IELM3250
HW4_Solution
Not due
1. Let T be the time you spend in the system; let Si be the service time of the I
person in queue; let R be the remaining service time of the person in service;
Let S be your service time. Then,
4
E[T] =E[R+S1+S2+S3+S4+S]=E[R

IELM3250
HW6 Solution
Not due
1. This problem can be modeled by an M/M/1 queue in which 6, 8. The average
cost rate will be
$10 per hour per machine * average number of broken machines
The average number of broken machines is just L, which can be computed

IELM 3250
HW5 Solution
Not due
1. Let N(t) denote the number of customers in the station at time t. Then cfw_N(t) is a birth
and death process with
n n
n
2. With the number of customers in the shop as the state, we get a birth and death process
with 0 1

IELM 325013
HW1_Solution
Not due
1
Pcfw_A wins= P cfw_A wins on (2n+1)st toss =
n 0
(1 p)
n 0
n
2n
p p[(1 p) ] p
2
n 0
Pcfw_B wins=1-Pcfw_A wins=
1
p
1
2
2
2 p
1 (1 p)
2p p
1 p
2 p
2.
E = event at least 1 six
P(E) = number of ways to get E/number of samp

IELM 3250
HW4
Rachel Zhang
Solution to HW-8
1. In M/M/1 queue, P0 is the probability that a customer see no people in the system
when he or she arrives. This is also the probability that a customer spends 0 time,
which equals to 1 = 1 .
P (a customer spen