window size in sliding window protocol

Question

A $50 kbps$ satellite channel with $550 ms$ round trip propagation delay using sliding window protocol sends 2000 bits frame then window size, w will be:

$w>=7.75 \text{bits}$

$w>=14.5 \text{bits}$

$w>=15.5 \text{bits}$

$w>=20.5 \text{bits}$

Answer 1

For maximum utilization the sender must send frames until ACK comes back. i.e., the frames must be sent until RTT.

$\text{Round trip propagation delay} = 550 ms$

$\text{Transmission time} = \frac{2000}{ 50} = 40 ms$

So, $RTT = 550 + 40 = 590 ms$.

Now, sender must send frames until $590 ms$. Time to send 1 frame = 40 ms. So, no. of frames required $=\left\lceil \frac{590}{40} \right \rceil = 15$. So, window size must be >= 15 frames.

The question doesn't mention maximum utilization and the fractional part in options doesn't make sense.

Comments

Sir, i agree with you that gate is  a scenario based examination but what i have noticed in most of the scenario based questions that generalized/derived results are used to solve more trickier scenario based questions. I think that once the idea/concept behind those results is understood there is no need to cram it. Coming back to ques.,..pls justify why minimum window size depends on the delay of the first frame here?

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Just because ACK is sent only after the entire frame is received. Well, now in GATE question they might mention some processing time at receiver and what will everyone do?

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sir i dont understand why you add transmission time in round trip time. rtt= 2*propagation time

Answer 2

My Answer is

Given RTT Propagation delay=550ms
      i.e 2*Propagation delay=550
      L=2000 bits
      B=50kbps
      Transmission time=2000/50 =40ms
    Window size=1+2a
               =1+(550/40)
               =1+13.75=14.75
 So window size >=14.75

Answer 3

window size>=1+2a

a=propogation delay/transmission time

Round trip time is 550ms so propogation delay will be 275 ms

frame size is 2000 bits

channel bandwidth is 50kbps

so transmission time will be 2000/(50*10³)  which is 40ms

window size >=1+2*(275/40)

window size>=14.75

so ans is second one