GATE CS 2014 Set 1 Q26 — Data Link Layer: Framing, Error Detection, MAC, Ethernet Bridging

To find the minimum time the monitoring station must wait before assuming the token is lost, we need to calculate the maximum possible time a token can take to complete one full rotation in the worst-case scenario.

1. Propagation Delay ($T_p$)

The propagation delay around the entire ring is given by:

2. Token Holding Time ($T_{tht}$)

Each station is allowed to hold the token for a maximum of $2\ \mu\text{s}$.

3. Worst-Case Wait Time Calculation

Depending on when the monitoring station starts its timer, there are two standard interpretations:

• Case 1: Excluding the monitoring station's own holding time
  If the timer starts immediately after the monitoring station transmits the token, the token only needs to visit the other $9$ stations before returning. $$\text{Wait Time} = T_p + (9 \times T_{tht}) = 10\ \mu\text{s} + (9 \times 2\ \mu\text{s}) = 28\ \mu\text{s}$$
• Case 2: Including the monitoring station's own holding time
  If the timer measures the entire cycle duration where all $10$ stations (including the monitoring station) can hold the token: $$\text{Wait Time} = T_p + (10 \times T_{tht}) = 10\ \mu\text{s} + (10 \times 2\ \mu\text{s}) = 30\ \mu\text{s}$$

Therefore, the minimum wait time for the monitoring station to safely assume the token is lost lies in the range of 28 to 30 $\mu\text{s}$.