# 计算机系统代写 | COMP9334 Assignment (Version 1.0)

这个作业是完成计算机系统和网络相关的编程

COMP9334 Capacity Planning of Computer Systems and

Networks

Assignment (Version 1.0)

Question 1 (3 marks)

An interactive computer system consists of a dual-core CPU and a disk. We will use core-1

and core-2 to refer to the two cores of the CPU. The system was monitored for 60 minutes

and the following measurements were taken:

Number of completed jobs 1347

Number of accesses to core-1 2087

Number of accesses to core-2 2348

Number of disk accesses 2412

Busy time of core-1 2828 seconds

Busy time of core-2 1728 seconds

Disk busy time 2665 seconds

Answer the following questions.

(a) Determine the service demands of core-1, core-2 and the disk.

(b) Use bottleneck analysis to determine the asymptotic bound on the system throughput

when there are 30 interactive users and the think time per job is 15 seconds.

Note: If you use a computer program to derive your numerical answers, you must include

your computer program in your submission. Do not forget to show us your steps to obtain

your answer.

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Question 2 (7 marks)

A call centre has 3 staff to deal with customer enquires. The centre has an automatic dispatcher to direct the calls to the staff. The dispatcher has a queue that can hold up to 2

calls but there are no queueing facilities at the staff’s terminals. The queueing network at

the support centre is depicted in Figure 1

The centre receives on average 12.7 queries per hour. The arrivals can be modelled by

using the Poisson distribution.

Each staff can complete on average 4.1 queries per hour. The amount of time required by

each query is exponentially distributed.

When a query arrives at the dispatcher, it will accept the query if the dispatcher queue

is not full, otherwise the query will be rejected. If a query is accepted and the queue is not

empty, the query will be placed at the end of the queue. If a query is accepted and the queue

is empty, then the query will be placed in the queue if all staff are busy, otherwise it will be

sent to an idling staff. A query will leave the system after its processing is completed. Whenever a staff becomes idle, he/she will take the query from the front of the queue if there is one.

Answer the following questions:

(a) Formulate a continuous-time Markov chain for a system described above with 3 staff

and 2 waiting slots. Your formulation should include the definition of the states and

the transition rates between states.

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(b) Write down the balance equations for the continuous-time Markov chain that you have

formulated.

(c) Derive expressions for the steady state probabilities of the continuous-time Markov chain

that you have formulated.

(d) Determine the probability that an arriving query will be rejected.

(e) Determine the mean waiting time of an accepted query in the queue.

Note: If you use a computer program to derive your numerical answers, you must include

your computer program in your submission. Do not forget to show us your steps to obtain

your answer.

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Question 3 (10 marks)

This question is based on the server farm in Figure 2. The server farm consists of a dispatcher

and two computer systems, which are labelled as Systems 1 and 2. Modern day server farms

typically consist of systems of heterogeneous hardware specifications. This is due to incremental expansion where the computer systems are purchased at different times. In this question,

we will assume that System 1 has a lower processing rate than System 2.