Computer Networks DRDO-2008

Question

Two ground stations are connected by a 10Mbps satellite link. The altitude of the satellite is 36,000km and the speed of the signal is 3x108 m/sec. What should be the packet size for channel utilization of 50% using GBN sliding window protocol. Window size is 100. Assume that the acknowledgement packets are negligible in size and there are no errors during communcations.

• A. 1.5 Kbytes
• B. 3 Kbytes
• C. 4.5 Kbytes
• D. 6 Kbytes

Comments

@srestha I am getting 2412.060 bits... Plz help me where I am going wrong.

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The data from node A will reach to satellite so that's 36000km, then from satellite will reach to node B that's 36000km, then the ack will travel from b to satellite that's 36000km and at last ack will travel from satellite to A again 36000 km

 

So 2*PT = 4*36000*10³/3*10⁸ = 0.48sec

 

Let frame size be x, so total = 100x in one transmission

Tt = 100x/10⁷ = 10-⁵x

 

Thus efficiency which is given as 0.5

 

0.5 = 10-⁵x/(0.48+10-⁵x)

0.24 + 10-⁵x/2 = 10-⁵x

10-⁵x = 0.48

x = 0.48/10-⁵

x = 48 * 10³

So x = 48kbites = 6kbytes

Answer 1

Here the altitude of the satellite is 36,000km, i.e. $d=36000 \times 1000$ m

speed of the signal  $(v) = 3\times 10^8 m/s$

Propagation delay $T_p =\frac{2 \times 36000 \times 1000 }{3 \times 10^8} =0.24 s.$

(Packet must propagate to the satellite and then back)

Let packet size = L

bandwidth of channel B= 10Mbps

then transmission time $T_t =L/(10\times 10^6)$

$\text{Efficiency} = \frac{\text{Data transmitted}}{\text{Maximum data that could be transmitted}}$

In Go-Back-N, before first ACK comes, $N$ packets can be sent. ACK comes back after $T_t + T_p + T_p +T_{ack}$. $T_{ack} = 0$ as per question. So, we consider this time and during $T_t$ a packet of size $L$ can be sent. So,

$\text{Efficiency} = \frac{N \times L} { L + 2T_p \times B}$

$0.5 = \frac{100L}{L + 2\times 0.24 \times 10 \times 10^6}$

$0.5L + 2400000 = 100L$

$L = 2400000/99.5 = 24120.6 \text{ bits} \approx 3 \text{ Kbytes}$

Comments

Very nicely explained. Thanks for the answer. :)

I got confused on one point though.

Generally, distance between two end points are given in these type of questions. In this question however, a satellite is mentioned as an intermediate between the two hosts, i.e. signal is reaching the satellite first (by travelling 36,000 kms) and being redirected to the ground station. Wouldn't this increase the total distance covered by the signal? As the satellite is 36000 kms away from both the stations, the distance should be 72000 kms. Is this assumption incorrect?

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yes, distance must be 72,000

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why the distance is doubled

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Sir, why don't we consider the Transmission time for transmission of a packet from Satellite to the link connecting station B ?

I was thinking this.

Time taken to send a packet from Station A to Satellite  = Tt + Tp
ACK from Satellite to Station A = Tt(ack) + Tp

Time taken to send a packet from Satellite to Station B = Tt + Tp
ACK from Station B to Satellite = Tt(ack) + Tp

Considering that Tt(ack) is nearly 0, then total cycle time  = 2Tt + 4Tp

Is this logic anyway right ? If so, then

Efficiency = Tt/(2Tt+4Tp)  

Please enlighten me on this.

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Plz tell me why we didn't add the "Transmission Time of satellite"

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Becuase generally the TT_ack is very less and it is mentioned in question that the Acknowledgement packets are Negligible in size.

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@srestha 
While finding the Propogation delay we multiplied it by 2 as in RTT it will be twice, But why we multiplied it by 2 again in effeciency, we already multiplied there na?

Please explain i am really confused. 

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@MiNiPanda

 

https://gateoverflow.in/32123/computer-networks-drdo-2008?show=155276#c155276

 

Comment on this.

I think the same

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Even if u multiply by 2 in Tt , you will get nearly the same answer just little difference in decimals.

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I think transmission time is time initially taken by the packet to get on the transmission link. And as soon as the bits of first packet reaches satellite from the source station. it's not accumulated to form a packet on the satellite, it will be trasmitted as soon as it is received by the satellite.
Only in this scenerio, we can ignore transmission time taken by the satellite to send packet to the destination station.

Correct me if i am wrong.

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@srestha mam, Why are we taking L in the denominator of efficiency.. See arjun sir's comment here https://gateoverflow.in/15759/throughput-calculation

Answer 2

=> (Efficiency) $\eta = \frac{N}{1 + \frac{4 * T_{P}}{T_{t}}}$

=> $\frac{1}{2} = \frac{100}{1 + \frac{4 * 12 * 10^{-2} * 10 * 10^{6}}{L}}$

=> L = $\frac{48 * 10^{5}}{199}$

=> L = 24120.6 bits = 3015 bytes = 3.015Kbytes ≌ 3Kbytes

Comments

then we would definitely consider TT at router, see its all acc to my perspective, just trying to convey what i understood.

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so if we had a router instead of a satellite, can we say the following???:

 useful time (u) = (2*transmission time)
total time (t)= (2*transmission time + 4*propagation time)

Efficiency = (N * u)/t, where N = 100

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useful time(u) will be only "transmission time",  not 2 * transmission time, (routers transmission time will not be taken into consideration in useful time however it is considered in total time)

coz we are calculating the efficiency of sender.