Chapter 6, Queueing Models of Computer Systems Video Solutions, Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Problem 1

Measurements of an interactive computer system at Piper's Pickles show that the average response time is 1.5 seconds, the number of active users is 100 , the CPU utilization is $75 \%$, and the average CPU time used per interaction was 0.3 seconds. What was the average think time?

Hast Aggarwal

Numerade Educator

01:07

Problem 2

An interactive computer system at Anchor Anchovies has 70 active terminals with a mean think time of 30 seconds. The paging disk averages 5 accesses per interaction with the average access time of 0.05 seconds. The paging disk has an average utilization of 0.5 . What is the average system response time?

Hast Aggarwal

Numerade Educator

02:16

Problem 3

During a period when the performance of a computer system at Weezl Words was being measured a particular disk was busy 30 percent of the time. If each transaction required 25 accesses to the disk, on the average, each of which takes 25 milliseconds, what was the average throughput of the system?

Sheryl Ezze

Numerade Educator

01:07

Problem 4

An interactive system at Harvey Wallbangers was measured during a period in which 10 terminals were active with an average think time of 10 seconds. If each interaction required half a second of CPU processing and the CPU utilization was 40 percent, what was the average response time?

Hast Aggarwal

Numerade Educator

02:00

Problem 5

The interactive system at Myth and Smesson was measured when 50 terminals were active, the average think time was 15 seconds, and the average response time was 1.5 seconds. What was the mean number of transactions active in the central subsystem?

Amy Jiang

Numerade Educator

Problem 6

Slobovian Scientific of Example 6.1.1 decides to upgrade their system so that the average file server service time is 0.5 seconds; all the other parameters are unchanged. Calculate $p_0, \rho, \lambda$, and $W$, assuming the system can be modeled as a machine repair queueing system.

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02:27

Problem 7

Consider Example 6.2.1. Suppose $\lambda$ and $W_s$ are as in the example but that $p=0.9999$. Calculate $\Lambda, \rho, \mathrm{L}$, and W.

Bobby Barnes

University of North Texas

Problem 8

if you have Mathematica and can use cent; 22 if you must write your own code.] The analysts at Image Power believe they can model their small batch computer system as a central server model using Algorithm 6.2.1. They have a $\mathrm{CPU}$ and two $I / O$ devices, with the total service demands of 2,1 , and 0.5 seconds, respectively. If the MPL (multiprogramming level) is 5 , find $\lambda, W, \rho_1, \rho_2$, and $\rho_3$.

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Problem 9

Consider Example 6.2.5. Suppose Rick upgrades the computer system so that the service demands are $1.5,0.5,1$, and 2 seconds, respectively, for the CPU and the three $I / O$ devices. If $\lambda=1 / 5$, find $W$ and $L$.

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Problem 10

if you have Mathematica; 25 if you must write your own code.] Suppose Peter Piper of Puerile Publications, Example 6.3.3, discovers that he must add 10 more workstations to their system (business is booming at Puerile). Use his model to do the following:
(a) Calculate $\lambda$ and $W$ for the current system with 10 more workstations, that is, $N=40$.
(b) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server that has $D_1=0.1, D_2=0.4$, and $D_3=0.2$ (all values in seconds).
(c) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server consisting of the original CPU but a single $I / O$ device, that is much faster because of caching and a faster disk drive so that $D_1=0.3$ seconds and $D_2=0.02$ seconds.

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Problem 11

Interactive Systems has a transaction processing computer system that processes two kinds of transactions. The analysts at Interactive feel they can model their system as an open multiclass model described in Section 6.3.2.1 with one CPU and two $I / O$ devices. The service demands and arrival rates are described in the table below. Calculate $W_1, W_2, L_1$, and $L_2$.
$$
\begin{array}{cccc}
c & k & D_{c k} & \lambda_c \\
\hline 1 & 1 & 0.2 & 1.0 \\
1 & 2 & 0.3 & - \\
1 & 3 & 0.4 & - \\
2 & 1 & 0.4 & 1.5 \\
2 & 2 & 0.3 & - \\
2 & 3 & 0.2 & - \\
\hline
\end{array}
$$

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Problem 12

if you have Mathematica; 25 if you must write your own code.] Consider Example 6.3.4. Suppose it is discovered that the think times have been recorded incorrectly and should be 40 seconds for the first terminal class and 60 seconds for the second. Assume the other values are correct and use Algorithm 6.3.4 to calculate the correct values for Table 6.3.3.

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06:26

Problem 13

if you have Mathematica; 20 if you must write your own code.] Calculate the approximate values for Exercise 12 using Algorithm 6.3 .5 with $\epsilon=0.001$.

Arnab Bose

Numerade Educator