Consider a network path P-Q-R between nodes P and R via router Q. Node P sends a file of size 106 bytes to R via this path by splitting the file into chunks of 103 bytes each. Node P sends these chunks one after the other without any wait time between the successive chunk transmissions. Assume that the size of extra headers added to these chunks is negligible, and that the chunk size is less than the MTU.
Each of the links P-Q and Q-R has a bandwidth of 106 bits/sec, and negligible propagation latency. Router Q immediately transmits every packet it receives from P to R, with negligible processing and queueing delays. Router Q can simultaneously receive on link P-Q and transmit on link Q-R.
Assume P starts transmitting the chunks at time \(t = 0\).
Which one of the following options gives the time (in seconds, rounded off to 3 decimal places) at which R receives all the chunks of the file?
GATE CS - 2024,
Answer: B
R receives the whole file at 8.008 s.
The file is \(10^{6}\) bytes = \(8 \times 10^{6}\) bits, in 1000 chunks of 8000 bits. Each chunk takes \(8000/10^{6} = 0.008\) s to transmit on either link. P sends the chunks back to back, so the last chunk leaves P at
\[ \begin{aligned} t_{P} &= \frac{8 \times 10^{6}}{10^{6}} = 8.000\ \text{s} \\ t_{R} &= 8.000 + 0.008 = 8.008\ \text{s} \end{aligned} \]
Q forwards each chunk as soon as it has received it, while receiving the next, so the two links work in a pipeline and only the last chunk's extra hop adds time. 8.000 ignores that hop, and 16.000 treats the transfer as store-and-forward of the whole file, sending it twice in sequence; 15.992 has no basis in the pipeline.
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