We've explored two extreme strategies for CSMA behavior:

• 1-persistent: When idle, transmit with probability 1 (certainty)
• Non-persistent: When busy, back off without monitoring

Each has clear disadvantages. 1-persistent causes guaranteed collisions among waiting stations. Non-persistent wastes channel capacity with unnecessary idle time.

p-Persistent CSMA offers an elegant middle ground: when sensing an idle channel, transmit with probability p < 1, and defer to the next slot with probability 1-p. This introduces controlled randomization that spreads transmissions over time, reducing collisions without abandoning the channel entirely.

The key insight behind p-persistent CSMA is this: even when the channel appears idle, multiple stations may be ready to transmit simultaneously. If all of them transmit immediately (as in 1-persistent), they collide.

What if, instead of everyone transmitting, each station flips a biased coin to decide whether to transmit?

• With probability p: Transmit now
• With probability 1-p: Wait for the next time slot, then try again

If p = 0.3 and three stations are ready:

• Expected transmitters = 3 × 0.3 = 0.9 (usually 0 or 1)
• Probability all three transmit = 0.3³ = 0.027 (2.7%)
• Probability exactly one transmits = 3 × 0.3 × 0.7² = 0.441 (44.1%)

By choosing p appropriately, we can dramatically reduce collision probability!

p-persistent CSMA operates in a slotted time structure. Time is divided into slots, where each slot duration typically equals the maximum propagation delay (τ). This slotting is crucial for synchronizing station behavior.

Note: Unlike slotted ALOHA where slots equal frame transmission time, p-persistent CSMA uses slots equal to propagation delay—much shorter.

Key characteristics:

1. Slotted time: Decisions are made at discrete slot boundaries (slot = τ, the propagation delay)
2. Persistent when busy: Like 1-persistent, stations monitor a busy channel continuously
3. Probabilistic when idle: Unlike 1-persistent, stations don't transmit with certainty
4. Defer with probability 1-p: Stations that 'lose' the coin flip wait one slot and try again
5. Repeating slots: A station may defer for multiple consecutive slots until it finally 'wins' the coin flip

Let's trace through p-persistent behavior with p = 0.5 (50% transmission probability per idle slot).

Scenario: Three waiting stations

Station X finishes transmitting. Stations A, B, C are all waiting with frames to send. Time is slotted with slot duration = τ.

Slot 1: Channel becomes idle

Collision! Both A and C transmitted.

After collision resolution (both back off)...

Stations A and C enter collision backoff. Station B still has its original frame.

Alternative scenario (same setup, different random values):

Slot 1:

No transmission! All three deferred.

Slot 2:

Success! Only A transmitted. B and C will try in subsequent slots.

Slot 2 + Transmission time: A is transmitting. B and C sense busy, monitor.

After A finishes:

Slot 1 (after A):

Success! B transmits. C defers again.

Eventually, C transmits successfully.

The performance of p-persistent CSMA depends critically on the choice of p. But what's the optimal value?

The tradeoff:

• p too large (e.g., p = 0.9): Multiple stations likely to transmit → High collision rate
• p too small (e.g., p = 0.1): Stations wait many slots before transmitting → High idle time

Optimal p depends on the number of competing stations (N):

If N stations are waiting, we want exactly ONE to transmit on average. This suggests:

$$p_{optimal} \approx \frac{1}{N}$$

With this choice:

• Expected transmitters = N × (1/N) = 1
• Probability of exactly 1 transmitter is maximized

The estimation problem:

The optimal p depends on N, the number of competing stations. But how can a station know N at any given moment? This is a fundamental challenge:

1. N varies over time: Stations come and go; traffic is bursty
2. N is not directly observable: A station can sense busy/idle, but not count competitors
3. Static p is suboptimal: A fixed p works well for one value of N, poorly for others

Solutions in practice:

1. Conservative static p: Choose p for expected worst-case N (e.g., p = 0.1)
2. Adaptive p: Adjust p based on observed collision rate (more collisions → lower p)
3. Hybrid approaches: p-persistent for initial transmission, exponential backoff for retries

The IEEE 802.11 approach: WiFi doesn't use pure p-persistent CSMA but uses a contention window that effectively adapts p. The window doubles after each collision (lowering effective p) and resets after success.

Let's analyze the throughput of p-persistent CSMA mathematically.

Model:

• G = Offered load (frames per transmission time)
• a = τ/T_frame = Propagation delay / Frame transmission time
• p = Transmission probability per idle slot
• S = Throughput (successful frame transmissions per unit time)

Simplified throughput derivation:

The analysis is complex due to the slotted structure and persistent monitoring. For the case when a << 1 (small slots relative to frame time), the throughput can be approximated as:

$$S \approx \frac{G \cdot e^{-G} \cdot (1 + a)}{1 + e^{-G}(1 - p^{-1})}$$

For the special case when p = 1 (1-persistent): $$S = \frac{G \cdot e^{-G} \cdot (1 + G + aG(1 + G + aG/2))}{\text{complex denominator}}$$

Throughput behavior:

The p-persistent framework provides a unifying view of CSMA variants. By adjusting p and channel-busy behavior, we can derive other protocols as special cases.

p-persistent generalizes CSMA:

The spectrum of aggressiveness:

We can order CSMA variants by how 'aggressively' they attempt transmission:

← More Conservative          More Aggressive →

Non-Persistent → p-Persistent (p small) → p-Persistent (p large) → 1-Persistent

• Conservative: Lower collision rate but higher latency and idle time
• Aggressive: Lower latency when successful but more collisions under load

Implementing p-persistent CSMA requires careful attention to several practical considerations.

Slotting requirements:

Random number generation:

Each decision requires a uniform random number in [0, 1]:

1. Hardware RNG: Best for security and true randomness
2. PRNG with unique seed: Each station uses different seed (e.g., based on MAC address)
3. Quality matters: Poor randomness causes statistical clustering → increased collisions

Collision handling:

p-persistent reduces but doesn't eliminate collisions. When collisions occur:

1. Detection: Via CSMA/CD (wired) or timeout/NAK (wireless)
2. Backoff: Typically exponential backoff rather than p-persistent retry
3. Retry: After backoff, frame is retransmitted using the normal algorithm

p-persistent CSMA introduces controlled randomization to the transmission decision. When sensing an idle channel, stations transmit with probability p (not certainty), spreading transmissions over time and reducing collisions.

What's next:

We've now covered the three major persistence strategies:

• 1-persistent: Simple, aggressive, good at low load
• Non-persistent: Spreads retries, good at high load
• p-persistent: Tunable middle ground, theoretically elegant

The final page of this module brings these together in a comprehensive efficiency analysis. We'll derive and compare throughput formulas, plot efficiency curves, and understand when each protocol excels. This completes our understanding of CSMA protocols.