Medium Access Control

Partitioning: TDMA/FDMA give R/N, no collisions, idle waste. ALOHA: pure S = G·e⁻²ᴳ (vulnerable 2T, max 0.184 at G = 0.5); slotted S = G·e⁻ᴳ (vulnerable T, max 0.368 at G = 1). CSMA: listen first (1-, non-, p-persistent); CSMA/CD: abort + jam, L_min = 2·T_p·B. Backoff: after n collisions K ∈ {0..2^min(n,10) − 1}, abort at 16. Taking turns: polling; token ring ETR 1/(1 + a/N), DTR 1/(1 + a(N+1)/N).

From 2.3.1 The multiple access problem; collisions; channel partitioning

• Collision: overlapping transmissions on a shared link; all involved frames lost.
• MAC families: partitioning (TDMA/FDMA), random access (send freely, recover from collisions), taking turns (an orderly schedule).
• TDMA/FDMA: R/N per station, no collisions, idle shares wasted, wait up to (N − 1) slots.

From 2.3.2 Pure and slotted ALOHA: vulnerable time, throughput, maximum efficiency

• T = frame time; G = attempts per T.
• Pure: vulnerable 2T, S = G·e⁻²ᴳ, max 1/(2e) ≈ 0.184 at G = 0.5.
• Slotted: vulnerable T, S = G·e⁻ᴳ, max 1/e ≈ 0.368 at G = 1.
• Finite N: P(success) = N·p·(1 − p)ᴺ⁻¹.

From 2.3.3 CSMA and its persistence variants; CSMA/CD; minimum frame size = 2·Tp·B

• CSMA: sense before sending; collisions still possible within T_p.
• 1-persistent / non-persistent / p-persistent: what to do when busy.
• CSMA/CD: listen while sending; on collision jam, stop, back off.
• L_min = 2·T_p·B; d_max = L_min·v/(2B); i.e. T_t ≥ 2T_p.
• CSMA/CA (Foundation): wireless avoids collisions instead of detecting them.

From 2.3.4 Binary exponential backoff; probability of winning

• After the n-th collision: K uniform in {0, …, 2^min(n,10) − 1}; wait K × slot; abort after 16.
• Slot = 512 bit times (51.2 µs at 10 Mbps).
• P(A wins) = #{K_A < K_B} / (a·b); both at range 2: win 1/4, tie 1/2.
• Capture: A at range 2 vs B at range 4 → A wins 5/8.

From 2.3.5 Controlled access: polling, token passing and its efficiency

• Polling: primary asks each station; η = T_t/(T_t + T_poll); single point of failure.
• Token passing: only the token holder sends (token holding time).
• Ring latency = d/v + N·b/R.
• ETR η = 1/(1 + a/N); DTR η = 1/(1 + a(N+1)/N).

1. NAT · 2 marks

   Slotted ALOHA, frame time 1 ms, stations attempt 2000 frames/s. Throughput in frames/s (nearest whole)?

   Write your answer before opening the key.

2. NAT · 2 marks

   CSMA/CD at 1 Gbps, longest path 200 m, v = 2 × 10⁸ m/s. Minimum frame size in bytes?

   Write your answer before opening the key.

3. MCQ · 1 mark

   Pure ALOHA reaches its maximum throughput at G =

   1. 0.25
   2. 0.5
   3. 1
   4. 2
4. NAT · 2 marks

   A at its 1st collision, B at its 3rd. P(A wins the next round) (3 decimals)?

   Write your answer before opening the key.

5. MSQ · 1 mark

   Which protocols are collision-free?

   1. TDMA
   2. Token passing
   3. Slotted ALOHA
   4. Polling
6. NAT · 1 mark

   Token ring, N = 8, a = 0.4, delayed token release. Efficiency (3 decimals)?

   Write your answer before opening the key.

7. MCQ · 1 mark

   In CSMA/CD the minimum frame size exists so that:

   1. frames fit in one slot of TDMA
   2. a sender is still transmitting when a collision report can return
   3. the CRC fits
   4. tokens are not lost
8. NAT · 1 mark

   TDMA among 25 stations on a 5 Mbps link. Rate per station in kbps?

   Write your answer before opening the key.

9. MCQ · 1 mark

   A 1-persistent station finding the channel busy:

   1. waits a random time then senses again
   2. keeps sensing and sends the moment it is idle
   3. sends with probability p
   4. gives up