課程名稱︰系統效能評估
課程性質︰選修
課程教師︰周承復
開課學院：電資學院
開課系所︰資工所、網媒所
考試日期（年月日）︰
考試時限（分鐘）：
試題 :
Performance Evaluation 2013
Final Exam.
1. (20%) Consider a non-preemptive system and two customer class A and B with
respective arrival and service rate λa, μa and λb, μb; if μa > μb,
λa Ta + λb Tb
show that the average delay per customer T = ──────── is smaller
λa + λb
when the priority of class A > the priority of class B than the priority of
class B > the priority of class A.
2. (25%) Consider the M/G/1 system with the difference that each busy period
is followed by a single vacation interval. Once this vacation is over, an
arriving customer to an empty system starts service immediately. Assume that
vacation intervals are independent, identically distributed, and independent
of the customer inter-arrival and service times. Prove that the average
＿＿ ＿＿
λx^2 V^2
waiting time in queue is W = ─────+ ───, where I is the average
2(1-ρ) 2I
length of an idle period, and show how to calculate I.
3. (25%) MVA (do 2 iterations)
■ Consider a timesharing system
■ Each user request makes ten I/0 requests to disk A, and five I/0 requests
to disk B.
■ The service times per visit to disk A and disk B are 300 and 200
milliseconds, respectively.
■ Each request takes two seconds of CPU time and the user think time is
four seconds.
╭─○─╮ ＿ ＿＿
╭─┤ ︰ ├──╮ ╲╱User╲
│ ╰─○─╯ │ ╭→ │ Disk ├─╮
│ ＿ ＿ │ │ ╱╲ ╱ │
│ ╲╱ ╲ │ │ ￣ ￣￣ │
╰┬→ │CPU ├─┴─┤ ＿ ＿＿ │
│ ╱╲ ╱ │ ╲╱Sys ╲ │
│ ￣ ￣ ╰→ │ Disk ├─┤
│ ╱╲ ╱ │
│ ￣ ￣￣ │
╰──────────────────╯
S_A = 0.3, V_A = 10 => D_A = 3
S_B = 0.2, V_B = 5 => D_B = 1
D_CPU = 2, V_CPU = V_A + V_B + 1 = 16 => S_CPU = 0.125
Z = 4, and N = 20
Initialization:
◆ Number of users: N = 0
◆ Device queue lengths: Q_CPU = 0, Q_A = 0, Q_B = 0
Iteration 1:
◆ Number of users: N = 1
◆ Device response times:
R_CPU = S_CPU * (1 + Q_CPU) = 0.125 * (1 + 0) = 0.125
R_A = S_A * (1 + Q_A) = 0.3 * (1 + 0) = 0.3
R_B = S_B * (1 + Q_B) = 0.2 * (1 + 0) = 0.2
◆ System Response Time:
R = R_CPU * V_CPU + R_A * V_A + R_B * V_B
= 0.125 * 16 + 0.3 * 10 + 0.2 * 5 = 6
4. (10%) Please state 3 major contributions of "Hibernator: Helping Disk Arrays
Sleep through the Winter".
5. (10%) Please explain (a) the non-prioritized scheme (NPS) and (b) the guard
channel scheme in the paper of Queueing Priority Channel Assignment
Strategies for PCS Hand-Off and Initial Access.
6. (10%) In p2p streaming model, please explain the relationship between p(i)
and p(i+1).
7. (10%) Please draw the 2-dimension Markov Chain for modeling the throughput
of 802.11.