GATE CS 2015 Set 2 Q34 — Transport Layer: Flow Control, Congestion Control, UDP, TCP, Sockets

To find the values of $\alpha$ and $\beta$, we analyze the standard TCP window limit and the window scale option:

1. Finding $\alpha$ (Threshold RTT):

   The standard TCP header has a 16-bit window size field, allowing a maximum window size of: $$W_{\text{max}} = 2^{16} - 1 = 65535 \text{ bytes}$$

   The bandwidth is given as $1048560 \text{ bits/sec}$. Converting this to bytes per second: $$\text{Bandwidth} = \frac{1048560}{8} = 131070 \text{ bytes/sec}$$

   The TCP window scale option is required when the Bandwidth-Delay Product (BDP) exceeds the maximum standard window size: $$\text{BDP} > W_{\text{max}} \implies \text{Bandwidth} \times \text{RTT} > 65535 \text{ bytes}$$ $$\text{RTT} > \frac{65535}{131070} = 0.5 \text{ seconds} = 500 \text{ milliseconds}$$ Thus, $\alpha = 500$ ms.

2. Finding $\beta$ (Maximum Window Size with Scale Option):

   According to RFC 1323, the TCP window scale option uses a 1-byte field to specify the scale factor (shift count). However, the maximum shift count allowed is limited to $14$ to prevent window sizes larger than $1 \text{ GB}$ (which could cause sequence number wrap-around issues).

   Therefore, the maximum possible window size is: $$\beta = 65535 \times 2^{14} \text{ bytes}$$

Thus, the correct option is C.