GATE CS 2018 Q55 — Data Link Layer: Framing, Error Detection, MAC, Ethernet Bridging

To prevent a collision, node $Q$ must detect node $P$’s ongoing transmission during its carrier-sensing phase and defer its own transmission.

1. Timeline of Events

• At $t = 0$: Node $P$ begins transmitting its packet.
• At $t = 0$: Node $Q$ starts carrier-sensing the medium.
• Carrier-sensing duration: Node $Q$ must sense the medium for $5$ units of time, which corresponds to the interval $[0, 5]$.

2. Condition for Collision Avoidance

For $Q$ to successfully avoid a collision, the signal transmitted by $P$ at $t = 0$ must reach $Q$ before or at the end of $Q$’s carrier-sensing phase (i.e., by $t = 5$). If the signal arrives after $t = 5$, $Q$ will assume the medium is free and proceed to transmit, causing a collision.

Let $au$ be the propagation delay from $P$ to $Q$. The signal from $P$ reaches $Q$ at time:

where:

• $d$ is the distance between $P$ and $Q$ (in meters).
• $v = 10\text{ meters/unit time}$ is the propagation speed.

For successful detection during the sensing phase:

Thus, the maximum distance $d$ that allows $Q$ to successfully avoid a collision is 50 meters.