14:332:423            Telecommunication Networks

Homework #4
(to be discussed in the recitations on November 4 2005)

1. [10 points]   Consider a single queue with a constant service time of 4 seconds and a Poisson input with mean rate of 0.20 items per second.
   1. Find the mean and standard deviation of queue size.
   2. Find the mean and standard deviation of the time a customer spends in system.



2. [10 points]   Messages arrive at random to be sent across a communications link with a data rate of 9600 bps. The link is 70% utilized, and the average message length is 1000 bytes. Determine the average waiting time for constant-length messages and for exponentially distributed length messages.



3. [10 points]   A facility of m identical machines is sharing a single repairperson. The time to repair a failed machine is exponentially distributed with mean 1/l. A machine, once operational, fails after a time that is exponentially distributed with mean 1/m. All failure and repair times are independent. What is the steady-state proportion of time where there is no operational machine?

Note 2: Please bring your own printed copy of the homework assignment, so the TA doesn't need to write the problem statement on the board.