课程名称︰系统效能评估
课程性质︰选修
课程教师︰周承复
开课学院：电资学院
开课系所︰资工所、网媒所
考试日期（年月日）︰2015.05.06
考试时限（分钟）：120
试题 :
Mid-term exam. Perf. 2015 (120 min)
1. (25%) Consider a system with two computers. Two jobs: a and b are submitted
to that system simultaneously. Job a and b are assigned directly to each
computer. What is the probability that job a is still in a system after
job b finished?
i. (5%) the service time for each job is exactly 10 mins
ii. (5%) the service time for each job are i mins with prob. 1/3,
i = 1, 2, 3
iii. (5%) the service time for job a is exponential with mean 15 mins,
the service time for job b is exponential with mean 10 mins?
iv. (10%) the service time for job a is uniformly distributed [0, 20 mins],
and the service time for job b is uniformly distributed [0, 10 mins]
2. (20%) Consider the failure of a link in a communication network. Failures
occur according to a Poisson process with rate 2.4 per day. Find
a) P[time between failures ≦ 10 days]
b) P[5 failures in 7 days]
c) Expected time between 2 consecutive failures
d) P[0 failures in next day]
3. (20%) Consider the following probability transition matrix for states 1, 2,
and 3.
P = 0.6 0.2 0.2
0.1 0.8 0.1
0.6 0.0 0.4
Prove that the chain is irreducible and determine the steady-state
probabilities.
4. (15%) f''(t) - 5f'(t) + 6f(t) = t, f(0) = 0, f'(0) = 0; find out f(t)
5. (10%) The number of transactions arriving into a database system forms a
Poisson process with rate λ. The database consists of 2 distinct files.
An arriving transaction requests 1st file with probability p, and 2nd file
with probability 1-p. With the usual independence assumption, prove that
the number of requests directed to 1st file forms a Poisson process of
rate λp.
6. (15%) Is it true that (if not, please explain the reason) :
i. N(t) ＜ n <=> S_n ＞ t
ii. N(t) ≦ n <=> S_n ≧ t
iii. N(t) ＞ n <=> S_n ＜ t
7. (10%) We wish to determine the maximum call rate can be supported by one
telephone booth. Assume that the mean duration of a telephone conversation
is 3 min, and that no more than a 3-min (average) wait for the phone may be
tolerated; what is the largest amount of incoming traffic can be supported?