Question 36

1. Ring propagation delay:

   $$\tau = \frac{\text{Ring length}}{\text{Signal speed}} = \frac{2000\text{ m}}{2 \times 10^8\text{ m/s}} = 10^{-5}\text{ s} = 10\ \mu\text{sec}$$

2. Number of stations = 10 (including 1 monitoring station).

   • Intermediate stations that can hold the token before it returns to the monitoring station = $10 - 1 = 9$ stations.
   • Each station can hold the token for at most $2\ \mu\text{sec}$.
   • Maximum holding time by the 9 stations = $9 \times 2\ \mu\text{sec} = 18\ \mu\text{sec}$.

3. Total round-trip time for the token to return to the monitoring station:

   $$\text{Total time} = \text{Propagation delay} + \text{Station holding times} = 10 + 18 = 28\ \mu\text{sec}$$

If the monitoring station's own holding time is also included, the value is $10 + 10 \times 2 = 30\ \mu\text{sec}$.

GATE official key accepts the range $[28, 30]$.