CS/ECE 438: Communication Networks for Computers Spring 2009
Problem Set 1 Due: start of class, Wednesday, February 4th
Network Overview, Utilities and Basic Probability
Assigned reading: Peterson and Davie: Chapter 1
All problems carry equal weight. To receive full credit, show all of your work.
1. Your company has a large data store to back up every week and you want to find the quickest possible way to
get your backup off site. You have two choices: (1) use your high-speed internet connection and transfer all of
the data over the internet or (2) copy your data to a number of flash drives and drive it over in your van. Your
internet connection is over a 44.736 Mbps T3 line, while your copy speed to your flash drive is 480 Mbps, each
flash drive holds 8 GB and you live 50 min away from your storage location. If you have 4TB of data to back
up every week, which transmission method has the higher data rate?
2. Consider two machines, A and B, connected by a 100 Mbps Ethernet with two store-and-forward relay switches
on the path between them. Suppose that no other machines are using the Ethernet, that each of the three links
introduces a propagation delay of 2s, and that a switch begins transmitting a packet immediately after
receiving the last bit of the packet.
a. What is the total transfer time for a 512B packet, as measured from transmission of the first bit at A to
receipt of the last bit at B?
b. What is the effective bandwidth for transmission of a large file from A to B, assuming that packets of
size 513B are used and that packet headers are 100B long? Assume that the nodes can send constantly,
and in particular that the switches can simultaneously receive a packet from one side while
transmitting a previous packet out the other side, and that A is not slowed down waiting for
acknowledgements.
c. What is the effective bandwidth if, after each transmission of a 512B packet, node A must wait for a
50-byte acknowledgement from B?
3. Suppose users share a 1 Gbps link. Also suppose each user requires 150 Mbps when transmitting, but each user
only transmits 5 percent of the time.
a. When circuit switching is used, how many users can be supported?
b. For the remainder of this problem, suppose packet switching is used. Suppose there are 50 users. Find
an equation for the probability that at any given time, n users are transmitting simultaneously.
c. What is the probability that the link will get overloaded?
4. For each of the following links, calculate the bandwidth x delay product using one-way delay. What percentage
of the total delay, measured from first bit sent to last bit received, is derived from the transmission delay?
a. 10 Gbps Ethernet with a delay of 5 µs.
b. 1.5-Mbps T1 link, with a one-way delay of 5 ms.
c. 10 Mbps link through a satellite in geosynchronous orbit, 35,900 km high. The only delay is speed-of-
light propagation delay.
5. Every year, an industrious graduate student heads to Las Vegas to play in a poker tournament. There are six
rounds in the tournament, and the student must win each round to advance to the next. The student wins (100*n)
chips in the nth round, if the student makes it that far, and has a 70% chance of winning each round they play.
Let m be the (statistical) mean number of chips earned by the grad student in a tournament, and let n be the
mean number of rounds played per tournament. Use cycle analysis to find:
a. What fraction of years does the student make it to the final round?
b. m
c. n
d. m/n. Note that this ratio is the student’s long-term rate of chips per round.
