(1) There are 3 questions in this assignment. Answer all questions.
(2) The total mark for this assignment is 20 marks.
(3) In answering the questions, it is important for you to show your intermediate steps and
state what arguments you have made to obtain the results. You need to note that both
the intermediate steps and the arguments carry marks. Please note that we are not just
interested in whether you can get the nal numerical answer right, we are more inter-
ested to nd out whether you understand the subject matter. We do that by looking at
your intermediate steps and the arguments that you have made to obtain the answer.
Thus, if you can show us the perfect intermediate steps and the in-between arguments
but get the numerical values wrong for some reason, we will still award you marks for
having understood the subject matter.
If you use a computer program to perform any part of your work, you must submit the
program or you lose marks for the steps.
(4) The submission deadline is 5:00pm Friday 19 March 2021. Late submission will cap the
maximum mark that you receive. Submissions after 5:00pm on Sunday 21 March will
no longer be accepted.
(5) Your submission should consist of:
(a) A report describing the solution to the problems. This report can be typewritten or
a scan of handwritten pages. This report must be in pdf format and must be named
assignment.pdf. The submission system will only accept the name assignment.pdf.
(b) One or more computer programs if you use them to solve the problems numerically.
You should use zip to archive all the computer programs into one le with the name
supp.zip. The submission system will only accept this name. The report must refer
to the programs so that we know which program is used for which part.
(6) Submission can be made via the course website.
(7) You can submit as many times as you wish before the deadline. A later submission will
over-write the earlier one.
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
Question 2 (7 marks)
A call centre has 3 sta to deal with customer enquires. The centre has an automatic dis-
patcher to direct the calls to the sta. The dispatcher has a queue that can hold up to 2
calls but there are no queueing facilities at the sta’s terminals. The queueing network at
the support centre is depicted in Figure 1.
Figure 1: Figure for Question 2.
The centre receives on average 12.7 queries per hour. The arrivals can be modelled by
using the Poisson distribution.
Each sta 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 sta are busy, otherwise it will be
sent to an idling sta. A query will leave the system after its processing is completed. When-
ever a sta 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 sta
and 2 waiting slots. Your formulation should include the denition of the states and
the transition rates between states.
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