--- title: "Multistage switching; TST vs STS" subject: "Telecommunications" chapter: 4 key: "semester_8/telecommunications:multistage-tst-sts-compare" source: https://www.bctengineer.com/q/semester_8/telecommunications/multistage-tst-sts-compare site: BCT Engineering --- # Multistage switching; TST vs STS Telecommunications · Chapter 4: Digital Switching - Asked in: 2080 Chaitra, 2+6 marks - Video: [Telecommunication Systems (19 - Multi-Stage TST or STS Switch)](https://www.youtube.com/watch?v=ipZmBPa4SdM) — Dr. Samy S. Soliman - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/multistage-tst-sts-compare - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4 ## Question What are advantages of multi-stage switching system over single stage switching system? Compare TST and STS switch in digital telephone exchange system with necessary diagram and its blocking probabilities. ## Short answer Multi-stage switches reduce crosspoints, improve utilization, provide alternative paths, modular growth, and concentration/expansion. TST (Time-Space-Time) uses internal slots: P_B = [1 - (1 - p/alpha)^2]^l, alpha = l/c; STS (Space-Time-Space) uses k time modules: P_B = [1 - (1 - p/beta)^2]^k, beta = k/N. TST yields much lower blocking and lower cost for large exchanges; STS suits small exchanges. ## Answer #### Advantages of multi-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 switch ```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 ``` An incoming time slot $i$ is moved by the first TSI to a free internal slot $j$, passed through the space matrix in slot $j$, and moved by the outgoing TSI to the wanted slot $m$. Blocking happens only if no internal slot is free on both the input and output highways. With $l$ internal slots and $p' = p\,c/l$: $$ \begin{aligned} p' &= \frac{p}{\alpha},\quad \alpha = \frac{l}{c} \\ P_B(\text{TST}) &= \left[1 - (1-p')^2\right]^{l} \end{aligned} $$ #### STS switch ```text incoming S stage T stage S stage outgoing PCM 1 --->+--------+--->[ TSI 1 ]--->+--------+---> PCM 1 PCM 2 --->| N x k |--->[ TSI 2 ]--->| k x N |---> PCM 2 ... | space | ... | space | PCM N --->+--------+--->[ TSI k ]--->+--------+---> PCM N ``` The first space stage connects the incoming highway (in its own slot) to one of $k$ time switches; the TSI moves the sample to the outgoing slot; the second space stage connects it to the outgoing highway. Blocking happens if none of the $k$ modules has both links free. With $p' = p/\beta$: $$ \begin{aligned} p' &= \frac{p}{\beta},\quad \beta = \frac{k}{N} \\ P_B(\text{STS}) &= \left[1 - (1-p')^2\right]^{k} \end{aligned} $$ #### Comparison of TST and STS | Point | TST | STS | |---|---|---| | Stages | Time – Space – Time | Space – Time – Space | | Alternative paths | $l$ internal time slots | $k$ time modules | | Blocking | Very low ($l$ large) | Higher ($k$ small) | | Main hardware | Memories (cheap) + one space matrix | Two space matrices + TSIs | | Cost for large N | Lower | Higher | | Expansion | Add internal slots or TSIs | Add space arrays and TSIs | | Control | More memory, simple space control | Simpler for small sizes | | Typical use | Large digital exchanges (e.g. AXE, E10) | Small/medium exchanges, some early systems | Example ($p' = 0.2$): STS with $k = 8$ gives $P_B = 0.36^8 \approx 2.8 \times 10^{-4}$, while TST with $l = 32$ gives $0.36^{32} \approx 6.3 \times 10^{-15}$. Hence TST is preferred for large exchanges. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What are the stage orders of TST and STS? A. TST is Time-Space-Time, STS is Space-Time-Space B. TST is Space-Time-Space, STS is Time-Space-Time C. Both are Time-Space-Time D. TST has only space stages Answer: A. The letters give the order of stages: time, space, time for TST and space, time, space for STS. (Key point: TST versus STS structure) 2. With p' = 0.2, why is STS (k = 8) blocking about 2.8e-4 while TST (l = 32) is about 6.3e-15? A. TST has higher occupancy B. TST has more alternative paths (32 against 8) C. STS has no blocking formula D. The formulas differ in the power of 2 Answer: B. Both use 0.36 per path, raised to 8 for STS and 32 for TST, so more paths means far lower blocking. (Key point: Blocking comparison) 3. Why is TST preferred for large digital exchanges? A. It uses two large space matrices B. It cannot be expanded C. It is cheap: mostly memories with one space matrix, and low blocking D. It needs no control memory Answer: C. TST does most switching in cheap memories, uses a single space matrix and gives low blocking. (Key point: Cost of large exchanges) ## Related in Telecommunications - [Telephone exchange structure; TST vs STS](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aexchange-structure-tst-sts) — Telecommunications, chapter 4 - [Multistage switching and STS blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-sts-blocking) — Telecommunications, chapter 4 - [Multistage switching and TST blocking](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-tst-blocking) — Telecommunications, chapter 4 - [Derive STS and TST blocking probabilities](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Asts-tst-blocking-derivation) — Telecommunications, chapter 4 - [Multistage advantage and TST switching](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultistage-advantage-tst) — Telecommunications, chapter 4, asked 2× - [TST vs STS and three-stage design](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atst-sts-design-crosspoints) — Telecommunications, chapter 4 ## Related in other subjects - [Crossbar switch vs multistage network](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Acrossbar-vs-multistage) — Computer Organization and Architecture, chapter 8