Consider a source computer (S) transmitting a file of size 106bits to a destination computer (D) over a network of two routers (R1and R2) and three links (L1, L2, and L3). L1connects S to R1; L2connects R1to R2; and L3connects R2to D. Let each link be of length 100 km. Assume signals travel over each link at a speed of 108meters per second. Assume that the link bandwidth on each link is 1Mbps. Let the file be broken down into 1000 packets each of size 1000 bits. Find the total sum of transmission and propagation delays in transmitting the file from S to D?a)1005 msb)1010 msc)3000 msd)3003 msCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Transmission Delay:
- The transmission delay is the time taken to push all the bits of a packet onto the link.
- Given that the link bandwidth is 1Mbps, and the packet size is 1000 bits, the transmission delay for each packet can be calculated as:
Transmission Delay = Packet Size / Link Bandwidth
= 1000 bits / 1Mbps
= 1000 bits / (1 x 10^6 bits/s)
= 1 ms

Propagation Delay:
- The propagation delay is the time taken for a bit to travel from the source to the destination.
- Given that the speed of the signal is 10^8 meters per second and the length of each link is 100 km (or 100,000 meters), the propagation delay for each link can be calculated as:
Propagation Delay = Link Length / Signal Speed
= 100,000 meters / (10^8 meters/s)
= 1 ms

Total Transmission and Propagation Delays:
- There are 1000 packets in total, so the total transmission delay would be:
Total Transmission Delay = Number of Packets x Transmission Delay
= 1000 packets x 1 ms/packet
= 1000 ms

- There are 3 links in total, so the total propagation delay would be:
Total Propagation Delay = Number of Links x Propagation Delay
= 3 links x 1 ms/link
= 3 ms

- Therefore, the total sum of transmission and propagation delays in transmitting the file from S to D would be:
Total Delay = Total Transmission Delay + Total Propagation Delay
= 1000 ms + 3 ms
= 1003 ms

Hence, the correct answer is option 'A' (1005 ms).

Answer

Data:

Number of packets = n =1000

Size of each Packet = L = 1000 bits

The link bandwidth on each link is = BW = 1Mbps =10⁶ bits/s

Each link be of length = d= 100 km

Signals travel over each link at a speed = v= 108m/s

Transmission delay = T

Propagation delay = P

Formula:

Calculation:

Propagation delay for the first packet to transmit S to R₁

So, the propagation delay for the first packet to transmit S to D

P =1 × 3 = 3ms

Transmission delay for the first packet to transmit S to R₁

So, the transmission delay for the first packet to transmit S to D

T=1 × 3 = 3ms

So, total time is taken to transmit the first packet from S to D =P +T=6ms

Using pipelining, the remaining packet follows the first packet

then remaining every packet take 1ms to transmit from S to D

So, the total time is taken to transmit all 1000 packets from S to D is

⇒ time for the first packet + time for the remaining 999 packets

⇒ 6ms + 999ms

⇒ 1005ms

So, the total time is taken to transmit all 1000 packets from S to D is 1005ms.

Answer

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