Consider a token ring network with a length of 2 km having 10 stations including a monitoring station. The propagation speed of the signal is $2 \times 10^8\text{ m/s}$ and the token transmission time is ignored. If each station is allowed to hold the token for $2\text{ }\mu\text{sec}$, the minimum time for which the monitoring station should wait (in $\mu\text{sec}$)before assuming that the token is lost is _________.

The maximum time required for the token to complete one full round trip through the ring is given by:

1. Propagation delay of the ring ($T_p$):

   $$T_p = \frac{\text{Length}}{\text{Propagation Speed}} = \frac{2000\text{ m}}{2 \times 10^8\text{ m/s}} = 10^{-5}\text{ s} = 10\ \mu\text{s}$$

2. Holding time of stations:

   • If the monitoring station is waiting for the token after releasing it, the remaining 9 stations may each hold the token for at most $2\ \mu\text{s}$:

     $$\text{Holding Time} = 9 \times 2\ \mu\text{s} = 18\ \mu\text{s}$$

     $$\text{Total Time} = 10\ \mu\text{s} + 18\ \mu\text{s} = 28\ \mu\text{s}$$

   • If all 10 stations (including the monitoring station's holding time) are considered:

     $$\text{Holding Time} = 10 \times 2\ \mu\text{s} = 20\ \mu\text{s}$$

     $$\text{Total Time} = 10\ \mu\text{s} + 20\ \mu\text{s} = 30\ \mu\text{s}$$

Both 28 and 30 $\mu\text{s}$ fall within the official allowed range of 28 to 30.