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

1. Vulnerable time of slotted ALOHA?
   Stuck? Peek at 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.

   Read lesson 2.3.2

2. Why does TDMA waste capacity?
   Stuck? Peek at 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.

   Read lesson 2.3.1

3. RTT for a tiny signal on a link with propagation delay T_p?
   Stuck? Peek at 1.3.3 RTT, bandwidth-delay product, utilisation and a = Tp/Tt

   • RTT = 2·T_p for tiny signals (add T_t / queuing if stated).
   • BDP = B × T_p bits in flight; B × RTT before any reply.
   • a = T_p / T_t.
   • Send-and-wait: U = T_t/(T_t + 2T_p) = 1/(1 + 2a); throughput = U·B.
   • To keep the link busy: about 1 + 2a units in flight.

   Read lesson 1.3.3

Polite people at a meeting listen before speaking, and if two start at once, both stop mid-sentence and try again later. Networks copy both habits: carrier sense (listen first) and collision detection (stop as soon as a clash is heard). But a speaker far away is heard only after a delay — and that delay sets a rule on how long every frame must be.

Station A starts sending. Station B at the far end of a cable cannot hear A until A's first bit arrives, T_p later. If B starts just before that, how long after A started can A first hear the collision?

Up to 2·T_p: A's signal takes T_p to reach B, and B's colliding signal takes another T_p to come back. If A finished sending before then, it would never know its frame was destroyed. So A must still be transmitting at 2·T_p: the frame must last at least 2·T_p.

CSMA: listen before talking

Collisions still happen because of propagation delay: two stations may both sense "idle" before each other's signal arrives. The vulnerable time shrinks to about T_p.

Persistence: what to do when the channel is busy

CSMA/CD: stop on collision

Collision detection works only on links where a station can hear while it sends (classic wired shared cables), i.e. it is a half-duplex scheme.

Minimum frame size L ≥ 2·T_p·B

To detect a collision, the sender must still be transmitting when the collision news returns, which can take up to the round trip 2·T_p across the longest path:

Equivalently, for a given minimum frame size, the cable can be at most d_max = L_min·v / (2B) long. A classic 10 Mbps shared LAN fixes L_min at 512 bits = 64 bytes, its slot time.

CSMA/CA (Foundation)

Putting it together

• CSMA listens first; CSMA/CD also listens while sending and aborts on collision.
• Persistence variants trade delay against collisions.
• Collision detection needs frames lasting at least 2·T_p: L_min = 2·T_p·B.

• Use the round trip 2·T_p, not T_p, in the minimum frame size.
• CSMA reduces but cannot eliminate collisions — propagation delay leaves a window.
• 1-persistent sends immediately when the channel frees, so waiting stations collide with each other.
• CSMA/CD needs to hear while sending: half-duplex shared wires, not wireless.

"You must still be talking when the echo of a clash comes back": T_t ≥ 2·T_p.

After a collision, both stations must retry — but if they retry at the same moment they collide again. Next (2.3.4): how do they pick random waiting times, and how likely is each to win the next round?

1. NAT

   CSMA/CD: rate 10 Mbps, longest path 2 km, v = 2 × 10⁸ m/s. Minimum frame size in bits?

   Write your answer before opening the key.

2. NAT

   Minimum frame 1000 bits at 1 Gbps, v = 2 × 10⁸ m/s. Maximum cable length in metres?

   Write your answer before opening the key.

3. MCQ

   A station that waits a random time whenever it finds the channel busy is:

   1. 1-persistent
   2. non-persistent
   3. p-persistent
   4. TDMA
4. MSQ

   Which are true of CSMA/CD?

   1. A station stops sending when it detects a collision.
   2. Collisions are impossible.
   3. Frames must last at least 2·T_p.
   4. A jam signal announces the collision.
5. MCQ

   Doubling the bit rate of a CSMA/CD network while keeping the minimum frame size requires the maximum length to:

   1. double
   2. halve
   3. stay the same
   4. quadruple

• 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.

• carrier sense, CSMA
• 1-persistent / non-persistent / p-persistent
• collision detection, CSMA/CD
• jam signal
• minimum frame size L_min = 2·T_p·B
• CSMA/CA (Foundation)

1. Minimum frame size for CSMA/CD?
   Reveal answer

   L_min = 2·T_p·B.
2. Why can CSMA still collide?
   Reveal answer

   Propagation delay: a station may sense idle before another's signal arrives.
3. Non-persistent behaviour when busy?
   Reveal answer

   Wait a random time, then sense again.

• L_min = 2·T_p·B; d_max = L_min·v/(2B). — CSMA/CD on a shared medium; T_p over the longest station-to-station path.
• Raising the rate B (same L_min) shrinks the allowed length proportionally. — fixed minimum frame size, same signal speed.