## CS 356 (Lam), Spring 2016

## Homework 2 (due at beginning of class on Feb. 10, 2016, Wed.)

PROBLEM 1 (20 points total)
Consider 6 jobs that have gone through a system during the
time interval [0, 15], where time is in seconds, as follows:
Job Arrival Time Departure Time
1 0.5 4.5
2 1.5 3.0
3 6.0 11.0
4 7.0 14.0
5 8.5 10.0
6 12.0 13.0
For the time duration [0, 15]:
(a) calculate throughput rate;
(b) plot number of jobs in system as a function of time from 0 to 15 and
calculate the average number over the duration [0, 15];
(c) calculate the average delay of the 6 jobs.
Verify that Little's Law is satisfied by the results in (a), (b) and (c).

**Note**: For Problems 2 and 3 below, assume that packet lengths have an
Exponential distribution so that average delay formulas for the M/M/1
special case are applicable.
PROBLEM 2 (20 points total)
Consider two single-server systems. System A has an arrival rate of
60 packets/second and system B has an arrival rate of 80 packets/second.
Each server has a transmission rate of 100 kilobits/second, and an
average packet length of 1000 bits.
(a) Calculate the average delay (waiting plus service) for packets
of system A.
(b) Repeat the calculation in part (a) for system B.
(c) What is the average number of packets (queueing and being served)
in both systems A and B.
(d) Apply Little's Law to calculate the average delay over all
packets served by both systems A and B. (You are required to
apply Little's Law, instead of using some other approach.
This requires some thinking.)
HINT: Think of a boundary that surrounds both system A and
system B. You make observations about all arrivals and
all departures in and out of this boundary.
PROBLEM 3 (10 points)
Suppose the two packet sources of systems A and B are combined
and served by a single queue and a single server. What is the
transmission rate of this server that will provide an average delay
equal to that in part (d) of Problem 2 ?