--- title: "Multistage advantage and TST switching" subject: "Telecommunications" chapter: 4 key: "semester_8/telecommunications:multistage-advantage-tst" source: https://www.bctengineer.com/q/semester_8/telecommunications/multistage-advantage-tst site: BCT Engineering --- # Multistage advantage and TST switching Telecommunications · Chapter 4: Digital Switching - Asked in: 2079 Bhadra, 3+4 marks; 2073 Shrawan, 2+6 marks (asked 2 times) - Video: [T 4.5 TDM Switching & Space -Time switching](https://www.youtube.com/watch?v=PEzhUtAsX0g) — Ramanikumar animations -Telecom and Wireless - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/multistage-advantage-tst - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4 ## Question What is the advantage of multi-stage switching system over single stage switching system? Explain TST Switching with neat diagram and its blocking probability. ## Short answer Multi-stage switches use far fewer crosspoints, better utilization, alternative paths, modular growth, and built-in concentration/expansion. In TST, incoming slot i is moved by first TSI to free internal slot j, switched by space matrix in slot j, then moved by second TSI to outgoing slot m. Blocking probability: P_B = [1 - (1 - p/alpha)^2]^l with alpha = l/c, extremely low. ## Answer #### Advantages of multi-stage over single-stage switching - **Far fewer crosspoints:** a single-stage $N \times N$ switch needs $N^2$ crosspoints (e.g. $10^6$ for 1000 lines); a three-stage switch needs only a small fraction, so cost and size fall. - **Better crosspoint utilisation:** in a single stage at most $N$ of the $N^2$ crosspoints can be in use at once (each input and output takes part in only one connection), so utilisation is at most $1/N$; in multi-stage each crosspoint is shared by many possible connections. - **Alternative paths:** a call can go through any of several middle-stage arrays, so failure of one crosspoint does not isolate a subscriber (better reliability). - **Modular growth:** capacity can be expanded by adding arrays. - **Concentration and expansion** can be built into the stages to suit traffic. - Drawbacks: some blocking may occur, and path search (control) is more complex. #### TST switching A **Time–Space–Time (TST)** switch is a three-stage digital switching network: an incoming **time stage**, a **space stage** in the middle, and an outgoing **time stage**. It is the most common structure in large digital exchanges. ```text incoming T stage S stage T stage outgoing highways (time slot (crosspoint (time slot highways interchange) matrix) interchange) PCM 1 --->[ TSI ]--->+-------------+--->[ TSI ]---> PCM 1 PCM 2 --->[ TSI ]--->| N x N |--->[ TSI ]---> PCM 2 ... | space sw. | PCM N --->[ TSI ]--->+-------------+--->[ TSI ]---> PCM N slot i -> slot j (internal) -> slot j -> slot m ``` **Operation (connect slot $i$ of PCM 1 to slot $m$ of PCM N):** 1. **First time stage:** the time slot interchanger (TSI) on PCM 1 writes incoming samples into its speech memory in order and reads the sample of slot $i$ out in a free **internal slot $j$** (chosen by the control). 2. **Space stage:** in internal slot $j$ the crosspoint connecting row 1 to column N is closed (set by the space-switch control memory), passing the sample to the outgoing side. The same crosspoint is reused by other connections in other slots. 3. **Second time stage:** the TSI on output highway N stores the sample and reads it out in the required outgoing slot $m$. 4. The reverse direction uses a related internal slot (often half a frame away, $j + l/2$, where $l$ is the number of internal slots) so both directions are set up together. Because the space stage only needs to find **one free internal slot common to both links**, the many internal time slots act like many middle-stage arrays, giving very low blocking at low cost. The time stages can also expand ($l > c$ internal slots) to reduce blocking further. #### Blocking probability of TST (Lee graph) ```text slot 1 +--- ... ---+ A ---+--- slot j-+--- B l parallel paths +--- ... ---+ (internal slots) slot l ``` Let $p$ = occupancy of an incoming channel, $c$ = channels per highway, $l$ = internal slots, time expansion $\alpha = l/c$. Each internal link is busy with probability $p' = p/\alpha$. A path is blocked if either of its two links is busy: $1-(1-p')^2$. The call is blocked only if all $l$ paths are blocked: $$ \begin{aligned} p' &= \frac{p}{\alpha},\quad \alpha = \frac{l}{c} \\ P_B(\text{TST}) &= \left[1 - (1-p')^2\right]^{l} \end{aligned} $$ Example: $p = 0.2$, $l = c = 32$: $P_B = (1 - 0.8^2)^{32} = 0.36^{32} \approx 6.3 \times 10^{-15}$, practically non-blocking. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the main advantage of multi-stage over single-stage switching? A. No blocking at all B. Simpler path search C. Far fewer crosspoints than N^2 D. Fewer alternative paths Answer: C. A single stage needs N^2 crosspoints; three stages need only a fraction, cutting cost and size. (Key point: Crosspoint saving) 2. Why does multi-stage switching improve reliability? A. A call can use any of several middle-stage arrays B. It uses fewer subscribers C. It has only one path D. It removes the control unit Answer: A. Multiple middle arrays give alternative paths, so one failed crosspoint does not isolate a subscriber. (Key point: Reliability from alternative paths) 3. In a TST switch, what does the space stage do? A. Changes the slot from i to m B. Connects the sample on the incoming highway to the outgoing highway in the internal slot j C. Writes samples into the speech memory D. Generates the tones Answer: B. The first TSI moves slot i to internal slot j, the space stage crosses highways in slot j, the last TSI moves it to slot m. (Key point: TST operation) 4. What is the TST blocking probability, with p' = p/alpha and l internal slots? A. p'^l B. 1 - (1-p')^l C. [1 - (1-p')^2]^l D. (1-p')^2 Answer: C. A path is free only if both links are free; blocked = 1-(1-p')^2, and the call blocks only if all l paths are blocked. (Key point: TST blocking formula) ## Related in Telecommunications - [Multistage switching and TST blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-tst-blocking) — 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 - [Multistage switching and STS blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-sts-blocking) — 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 - [GOS and blocking probability in a loss system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-blocking-loss-system) — Telecommunications, chapter 6 - [Clos network and STS/TST blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aclos-network-sts-tst-blocking) — Telecommunications, chapter 4 ## Related in other subjects - [Pipelining and multi-stage pipeline](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Apipelining-stages) — Embedded System, chapter 2, asked 3×