1
   C. l >= c/2
   D. l >= c^2
   Answer: B. By the same reasoning with time slots in place of middle arrays, l >= 2c - 1. (Key point: TST non-blocking condition)

4. Compared with a blocking switch, a non-blocking switch has
   A. Fewer crosspoints and lower cost
   B. More hardware and higher cost but zero internal loss
   C. The same hardware
   D. Lower grade of service
   Answer: B. Non-blocking designs need more crosspoints and cost more, but there is no internal loss. (Key point: Cost trade-off)

## Related in Telecommunications

- [Digital exchange principles; non-blocking 3-stage](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-exchange-nonblocking-3-stage) — Telecommunications, chapter 4
- [Strictly non-blocking 3-stage condition](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Astrictly-nonblocking-3-stage) — Telecommunications, chapter 4
- [TST time slots for non-blocking operation](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atst-time-slots-numerical) — Telecommunications, chapter 4
- [Digital switching system and its functions](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-switching-functions) — Telecommunications, chapter 4
- [Multistage switching and TST blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-tst-blocking) — Telecommunications, chapter 4
- [Multistage switching and STS blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-sts-blocking) — Telecommunications, chapter 4

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- [Dipole potential; no work along bisector](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adipole-potential-no-work-perpendicular) — Engineering Physics, chapter 7
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