CS 330: Homework: Chapter 1 Answers

Chapter 1 Homework Answers

Problem 1 (15 pts)

Consider a single router transmitting packets, each of length L bits, over a single link with transmission rate R Mbps to another router at the other end of the link. Suppose that the packet length is L = 18000 bits, and that the link transmission rate along the link to router on the right is R = 800 Mbps. Round your answer to two decimals after leading zeros.

• Compute the one-hop transmission delay:
  L/R = 18,000/800,000,000 = 0.0000225 sec.

• What is the maximum number of packets per second that can be transmitted by this link?
  R/L = 800,000,000/18,000 = 44,444 packets per sec.

Problem 2 (25 pts)

Consider a network with three links, each with the specified transmission rate and link length. Link 1 transmission rate is 100 Mbps with length of 5 Km. Link 2 transmission rate is 10 Mbps and length 5000 Km, Link 3 transmission rate is 100 Mbps and length is 1 Km. The packet we are trying to send has a length of 6000 bits. The speed of light is 3*10⁸ m/sec. Round your answers to two decimals after leading zeros.

• Calculate the transmission and propagation delays for Link 1, 2 and 3.
  Transmission Delay: L/R
1) 6,000/100,000,000 = 0.00006 sec.
2) 0.0006 sec.
3) 0.00006 sec.

Propagation Delay: d/s
1) 5,000/3*10^8 = 0.00016 sec.
2) 0.016 sec.
3) 0.0000033 sec.


• What is the end to end delay for the packet?
  Total Delay = ~0.018


Problem 3 (10 pts)

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

• List the delay components in the end-to-end delay.
  The delay components are processing delays, transmission delays, propagation delays, and queuing delays.

• Which of these delays are constant and which are variable?
  All of these delays are fixed, except for the queuing delays, which are variable.

Problem 4 (45 pts)

Consider the two scenarios below:

A circuit-switching scenario in which N_cs users, each requiring a bandwidth of 20 Mbps, must share a link of capacity 150 Mbps. A packet-switching scenario with N_ps users sharing a 150 Mbps link, where each user again requires 20 Mbps when transmitting, but only needs to transmit 20 % of the time. Round your answer to two decimals after leading zeros.

• When circuit switching is used, what is the maximum number of users that can be supported?
  Max Users: 150 Mbps / 20 Mbps = 7 Users
• When packet switching is used, if there are 13 packet-switching users, can this many users be supported under circuit-switching?
  No. 13 Users * 20 Mbps = 260 Mbps, which is greater than 150 Mbps

• 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 = 0.2
𝑝 ∗ (1 − 𝑝)(13 − 1) = 0.0137438953472 ~ 0.014

• What is the probability that one user (any one among the 13 users) is transmitting, and the remaining users are not transmitting?
  13 ∗ 𝑝 ∗ (1 − 𝑝)(13 − 1) = 0.1786706395136 ~ 0.18

• When one user is transmitting, what fraction of the link capacity will be used by this user? Write your answer as a decimal number.
  20 Mbps over the 150 Mbps link or 13% of the link’s capacity when busy

• When packet switching is used, what is the probability that any 7 users (of the total 13 users) are transmitting and the remaining users are not transmitting?
  (13 choose 7) * 𝑝7 ∗ (1 − 𝑝)(13-7) = 0.0057579405312 ~ 0.0058

• 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 => 0.0012456206336 ~ 0.0012

Problem 5 (5 pts)

What layer in the TCP/IP stack best corresponds to saying: ‘handles messages from a variety of network applications’?
Application layer

Submit

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