GATE CS 2015 Set 2 Q.44 (CS Q.34): Transport Layer: UDP, TCP Flow and Congestion Control, Sockets

Assume that the bandwidth for a TCP connection is 1048560 bits/sec. Let $\alpha$ be the value of RTT in milliseconds (rounded off to the nearest integer) after which the TCP window scale option is needed. Let $\beta$ be the maximum possible window size with window scale option. Then the values of $\alpha$ and $\beta$ are

63 milliseconds, $65535 \times 2^{14}$

63 milliseconds, $65535 \times 2^{16}$

500 milliseconds, $65535 \times 2^{14}$

500 milliseconds, $65535 \times 2^{16}$

Official answer and solution

Official answer: C
From: Official GATE 2015 answer key

Solution

Relate the maximum 16-bit TCP receive window to the Bandwidth-Delay Product (BDP) and apply RFC 1323 scale factor constraints.

Calculating $\alpha$ :
The standard TCP header includes a 16-bit window size field, allowing a maximum unscaled window of:

W_{\max} = 2^{16} - 1 = 65535\text{ bytes} = 65535 \times 8\text{ bits} = 524280\text{ bits}.

The TCP Window Scale option is required when the Bandwidth-Delay Product exceeds this unscaled limit:

\text{Bandwidth} \times \text{RTT} > 524280\text{ bits}

Given $\text{Bandwidth} = 1048560\text{ bits/sec}$ :

\text{RTT} > \frac{524280\text{ bits}}{1048560\text{ bits/sec}} = 0.5\text{ seconds} = 500\text{ milliseconds}.

Hence, $\alpha = 500\text{ ms}$ .

Calculating $\beta$ :
RFC 1323 specifies that the Window Scale option carries a 1-byte scale factor shift count up to 14 (shift values larger than 14 are prohibited because $16 + 14 = 30$ bits, fitting comfortably within the 32-bit TCP sequence space).

With a scale factor of $2^{14}$ , the maximum possible window size is:

\beta = 65535 \times 2^{14}\text{ bytes}.

Thus, $\alpha = 500\text{ milliseconds}$ and $\beta = 65535 \times 2^{14}$ (option C).

Final answer

Common trap

Assuming a 16-bit scale factor ( $2^{16}$ ) rather than the RFC 1323 limit of 14 bits ( $2^{14}$ ).

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 2
Question: 44 of 65, printed as CS Q.34
Section: Computer Science and Information Technology

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