1
COMP SCI/SFWR ENG 4E03 - Sample Questions for Test 2
1. A system has three machines operating in parallel and two repairmen. The machines fail
independently, with time to fail exponentially distributed with mean 10 hours. A repair
takes an exponentially

COMP SCI/SFWR ENG 4E03 - Sample Questions for Test 2
Solutions
4.a) Solve for such that E[RQ ] < 5. This system is an M/M/1 queue, therefore E[RQ ] =
1
1
.
1
4<5
0.25
1 < 9(0.25 )
9 < 1.25
< 1.25/9
< 0.139
4.b) No. Due to the underlying distribution

COMP SCI/SFWR ENG 4/6E03 Assignment 8 Solutions
1. You can use the values to get the expected number in the system and response time
directly.
1
2
3
+
+
1 1 1 2 1 3
= 12.667.
E[N ] =
E[R] = E[N ]/(r1 + r2 ) = 2.111s
2. See the CSIM section of content to s

COMP SCI/SFWR ENG 4/6E03 Assignment 6 Solutions
1. Firstly, get the steady state distribution. Using the typical approach we get,
n = (n + 1)
n
0 .
Therefore,
1=
i = 0
i=0
Therefore, 0 = (1
weighted sum.
)2 .
d
(i + 1) = 0
d
i
i=0
i+1 = 0
i=0
1
.
(1 )2
T

COMP SCI/SFWR ENG 4/6E03 Midterm 1
Solutions.
1. Short Answer
(a) True. The rates in a birth death process can be 0.
(b) False. The minimum of two exponential random variables is also an exponential random
variable.
(c) False. Only the external arrivals f