Chapter 1 Homework

Network Transmission Scenario (15 pts)

Consider a single router transmitting packets, each of size L bits, over a single link to another router. The link has a transmission rate of R Mbps.

Given:

• Packet size: L = 12,000 bits
• Link transmission rate: R = 600 Mbps

Questions:

1. Compute the one-hop transmission delay.
   • Express your answer in seconds, rounded to two decimal places after leading zeros.
     Transmission delay = L / R = 12,000 / (600 × 10^6) = 0.00002 sec
2. Determine the maximum number of packets per second that can be transmitted over this link.
   Packets/sec = R / L = (600 × 10^6) / 12,000 = 50,000 packets/sec

Multi-Link Network Delay Calculation (25 pts)

Consider a network with three links, each with the specified transmission rate and link length:

• Link 1: Transmission rate = 200 Mbps, Length = 10 Km
• Link 2: Transmission rate = 50 Mbps, Length = 3000 Km
• Link 3: Transmission rate = 150 Mbps, Length = 2 Km

The packet being transmitted is 9,000 bits in size.
Assume the speed of light is 3 × 10⁸ m/sec.

Questions:

1. Calculate the transmission and propagation delays for each of the three links.
   • Express all answers in seconds, rounded to two decimal places after leading zeros.
     Link 1 Transmission delay: 9000 / (200 × 10^6) = 0.000045 sec
Link 1 Propagation delay: 10,000 / (3 × 10^8) = 0.000033 sec
Link 2 Transmission delay: 9000 / (50 × 10^6) = 0.00018 sec
Link 2 Propagation delay: 3,000,000 / (3 × 10^8) = 0.01 sec
Link 3 Transmission delay: 9000 / (150 × 10^6) = 0.00006 sec
Link 3 Propagation delay: 2,000 / (3 × 10^8) = 0.0000067 sec

2. Compute the total end-to-end delay for transmitting the packet from the source to the destination across all three links.

End-to-End Packet Delay Analysis (10 pts)

Consider sending a packet from a source host to a destination host over a fixed network route.

Questions:

1. List and briefly describe the major components of the end-to-end delay experienced by the packet.
   The delay components are processing delays, transmission delays, propagation delays, and queuing delays.

2. Classify each delay component as either constant or variable, and explain why.
   All of these delays are fixed, except for the queuing delays, which are variable.

Circuit vs. Packet Switching Scenario(45 pts)

Consider the two scenarios below:

• A circuit-switching scenario in which N_cs users, each requiring a bandwidth of 30 Mbps, must share a link of capacity 180 Mbps.
• A packet-switching scenario with N_ps users sharing the same 180 Mbps link, where each user again requires 30 Mbps when transmitting, but only needs to transmit 25% of the time.

Round all your answers to two decimal places after leading zeros.

Questions:

1. When circuit switching is used, what is the maximum number of users that can be supported?
   Max Users: 180 Mbps / 30 Mbps = 6 Users

2. When packet switching is used, if there are 13 users, can this many users be supported under circuit-switching?
   No. 13 Users * 30 Mbps = 390 Mbps, which is greater than 180 Mbps

3. If there are 13 packet-switching users, what is the probability that a given user is transmitting, and the remaining users are not transmitting?
   p = 0.25
𝑝 ∗ (1 − 𝑝)(13 − 1) = (0.25) × (0.75)^12 ~ 0.007919 ~ 0.0079

4. What is the probability that one user (any one among the 13) is transmitting, and the remaining users are not transmitting?
   (Assume packet switching is used.)
   13 ∗ 𝑝 ∗ (1 − 𝑝)(13 − 1) = 13 * (0.25) × (0.75)^12 ~ 0.1029 ~ 0.10

5. When one user is transmitting, what fraction of the link capacity is used by this user?
   Write your answer as a decimal number.
   30 Mbps over the 180 Mbps link or 16.66% of the link’s capacity when busy

6. When packet switching is used, what is the probability that exactly 7 users (of the total 13) are transmitting and the remaining users are not transmitting?
   (13 choose 7) * 𝑝7 ∗ (1 − 𝑝)(13-7) = (13 choose 7) * 0.257 * 0.75(13-7) ~ 0.01864 ~ 0.019
   Wolfram Alpha

7. When packet switching is used, what is the probability that more than 7 users are transmitting?
   Sum{(13 choose n) * p n * (1 - p)(13 - n)}, for n = 8 to 13 => sum{(13 choose n) * 0.25n * 0.75(13-n)}, for n = 8 to 13 => 0.0056493282318115234375 ~ 0.0056
   Wolfram Alpha

TCP/IP Stack Concept Check (5 pts)

Which layer of the TCP/IP protocol stack is responsible for handling messages from various network applications?
Application layer

Submit

Post your solutions in Marmoset by the scheduled due date in the syllabus.