TELCOM 2120 Network Performance
Homework 1 Due Date: 1/21/04
Problem 1
Consider a binary digital communication channel. To transmit a digital 0 the sender places
a voltage of -1 volt on the channel for the symbol duration time. To transmit a digital 1 the
sender places a voltage of +1 volt on the channel for the symbol duration time. The
reciever detects the symbol on the communication channel as signal Y = v + N where v is
1 or -1 volt depending on the symbol transmitted and N is Gaussian white noise which is
modeled at a Normally distributed random variable with mean 0 and variance 2. The
receiver decides a 0 was sent if the voltage Y is negative and a 1 otherwise.
(a) Find the probability of the receiver making an error if a digital 0 is sent.
(b) What is the probability of making the correct decision if a digital 1 is transmitted.
Problem 2
It has been shown by analysis of measurements data that file sizes in bytes on Unix based
WWW servers follow a Pareto distribution as shown below with a = 1.2
F(x) = 1 - (2730/x)a x > 2730
(a) What is the median file size in bytes
(b) What is the percentage of files that are between 6K bytes and 8K bytes.
(c) Assuming that an IP packet has a maximum 900 byte payload, determine the following.
What is the probability that a file transfer requires more than 10 packets? repeat for 100 or
more?
Problem 3
Consider phone calls in a long distance telephone network, the length of calls are exponentially
distributed with mean 4 minutes.
(a) What is the percentage of the calls are longer than 10 minutes?
(b) What percentage of the calls are between 2 and 5 minutes?
(c) What length of time are 95% of the calls less than?
