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

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
(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
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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.
(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
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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.

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