GATE CS 2024 Set 2 — Question 55

In an Ethernet network using CSMA/CD, to ensure that a collision is detected by the transmitting station before it finishes transmitting the frame, the transmission time ($T_t$) must be at least twice the propagation delay ($T_p$) between the two farthest points in the segment.Given:

• Transmission speed (Bandwidth, $B$) = $10^8$ bits/sec
• Maximum segment length ($d$) = 500 meters
• Speed of propagation ($v$) = $2 \times 10^8$ meters/sec

Condition for collision detection:$$T_t \geq 2 \times T_p$$Where:

• $T_t = \frac{\text{Minimum Frame Size (L)}}{B}$
• $T_p = \frac{d}{v}$

Substituting the expressions into the condition:$$\frac{L}{B} \geq 2 \times \frac{d}{v}$$Solving for $L$:$$L \geq 2 \times \frac{d}{v} \times B$$Substituting the given values:$$L \geq 2 \times \frac{500}{2 \times 10^8} \times 10^8$$$$L \geq 2 \times \frac{500}{2}$$$$L \geq 500 \text{ bits}$$Thus, the minimum frame size required for collision detection is 500 bits.