GATE CS 2009 Q57 — Transport Layer: Flow Control, Congestion Control, UDP, TCP, Sockets

To find the minimum number of bits ($I$) required to represent the sequence numbers distinctly, we first determine the maximum number of frames that can be present in transit (within the link) at any given instant.

1. Calculate Transmission Delay ($T_t$)

The transmission delay is the time taken to push all the bits of a frame onto the link:

2. Calculate the Number of Frames in Transit

The propagation delay ($T_p$) is given as $25 \text{ ms}$.

The maximum number of frames that can be "in transit" (one-way on the link) at any time is determined by the ratio of propagation delay to transmission delay:

Alternative approach using Bandwidth-Delay Product (BDP):

3. Determine the Number of Bits ($I$)

To uniquely identify each of the $25$ frames simultaneously present in transit, we need at least $25$ distinct sequence numbers.

The number of bits $I$ required to represent at least $25$ distinct values must satisfy:

Taking the ceiling logarithm:

Thus, the minimum number of bits required is $5$.