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Throughout this module, we've explored carrier sensing and three persistence strategies: 1-persistent, non-persistent, and p-persistent CSMA. Each makes different tradeoffs between collision avoidance, channel utilization, and implementation complexity.
This final page brings everything together with a comprehensive efficiency analysis. We'll derive throughput formulas, compare performance under various conditions, and establish clear guidelines for protocol selection. Understanding these efficiency characteristics is essential for network design and protocol evaluation.
By the end of this page, you will understand: (1) Throughput formulas for all CSMA variants, (2) How the 'a' parameter affects efficiency, (3) Comparative analysis: when each protocol wins, (4) CSMA vs ALOHA efficiency improvements, and (5) Real-world factors affecting practical efficiency.
Before comparing protocols, let's establish the fundamental parameters and metrics used in CSMA efficiency analysis.
Key parameters:
| Parameter | Symbol | Definition | Typical Values |
|---|---|---|---|
| Offered Load | G | Total frame generation rate (frames per transmission time) | 0.1 - 10 |
| Throughput | S | Rate of successful frame transmissions | 0 - 1 (0-100%) |
| Propagation Delay | τ | End-to-end signal propagation time | μs to ms |
| Transmission Time | T | Time to transmit one frame = L/R | μs to ms |
| Normalized Delay | a | τ/T (propagation/transmission ratio) | 0.001 - 1 |
| Channel Capacity | R | Data rate in bits per second | Mbps to Gbps |
| Frame Length | L | Frame size in bits | Hundreds to thousands |
The 'a' parameter is crucial:
The normalized propagation delay a = τ/T is the single most important parameter determining CSMA efficiency:
$$a = \frac{\tau}{T} = \frac{\text{Propagation Delay}}{\text{Transmission Time}} = \frac{d/v}{L/R} = \frac{d \cdot R}{v \cdot L}$$
Where:
What 'a' represents:
CSMA works best when 'a' is small: short distances, large frames, moderate data rates. As networks become faster (higher R), frames become smaller (lower L), or distances increase (higher d), 'a' grows and CSMA efficiency degrades.
Let's present the throughput formulas for each CSMA variant. These formulas are derived from detailed queueing and probability analysis.
1. Non-Persistent CSMA:
$$S = \frac{G \cdot e^{-aG}}{G(1 + 2a) + e^{-aG}}$$
When a → 0: $$S = \frac{G}{1 + G}$$
Maximum throughput: S_max → 1 as G → ∞ (for a → 0)
2. 1-Persistent CSMA:
$$S = \frac{G \cdot e^{-G(1+2a)} \cdot [1 + G + aG(1 + G + aG/2)]}{G(1 + 2a) - (1 - e^{-aG}) + (1 + aG) \cdot e^{-G(1+a)}}$$
When a → 0: $$S = \frac{G(1 + G) \cdot e^{-G}}{G + e^{-G}}$$
Maximum throughput: S_max ≈ 53% at G ≈ 1 (for a = 0)
3. Slotted Non-Persistent CSMA:
$$S = \frac{aG \cdot e^{-aG}}{1 - e^{-aG} + a}$$
4. Slotted 1-Persistent CSMA:
$$S = \frac{G(1 + a - e^{-aG}) \cdot e^{-G(1+a)}}{(1 + a)(1 - e^{-aG}) + a \cdot e^{-G(1+a)}}$$
Note: Slotted variants assume time is divided into slots of duration τ, which simplifies analysis and provides modest efficiency improvements.
| Protocol | Formula (simplified) | S_max | G at S_max |
|---|---|---|---|
| Pure ALOHA | G·e^(-2G) | 18.4% | 0.5 |
| Slotted ALOHA | G·e^(-G) | 36.8% | 1.0 |
| 1-Persistent CSMA | Complex (see above) | ~53% | ~1.0 |
| Non-Persistent CSMA | G·e^(-aG)/(G(1+2a)+e^(-aG)) | ~90% | ~3.0 |
| Slotted Non-Persistent | aG·e^(-aG)/(1-e^(-aG)+a) | ~85% | ~2.5 |
These formulas are derived under idealized assumptions: Poisson arrivals, identical stations, immediate collision detection, etc. Real networks deviate, but the formulas capture fundamental behavior and relative rankings remain valid.
Let's compare the throughput curves for all protocols. The following table provides throughput values at various offered loads for a = 0.01 (typical LAN scenario).
| G | Pure ALOHA | Slotted ALOHA | 1-Persistent | Non-Persistent |
|---|---|---|---|---|
| 0.1 | 0.016 | 0.090 | 0.095 | 0.091 |
| 0.25 | 0.038 | 0.195 | 0.220 | 0.199 |
| 0.5 | 0.065 | 0.303 | 0.420 | 0.329 |
| 1.0 | 0.074 | 0.368 | 0.531 | 0.476 |
| 2.0 | 0.037 | 0.271 | 0.464 | 0.587 |
| 3.0 | 0.015 | 0.149 | 0.353 | 0.656 |
| 5.0 | 0.002 | 0.034 | 0.185 | 0.752 |
| 10.0 | ~0 | ~0 | 0.046 | 0.869 |
Key observations from the data:
At low load (G < 0.5): 1-persistent performs best due to minimal latency and rare collisions
At moderate load (G ≈ 1): 1-persistent still leads, but non-persistent is catching up
At high load (G > 2): Non-persistent dramatically outperforms 1-persistent. The crossover occurs around G ≈ 1.5
At very high load (G > 5): Non-persistent continues improving toward its theoretical maximum, while 1-persistent collapses
CSMA vs ALOHA: All CSMA variants significantly outperform ALOHA, especially at low to moderate loads
Notice that 1-persistent throughput DECREASES as load increases beyond G ≈ 1. This is 'throughput collapse'—more offered traffic results in LESS successful throughput due to cascading collisions. Network design must avoid this region or use non-persistent approaches.
The normalized propagation delay 'a' dramatically affects CSMA efficiency. Let's analyze how throughput varies with 'a' for each protocol.
Maximum throughput vs 'a':
| a | 1-Persistent S_max | Non-Persistent S_max | Slotted ALOHA (reference) |
|---|---|---|---|
| 0.001 | ~75% | ~99% | 36.8% |
| 0.01 | ~53% | ~90% | 36.8% |
| 0.05 | ~42% | ~75% | 36.8% |
| 0.1 | ~35% | ~65% | 36.8% |
| 0.5 | ~25% | ~45% | 36.8% |
| 1.0 | ~20% | ~35% | 36.8% |
Critical observations:
CSMA degrades with increasing 'a': The benefit of carrier sensing diminishes as propagation delay increases relative to frame transmission time.
Non-persistent degrades slower: Non-persistent maintains higher efficiency at larger 'a' values because it avoids synchronized collisions.
Crossover with ALOHA: Around a ≈ 0.5-1.0, CSMA's advantage over slotted ALOHA becomes marginal. For a >> 1, CSMA may even perform WORSE than slotted ALOHA!
Satellite networks (a >> 1): CSMA is impractical; the propagation delay is so long that carrier sensing provides almost no benefit.
Calculating 'a' for real networks:
Example 1: 10 Mbps Ethernet, 2.5 km, 1500-byte frames
Example 2: 1 Gbps Ethernet, 2.5 km, 1500-byte frames
Example 3: 1 Gbps Ethernet, 100 m (office), 1500-byte frames
Example 4: Satellite, 72,000 km round-trip, 1500-byte frames, 10 Mbps
To keep 'a' small: (1) Limit network diameter (use switches to create small collision domains), (2) Use larger frames (jumbo frames improve efficiency), (3) Don't push data rates beyond where 'a' stays reasonable for your topology.
Carrier sensing fundamentally improves upon ALOHA by reducing the vulnerable period. Let's quantify this improvement.
Vulnerable period comparison:
| Protocol | Vulnerable Period | Collision Condition |
|---|---|---|
| Pure ALOHA | 2T | Any transmission starting within ±T of ours |
| Slotted ALOHA | T | Any transmission in the same slot |
| CSMA | τ = aT | Any transmission starting within propagation delay |
The reduction factor:
CSMA reduces the vulnerable period from T (slotted ALOHA) to aT (CSMA):
$$\text{Reduction Factor} = \frac{T}{aT} = \frac{1}{a}$$
For a = 0.01: Vulnerable period is reduced by factor of 100!
Throughput improvement ratio:
At optimal operating points, the improvement of CSMA over ALOHA:
| Comparison | Improvement | Conditions |
|---|---|---|
| 1-persistent vs Pure ALOHA | ~3x | a = 0.01 |
| 1-persistent vs Slotted ALOHA | ~1.5x | a = 0.01 |
| Non-persistent vs Pure ALOHA | ~5x | a = 0.01 |
| Non-persistent vs Slotted ALOHA | ~2.5x | a = 0.01 |
The intuition:
CSMA's improvement comes from carrier sensing's ability to:
| Metric | Slotted ALOHA | 1-Persistent | Non-Persistent |
|---|---|---|---|
| Throughput | 36.8% | 53.1% | 47.6% |
| Collisions per success | 1.72 | 0.88 | 1.10 |
| Channel busy time | 100% | 100% | 85% |
| Channel idle time | 0% | 0% | 15% |
| Effective utilization | 36.8% | 53.1% | 47.6% |
Carrier sensing provides substantial efficiency improvements, especially when 'a' is small. The simple act of 'listening before talking' dramatically reduces wasted channel capacity, enabling practical networking at efficiency levels much higher than random access.
The theoretical analysis assumes ideal conditions. Real networks face additional factors that affect practical efficiency.
Practical efficiency examples:
Traditional Ethernet (shared 10 Mbps):
Switched Gigabit Ethernet (full-duplex):
WiFi (802.11n/ac):
Based on our comprehensive analysis, here are guidelines for selecting among CSMA variants and understanding when carrier sensing is appropriate.
| Condition | Recommended Protocol | Rationale |
|---|---|---|
| a < 0.05, low-moderate load | 1-Persistent + CD | Simple, low latency, CD handles collisions |
| a < 0.05, high/variable load | Non-Persistent or Adaptive | Better stability under congestion |
| a ≈ 0.1-0.5, any load | Non-Persistent preferred | More tolerant of larger 'a' |
| a > 1.0 | Consider TDMA/reservation | CSMA provides minimal benefit |
| Wireless (hidden terminals) | CSMA/CA with RTS/CTS | Virtual sensing addresses hidden nodes |
| Low latency critical | 1-Persistent or p-persistent (p high) | Immediate transmission when possible |
| Throughput critical | Non-Persistent | Better sustained throughput under load |
Decision flowchart for protocol selection:
In modern wired networks, switches have made CSMA/CD largely obsolete—each port is its own collision domain with one device. However, CSMA/CA remains critical for WiFi, and understanding CSMA efficiency helps evaluate wireless performance and design WiFi deployments.
This page provided a comprehensive efficiency analysis of CSMA protocols, comparing throughput formulas, examining the role of the 'a' parameter, and establishing protocol selection guidelines.
| Protocol | Best Case | Weakness | Used In |
|---|---|---|---|
| 1-Persistent | Low load, minimal latency | Collision cascade at high load | Classic Ethernet |
| Non-Persistent | High load stability | Wasted idle time at low load | Some wireless variants |
| p-Persistent | Theoretical optimality | Requires tuning p | Analysis/comparison |
| CSMA/CD | Wired, collision detection | Minimum frame size constraint | Legacy Ethernet |
| CSMA/CA | Wireless environments | ACK overhead, hidden terminals | WiFi (802.11) |
Congratulations! You've completed the CSMA Protocols module. You now understand carrier sensing, all major persistence strategies (1-persistent, non-persistent, p-persistent), and comprehensive efficiency analysis. This knowledge forms the foundation for understanding Ethernet, WiFi, and countless networking systems. The next module explores CSMA/CD—adding collision detection to create the protocol that powered the first decades of local area networking.