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A $1$ $\text{Mbps}$ satellite link connects two ground stations. The altitude of the satellite is $36,504$ $\text{km}$ and speed of the signal is 3 × 108 m/s. What should be the packet size for a channel utilization of $25$$\text{%}$ for a satellite link using go-back-$127$ sliding window proto­col? Assume that the acknowledgment packets are negligible in size and that there are no errors during communication.

  1. $120$ $\text{bytes}$
  2. $60$ $\text{bytes}$
  3. $240$ $\text{bytes}$
  4. $90$ $\text{bytes}$
asked in Computer Networks by Boss (19.1k points)
edited by | 4.9k views
here they asked for  channel utilization, why every one is calculating for sender utilization?
Both are same !!

2 Answers

+54 votes
Best answer

Distance from Station A to Satellite $= 36504 \times 10^3$ m

Time to reach satellite $= \dfrac{36504000}{300000000} = 0.12168 s$

RTT $\text{(for a bit)} = 4\times \text{Time to reach satellite}( S1 \to Satellite,
Satellite \to S2, S2 \to Satellite, Satellite \to S1)$

Efficiency is the ratio of the amount of data sent to the maximum amount of data that
could be sent. Let $X$ be the packet size.

In Go-Back-N, within RTT we can sent $n$ packets. So, useful data is $n \times X$,
where $X$ is the packet size. Now, before we can sent another packet $\text{ACK}$
must reach back. Time for this is transmission time for a packet (other packets are
pipelined and we care only for first $\text{ACK}$ ), and $\text{RTT}$ for a bit,

$($propagation times for the packet $+$ propagation time for $\text{ACK}\ +$
transmission time for $\text{ACK}\ -$ neglected as per question$)$

$\text{Efficiency} = \dfrac{\text{Transmitted Data Size}}{Packet Size + RTT_{bit} \times \text{Bandwidth}}$

$0.25= \dfrac{127\times X}{{X} + 4\times 0.12168 \times B}$

$0.25{X} +  0.25 \times 4 \times 0.12168 \times B = 127X$

$0.25 \times X + 0.12168 \times 10^6 = 127 X$

$ 121680 = 126.75X$

$X = 9.6 \times 10^{-4} \times 10^6 = 960$

Packet Size $=960\text{ bits}=120\text{ Bytes}$

So, option (A) is answer.

answered by Active (3.8k points)
edited ago by
Dont you think, distance should be 2 * 36504 km ( A->S : S->B )
it's round trip time, so after reaching B it will come back travelling same distance which is 2*36504 km.

total distance will be 4* 36504.
why rtt = 4*(time to reach satellite)....why not 2*(time to reach satellite)
Your answer is correct. Just not well explained.Let me reexplain it.

eff=N/(1+2a) =N/(1+2*(d/v)*(B/L))

now N=127,   d=2*36504*1000 meters   v=3*10^8 meters,  B=10^6,  Put thesse values in the formula you will get the answer 120 bytes that is the correct answer.
Are u sure .When I calculte then I found 60byte not 120byte.Then above guys is right.

ans is 120 byte and given is altitude of satelite is 36504 km and two ground station A and B linked to this satelite and station A sends the packets to station 2 now total length will be 2*36504  speed not matter everything same

hope you got the point

Isn't it that RTT = transmission time + propagation delay?
So RTT= 2*transmission time ( 1 transmission by station A and other by Satellite) + 4*propagation delay ( which is time to reach satellite).
why you didn't consider transmission time of data packet from  satellite?
Why u have taken distance=2*36504 km  ?  

It should be only d=36504 km . Plz confirm.
the formula for RTT says RTT = 2 * Tp

where Tp is transmission time , now see how Tp is calculated here

in this question RTT is calculated = 4 * time to reach the satellite one time , just bcoz RTT = time to send the signal + time to get acknowledge the signal

so here from station A to satellite S then S to station B = time to send the signal
and reverse path means from B to S then  again S to A = time to get acknowledge

RTT = time to send the signal + time to get the acknowledge  =  distance from station A to satellite S then S to station B + distance from station B to satellite S then S to station A

this way RTT is calculated without any formula used here.
Its quite logical . However in the exam its bit difficult to hit at the first go .I think without figure it can not be understood . Thanks @Bikram Sir :)
here packet is transmitted two times once by sender and again by satelite .then why transmission time is not multiplied by 2 ?
In this particular question,


= time to send the signal + time to get the acknowledge  

=  distance from station A to satellite S then S to station B + distance from station B to satellite S then S to station A

= 4 * time to reach the satellite one time ,

because RTT = time to send the signal + time to get acknowledge the signal

yeah it is clear to me why we multiply 4 into time to reach the satelite one time . but i am asking about tranmission time. packet is transmitted two time first when sender A send it to satelite S and satelite again transmit it towards B .

Transmission from A + Retransmission from B ( get that acknowledgement )

= ( distance from station A to satellite S then S to station B )+  ( distance from station B to satellite S then S to station A )

Why is Time taken for transmission (Tt) from satellite to link connecting station B not considered ?

Maximum data that can be sent is taken as (PacketSize + Rtt * BandWidth). I did not understand why the packet size is being added. Plz explain.
efficeancy = $\frac{TT}{TT+ RTT}$

TT = packet size / bandwidth

now put in place of TT in above formula you will get same
+2 votes

Ans B) 60 Bytes

Satellite Bandwidth(B)=1Mbps=$10^{6}$bps

Satellite distance(d)=36504km=$36504\times 10^{3}$m

speed(v)=$3\times 10^{8}$m/s

utilization$\left ( \eta \right )$=0.25


So, we know

$\left ( \eta \right )$=$\frac{N}{1+2a}$    [a=$\frac{t_{p}}{t_{t}}$,$t_{p}=\frac{d}{v}$,$t_{t}=\frac{L}{B}$]

Now, putting all values,

L=60 Bytes

answered by Veteran (86.8k points)
somewhere I read in this cases round trip time is taken as 4Tp  [A->satelite,satelite->B,B->satelite,satelite->A]  ??
120 should be ans
same way as explained srestha ... only distance doubled... you will get 120B
but why u take A->satelite as tp?

means we can take A->B as tp.rt?

i think... in this question arjun sir also says the same thing....

yes. Tp is distance between sender and receiver. but distance must be doubled. so 160  Bytes should be right

I am sorry

but in selected ans it is not considered, rt?

@shrestha @gabbar
 what will be the final soln?
arjun sir too confirmed on " " that distance must be doubled.


there Tp is taken 4 Tp as I mentioned above. I m confused now


It should be 120 Bytes. Since the distance given is from station to satellite (A--> S) but to reach signal/data packet into B it has to further travel that is (S-->B), basically twice the distance it has to cover. So in formula instead of distance Satellite distance(d)=36504km substitute d= 2*36504, then you will get answer as 120 Bytes.


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