COMP SCI/SFWR ENG 4/6E03 Midterm 1
Solutions.
1. Short Answer
(a) False. A device is the bottleneck if and only if it has the highest demand.
(b) True. A continuous random variable has the memoryless property if and only if it is exponentially
distributed

COMP SCI/SFWR ENG 4/6E03 Assignment 6 Solutions
1. The steady state distribution is as follows:
n =
( )n 0
n<T
1
( 2 )nT +1 ( )n 0
nT
Solving for 0 :
1=
i
i=0
T 1
= 0
i=0
T 1
= 0
i=0
T 1
= 0
i=0
i
i
i
+
i=T
+
+
1
2
iT +1
T 1
i=1
T 1
i
2
i
/2
1 /2
For T =

1
COMP SCI/SFWR ENG 4/6E03 Assignment 6
Due Monday November 2nd
1. A system operates as follows: requests arrive according to a Poisson process with rate
1 per second. There are two processors, each with exponentially distributed processing
times with mea

COMP SCI/SFWR ENG 4/6E03 Assignment 5 Solutions
1. (a) The streams are independent so the information of the green stream has no eect on
the yellow. Therefore,
E[NY ellow ] = P (A packet is yellow) = 47.5
(b) Fit the problem to a binomial distribution:
P

1
COMP SCI/SFWR ENG 4/6E03 Assignment 5
Due Monday October 26
1. 11.5 from the text:
(a) Consider a stream of packets arriving according to a Poisson process with rate =
50 packets/sec. Suppose each packet is of type green with probability 0.05 and of
typ

COMP SCI/SFWR ENG 4/6E03 Assignment 2 Solutions
1. You rstly, must derive the CDF. Taking the anti-derivative.
1
F (x) = x2 + C
4
for 0 x 2. It is also know that F (0) = 0 which implies C = 0. Secondly you must
take the inverse of F (x).
1
F (x) = x2
4
1

COMP SCI/SFWR ENG 4/6E03 Assignment 4
Due Monday October 19 at 5:00pm
1. You wish to generate a sample from a distribution with the following density:
f (x) =
x/2
0
0x2
otherwise
How would you do this given that you can generate a sample from unif orm[0,

COMP SCI/SFWR ENG 4/6E03 Assignment 3 Solutions
All you had to do for this assignment was slightly modify the le example open.c. This is done
by modify the following lines with the correct parameters.
if (r < 0.05) if (r < 0.1)
if (r < 0.3) if (r < 0.4)

1
COMP SCI/SFWR ENG 4/6E03 Assignment 3
Due Monday October 5
Consider the following system with two devices. Jobs arrive to the rst device and the expected
amount of time between arrivals is 275ms. Once completed at the rst node, a job leaves the
system w

COMP SCI/SFWR ENG 4/6E03 Assignment 2 Solutions
1. (a)
Xi = E[Vi ]X
Xdisk = (4.5operations/trans) (2trans/s) = 9operations/s
(b)
i = Xi E[Si ]
disk = 9 0.02 = 0.18
2. Assuming are 500 jobs in circulating through the system:
E[N ] = X(E[R] + E[Z])
E[Z] = E

1
COMP SCI/SFWR ENG 4/6E03 Assignment 2
Due Monday September 28th at 5:00pm
1. Database transactions perform an average of 4.5 disk operations on a database server with
a single disk (each transaction require 4.5 visits to the disk on average). The databa

1
COMP SCI/SFWR ENG 4/6E03 Assignment 1
Due Monday September 21
1. Suppose that X has probability density function
f (x) = cx1.8 ,
1 < x < 10,
Calculate c, E[X], and P cfw_X > E[X].
2. Download requests arrive to a system of servers with rate = 10 per hou