COMP9334 Project, Term 1, 2024:
Computing clusters
Due Date: 5:00pm Friday 19 April 2024
Version 1.01
Updates to the project, including any corrections and clarifications, will be posted on the
course website. Make sure that you check the course website regularly for updates.
Change log
• Version 1.01 (27 March 2024). There is a mistake in the denominators of the two probability
density functions in Section 5.1.1. For g0(t), it should be t raised to the power of η0+1 where
the +1 was missing. A similar error appeared in g1(t), it should be t raised to the power of
η1+1.
• Version 1.00. Issued on 19 March 2024.
1 Introduction and learning objectives
You have learnt in Week 4A’s lecture that a high variability of inter-arrival times or service times
can cause a high response time. Measurements from real computer clusters have found that the
service times in these clusters have very high variability [1]. The reference paper [1] also has a
number of suggestions to deal with this issue. One suggestion is to separate the jobs according
to their service time requirements, and have one set of servers processing jobs with short service
times and another set of servers for jobs with long service times. This arrangement is the same
as supermarkets having express checkouts for customers buying not more than a certain number
of items and other checkouts that do not have a limit on the number of items. You had seen this
theory in action in Week 4A’s revision Problem 1. We also highly recommend you to read the
paper [1].
In this project, you will use simulation to study how to reduce the response time of a server
farm that uses different servers to process jobs with different service time requirements.
In this project, you will learn:
- To use discrete event simulation to simulate a computer system
- To use simulation to solve a design problem
- To use statistically sound methods to analyse simulation outputs
We mentioned a number of times in the lectures that simulation is not simply about writing
simulation programs. While it is important to get your simulation code correct, it is also important
that you use statistically sound methods to analyse simulation outputs. There, roughly half of
the marks of this project is allocated to the simulation program, and the other half to statistical
analysis; see Section 7.2.
1
Server 0
Group 0 →
Dispatcher
Queue 0 ↓
New jobs
submitted
by users
Jobs killed by servers in
Group 0
Queue 1 ↑
Group 1 →
•
•
•
Server n0 - 1
Server n0
•
•
•
Server n - 1
Figure 1: The multi-server system for this project.
Jobs that are killed are
sent back
to the dispatcher
Jobs that have completed
their processing will
depart the system
permanently
Jobs that have completed
their processing will
depart the system
permanently
2 Support provided and computing resources
If you have problems doing this project, you can post your question on the course forum. We
strongly encourage you to do this as asking questions and trying to answer them is a
great way to learn. Do not be afraid that your question may appear to be silly, the
other students may very well have the same question! Please note that if your forum post
shows part of your solution or code, you must mark that forum post private.
Another way to get help is to attend a consultation (see the Timetable section of the course
website for dates and times).
If you need computing resources to run your simulation program, you can do it on the VLAB
remote computing facility provided by the School. Information on VLAB is available here: https:
//taggi.cse.unsw.edu.au/Vlab/
3 Multi-server system configuration with job isolation
The configuration of the multi-server system that you will use in this project is shown in Figure - The system consists of a dispatcher and n servers where n ≥ 2. The n servers are parti
tioned into 2 disjoint groups, called Groups 0 and 1, with at least one server in each group. The
number of servers in Groups 0 and 1 are, respectively, n0 and n1 where n0,n1 ≥ 1 and n0+n1 = n.
The servers in Group 0 are used to process short jobs which require a processing time of no
more than a time limit of Tlimit. The servers in Group 1 do not impose any limit on service time.
2
The dispatcher has two queues: Queue 0 and Queue 1. The jobs in Queue i (where i = 0, 1)
are destined for servers in Group i. Both queues have infinite queueing spaces.
When a user submits a job to this multi-server system, the user needs to indicate whether the
job is intended for the servers in Group 0 or Group 1. The following general processing steps are
common to all incoming jobs:
• If a job is intended for a server in Group i (where i = 0, 1) arrives at the dispatcher, the job
will be sent to a server in Group i if one is available, otherwise the job will join Queue i.
• When a job departs from a server in Group i, the server will check whether there is a job at
the head of Queue i. If yes, the job will be admitted to the available server for processing.
Recall that the servers in Group 0 have a service time limit. The intention is that the users
make an estimate of the service time requirement of their submitted jobs. If a user thinks that
their job should be able to complete within Tlimit, then they submit it to Group 0; otherwise, they
should send it to the Group 1.
Unfortunately, the service time estimated by the users is not always correct. It is possible that
a user sends a job which cannot be completed within the time limit to Group 0. We will now
explain how the multi-server system will process such a job. Since the user has indicated that the
job is destined for Group 0, the job will be processed according to the general processing steps
explained earlier. This means the job will receive processing by a server in Group 0. After this
job has been processed for a time of Tlimit, the server says that the service time limit is up and
will kill the job. The server will send the job to the dispatcher and tell it that this is a killed job.
The dispatcher will check whether a server in Group 1 is available. If yes, the job will be send to
an available server; otherwise, it will join Queue 1 to wait for a server to become available. When
a server in Group 1 is available to work on this job, it will process the job from the beginning,
i.e., all the previous processing in a Group 0 server is lost.
If a job has completed its processing at a Group 0 server, which means its service time is less
than or equal to Tlimit, then the job leaves the multi-server system permanently. Similarly, a job
completed its processing at a Group 1 server will leave the system permanently.
We make the following assumptions on the multi-server system in Figure 1. First, it takes
the dispatcher negligible time to classify a job and to send a job to an available server. Second,
it takes a negligible time for a server to send a killed job to the dispatcher. Third, it takes a
negligible time for a server to inform the dispatcher on its availability. As a consequence of these
assumptions, it means that: (1) If a job arriving at the dispatcher is to be sent to an available
server right away, then its arrival time at the dispatcher is the same as its arrival time at the
chosen server; (2) The departure time of a job from the dispatcher is the same as its arrival time
at the chosen server; and (3) The departure time of a killed job from a server is the same as its
arrival time at the dispatcher. Ultimately, these assumptions imply that the response time of the
system depends only on the queues and the servers.
We have now completed our description of the operation of the system in Figure 1. We will
provide a number of numerical examples to further explain its operation in Section 4.
You will see from the numerical examples in Section 4 that the number of Group 0 servers n0
can be used to influence the mean response time. So, a design problem that you will consider in
this project is to determine the value of n0 to minimise the mean response time.
Remark 1 Some elements in the above description are realistic but some are not. Typically,
users are required to specify a walltime as a service time limit when they submit their jobs to a
computing cluster. If a server has already spent the specified walltime on the job, then the server
3
will kill the job. All these are realistic.
The re-circulation of a killed job is normally not done. A user will typically have to resubmit
a new job if it has been killed. If a killed job is re-circulated, then it may be given a lower priority,
rather than joining the main queue which is the case here.
Some programming technique (e.g., checkpointing) allows a killed job or crashed job to resur
rect from the last state saved rather than from the beginning. However, that may require a sizeable
memory space.
In order to make this project more do-able, we have simplified many of the settings. For
example, we do not use lower priority for the re-circulated killed jobs.
4 Examples
Wewill now present three examples to illustrate the operation of the system that you will simulate
in this project. In all these examples, we assume that the system is initially empty.
4.1 Example 0: n=3, n0 =1, n1 =2 and Tlimit = 3
In this example, we assume the there are n = 3 servers in the farm with 1 (= n0) server in Group
0 and 2 (= n1) servers in Group 1. The time limit for Group 0 processing is Tlimit = 3.
Table 1 shows the attributes of the 8 jobs that we will use in this example. Each job is given
an index (from 0 to 7). For each job, Table 1 shows its arrival time, service time and the server
group that the user has indicated. For example, Job 1 arrives at time 10, requires 4 units of time
for service and the user has indicated that this job needs to go to a Group 0 server. Since the
service time requirement for this job exceeds the time limit Tlimit of 3, this job will be killed after
3 time units of service and will be sent to dispatcher after that.
Note that, a job which a user sends to a Group 0 server will be completed if its service time
is less than or equal to the service time limit Tlimit being imposed. So, Job 6 in Table 1 will be
completed in a Group 0 server and this job will not be killed.
Job index Arrival time Service time required Server group indicated
0
2
1
2
3
4
5
6
7
10
11
12
14
15
19
20
5
4
9
2
8
5
3
1
0
0
0
1
0
0
6
Table 1: Jobs for Example 0.
1
Remark 2 We remark that the job indices are not necessary for carrying out the discrete event
simulation. We have included the job index to make it easier to refer to a job in our description
below.
The events in the system in Figure 1 are
• The arrival of a new job to the dispatcher; and,
4
• The departure of a job from a server.
We remark that for a Group 1 server, a departed job has its service completed. However, for
a Group 0 server, a departed job can be a killed job or a completed job. Note that we have not
included the arrival of a re-circulated killed job to the dispatcher as an event. This is because the
arrival of a re-circulated job at the dispatcher is at the same time as the departure of that job
from a Group 0 server. So the simulation will handle these events together: the departure of a
killed job and its handling by the dispatcher.
We will illustrate the simulation of the system in Figure 1 using “on-paper simulation”. The
quantities that you need to keep track of include:
• Next arrival time is the time that the next new job (i.e, not a killed job) will arrive
• For each server, we keep track its server status, which can be busy or idle.
• We also keep track of the following information on the job that is being processed in the
server:– Next departure time is the time at which the job will depart from the server. If the
server is idle, the next departure time is set to ∞. Note that there is a next departure
time for each server.– Thetime that this job arrived at the system. This is needed for calculating the response
time of the job when it permanently departs from the system.
• The contents of Queues 0 and 1. Each job in the queue is identified by a 2-tuple of (arrival
time, service time).
There are other additional quantities that you will need to keep track of and they will be
mentioned later on.
The “on-paper simulation” is shown in Table 2. The notes in the last column explain what
updates you need to do for each event. Recall that the two event types in this simulation are the
arrival of a new job to the dispatcher and the departure from a server, we will simply refer to
these two events as Arrival and Departure in the “Event type” column (i.e., second column) in
Table 2.
5
Master
clock
Event
type
Next
arrival
time
Server0
Group0
Server 1
Group1
Server 2
Group1
Queue0 Queue1 Notes
0–2 Idle,∞ Idle,∞ Idle,∞–– Weassumetheserversareidleandqueuesareemptyatthestart
of thesimulation. Thenextdeparturetimes forall serversare
∞.The“–”indicatesthatthequeuesareempty.
2 Arrival 10 Idle,∞ Busy,
(2,7)
Idle,∞–– ThiseventisthearrivalofJob0foraGroup1server. Sinceboth
Group1serversare idlebeforethisarrival, thejobcanbesent
toanyoneoftheidleservers.Wehavechosentosendthisjobto
Server1.Thejobrequiresaservicetimeof5, soitscompletion
timeis7.Notethattherecordofthejobintheserverisa2-tuple
consistingof(arrivaltime,scheduleddeparturetime).Lastly,we
needtoupdatethearrival timeofthenextjob,whichis10.
7 Departure 10 Idle,∞ Idle,∞ Idle,∞–– ThiseventisthedepartureofajobfromServer1. SinceQueue
1isempty,Server1becomesidle.
10 Arrival 11 Busy
(10,13,4)
Idle,∞ Idle,∞–– This event is thearrival of Job1 foraGroup0server. Since
Server0is idle, thejobcanbesenttotheidleserver. This job
requiresaservicetimeof4whichexceedstheservicetimelimit
of3forGroup0servers,sothesimulationneedstoschedulethis
jobtodepartServer0attime13becausethisisthetimethatthis
jobwillbekilledbytheserver.Weusethe3-tupleconsistingof
(arrivaltime,scheduleddeparturetime,servicetime),whichfor
thisjobis(10,13,4),toindicatethatthisjobarrivesattime10,
isscheduledtodepartattime13anditsservicetimerequirement
is4timeunits.Weneedtoincludetheservicetimeof the job
becausewewillneedit laterwhenthe jobisre-circulatedtoa
Group1server.Notethat ifyouseea3-tuplejobinaGroup0
server, itmeansthatthe jobwillbekilledandre-circulatedto
aGroup1server. Lastly,weneedtoupdatethearrival timeof
thenextjob,whichis11.
6
11 Arrival 12 Busy
(10,13,4)
Idle,∞ Idle,∞ (11,9)–This event is thearrival of Job2 foraGroup0server. Since
Server0isbusy,thisjobwilljoinQueue0.Thequeuestoresthe
2-tuple(arrival time, servicetime)whichis (11,9) for this job.
Wealsoneedtoupdatethearrival timeof thenext job,which
is12.
12 Arrival 14 Busy
(10,13,4)
Idle,∞ Idle,∞ (11,9),
(12,2)–This event is thearrival of Job3 foraGroup0server. Since
Server0isbusy,thisjobwill joinQueue0withthejobinforma
tion(12,2).Wealsoneedtoupdatethearrivaltimeofthenext
job,whichis14.
13 Departure 14 Busy
(11,16,9)
Busy
(10,17)
Idle,∞ (12,2)–Thisevent isthedepartureofakilledjobfromServer0. This
jobwillbere-circulatedtothedispatcher. SincebothGroup1
serversare idle, this jobcangotoanyoneof them. Wehave
chosentosendittoServer1. Sincethisjobrequires4timeunits
of service, it isscheduledtodepartServer1attime17.The2
tuple(10,17)indicatesthatthisjobarrivesat10andwilldepart
attime17. Sincethis isadeparturefromaGroup0server,we
willalsoneedtocheckQueue0,whichhas2jobs. Sothejobat
theheadofthequeuewilladvancetoServer0whichisbecoming
available.Thisjobrequires9unitsofservicetimewhichexceeds
theservicetimelimit. So, thejobwillbekilledattime13+3
=16timeunits.
14 Arrival 15 Busy
(11,16,9)
Busy
(10,17)
Busy
(14,22)
(12,2)–ThiseventisthearrivalofJob4foraGroup1server.Sincethere
isaGroup1serveravailable, this jobgoestoServer2directly.
This jobrequires8unitsof service, sothe job is scheduledto
departat time22.Wealsoneedtoupdatethearrival timeof
thenextjob,whichis15.
15 Arrival 19 Busy
(11,16,9)
Busy
(10,17)
Busy
(14,22)
(12,2)
(15,5)–ThiseventisthearrivalofJob5foraGroup0server. Sinceall
Group0serversarebusy, this jobjoinsQueue0.Wealsoneed
toupdatethearrival timeofthenextjob,whichis19.
7
16 Departure 19 Busy
(12,18)
Busy
(10,17)
Busy
(14,22)
(15,5) (11,9) Thisevent isthedepartureofakilledjobfromServer0. This
jobwillbere-circulatedtothedispatcher. SincebothGroup1
serversarebusy,thisjobwill joinQueue1.Thejobatthehead
ofQueue0will advance toServer0. This jobrequiresonly2
unitsof servicewhichiswithinthe limit.Weusea2-tupleto
rememberthisjobbecausethejobiswithinthetimelimitsoit
willnotbekilled.
17 Departure 19 Busy
(12,18)
Busy
(11,26)
Busy
(14,22)
(15,5)-Thisevent isthedepartureofafinishedjobatServer1. Since
thereisajobinQueue1, thejobwillmoveintoServer1.
18 Departure 19 Busy
(15,21,5)
Busy
(11,26)
Busy
(14,22)-- Thisevent is thedepartureofafinishedjobatServer0. This
jobwilldepart fromthesystempermanently.Wecantell that
becauseitisa2-tupleintheserverratherthana3-tuple. Since
thereisajobinQueue0, thejobwillmoveintoServer0.
19 Arrival 20 Busy
(15,21,5)
Busy
(11,26)
Busy
(14,22)
(19,3)-ThiseventisthearrivalofJob6foraGroup0server. Sinceall
Group0serversarebusy, this jobjoinsQueue0.Wealsoneed
toupdatethearrival timeofthenextjob,whichis20.
20 Arrival ∞ Busy
(15,21,5)
Busy
(11,26)
Busy
(14,22)
(19,3) (20,6) ThiseventisthearrivalofJob7foraGroup1server. Sinceall
Group1serversarebusy,thisjobjoinsQueue1. Sincethereare
nomorejobsarriving,weupdatethenextarrival timeto∞
21 Departure ∞ Busy
(19,24)
Busy
(11,26)
Busy
(14,22)-(20,6),
(15,5)
Thisevent isthedepartureofakilledjobfromServer0. This
jobwillbere-circulatedtothedispatcher. SincebothGroup1
serversarebusy,thisjobwill joinQueue1.Thejobatthehead
ofQueue0will advance toServer0. This jobrequiresonly3
unitsofservicewhichiswithinthelimit.Weonlyneeda2-tuple
torememberthatthis jobarrivesattime19andwilldepartat
time24.
22 Departure ∞ Busy
(19,24)
Busy
(11,26)
Busy
(20,28)-(15,5) Thisevent isthedepartureofafinishedjobatServer2. Since
thereisajobinQueue1, thejobwillmoveintoServer2.
24 Departure ∞ Idle,∞ Busy
(11,26)
Busy
(20,28)-(15,5) Thisevent isthedepartureofafinishedjobatServer0. Since
Queue0isempty,Server0isnowidle.
26 Departure ∞ Idle,∞ Busy
(15,31)
Busy
(20,28)-- ThiseventisthedepartureofafinishedjobatServer1.Thejob
attheheadofQueue1advancestoServer1.Thequeueisnow
empty.
8
28
Departure
∞
Idle, ∞
Busy
(15, 31)
Idle, ∞–
This event is the departure of a finished job at Server 2. Server
2 is now idle as Queue 1 is empty.
31
9
Departure
∞
Idle, ∞
Idle, ∞
Idle, ∞–
This event is the departure of a finished job at Server 1. Server
1 is now idle as Queue 1 is empty.
Table 2: “On paper simulation” illustrating the event updates of
the system.
The above description has not explained what happens if an arrival event and a departure
event are at the same time. We will leave it unspecified. If we ask you to simulate in trace driven
mode, we will ensure that such situation will not occur. If the inter-arrival time and service time
are generated randomly, the chance of this situation occurring is practically zero so you do not
have to worry about it.
Table 3 summarises the arrival, departure, job classification and response times of the jobs in
this example. In the table, we classify the jobs into 3 types:
• Group 0 jobs that are completed (i.e., not killed) within the time limit. We will refer to
these jobs as completed Group 0 jobs from now on. These jobs are marked as 0.
• Group 0 jobs that are recirculated. They are marked as r0.
• Jobs that are indicated for Group 1 by the users. They are marked as 1.
In Table 3, we have included the response times for completed Group 0 jobs and Group 1 jobs.
The mean response time for completed Group 0 jobs is 11
2 = 5.5 and the mean response time for
Group 1 jobs is 21
3 = 7.
Later on, you will work on a design problem to reduce a weighted sum of the mean response
times of the completed Group 0 jobs and the Group 1 jobs. Here we have purposely neglected
the re-circulated jobs because we will not attempt to reduce their response time. The reason is
that we do not want to incentivise users to give poor estimation of the service time requirement
of their jobs.
Job Arrival time Departure time Job classification
Response time
Group 0 within limit Group 1
0
2
7
1
2
3
4
5
6
7
10
11
12
14
15
19
20
17
26
18
22
31
24
28
1
r0
r0
0
1
r0
0
5
6
5
8
1
Table 3: The arrival and departure times of the jobs in Example 0.
8
10
4.2 Example1: n=4,n0=2,n1=2andTlimit=3.5
For thisexample,weassumethat thesystemhasn=4servers. BothGroups0and1have2
serverseach, i.e.,n0=n1=2.Theservicetime-limitforGroup0serverisTlimit=3.5.
Table4showstheattributesofthejobswhichwillarriveatthissystem.Table5summariesthe
resultsofthesimulation.ThemeanresponsetimeofthecompletedGroup0jobs is 23.9
4 =5.975
andthemeanresponsetimeoftheGroup1jobsis 36.8
5 =7.36.
Jobindex Arrival time Servicetimerequired Servergroupindicated
0 2.1 5.2 1
1 3.4 4.1 1
2 4.1 3.1 0
3 4.4 3.9 0
4 4.5 3.4 0
5 4.7 4.4 1
6 5.5 4.7 1
7 5.9 4.1 0
8 6.0 2.5 0
9 6.5 8.6 1
10 7.6 4.1 0
11 8.1 2.6 0
Table4: JobsforExample1.
Job Arrival time Departuretime Jobclassification Responsetime
Group0withinlimit Group1
0 2.1 7.3 1 5.2
1 3.4 7.5 1 4.1
2 4.1 7.2 0 3.1
3 4.4 16.1 r0
4 4.5 10.6 0 6.1
5 4.7 11.7 1 7.0
6 5.5 12.2 1 6.7
7 5.9 20.2 r0
8 6.0 13.1 0 7.1
9 6.5 20.3 1 13.8
10 7.6 24.3 r0
11 8.1 15.7 0 7.6
Table5:ThearrivalanddeparturetimesofthejobsinExample1.
11
4.3 Example2: n=4,n0=1,n1=3andTlimit=3.5
Thisexampleis identical toExample1exceptthatn0=1.Table6summariestheresultsofthe
simulation.ThemeanresponsetimeofthecompletedGroup0jobsis 44.9
4 =11.225andthemean
responsetimeoftheGroup1jobsis 29.8
5 =5.96. Itisnotsurprisingthatthemeanresponsetime
of thecompletedGroup0jobshasgoneupwhilethatofGroup1jobshasgonedown. This is
becauseinthisexample, therearefewerserversinGroup0.
Job Arrival time Departuretime Jobclassification Responsetime
Group0withinlimit Group1
0 2.1 7.3 1 5.2
1 3.4 7.5 1 4.1
2 4.1 7.2 0 3.1
3 4.4 14.6 r0
4 4.5 14.1 0 9.6
5 4.7 9.1 1 4.4
6 5.5 12.0 1 6.5
7 5.9 21.7 r0
8 6.0 20.1 0 14.1
9 6.5 16.1 1 9.6
10 7.6 27.7 r0
11 8.1 26.2 0 18.1
Table6:ThearrivalanddeparturetimesofthejobsinExample2.
12
5 Project description
This project consists of two main parts. The first part is to develop a simulation program for the
system in Figure 1. The system has already been described in Section 3 and illustrated in Section - In the second part, you will use the simulation program that you have developed to solve a
design problem.
5.1 Simulation program
You must write your simulation program in one (or a combination) of the following languages:
Python 3 (note: version 3 only), C, C++, or Java. All these languages are available on the CSE
system.
We will test your program on the CSE system so your submitted program must be able to
run on a CSE computer. Note that it is possible that due to version and/or operating system
differences, code that runs on your own computer may not work on the CSE system. It is your
responsibility to ensure that your code works on the CSE system.
Note that our description uses the following variable names: - A variable mode of string type. This variable is to control whether your program will run
simulation using randomly generated arrival times and service times; or in trace driven mode.
The value that the parameter mode can take is either random or trace. - A variable time_end which stops the simulation if the master clock exceeds this value. This
variable is only relevant when mode is random. This variable is a positive floating point
number.
Note that your simulation program must be a general program which allows different param
eter values to be used. When we test your program, we will vary the parameter values. You can
assume that we will only use valid inputs for testing.
For the simulation, you can always assume that the system is empty initially.
Hint: Do not write two separate programs for the random and trace modes because they share
a lot in common. A few if–else statements at the right places are what you need to have both
modes in one program.
5.1.1 The random mode
When your simulation is working in the random mode, it will generate the inter-arrival times
and the workload of a job in the following manner. - We use {a1,a2,…,ak,…,…} to denote the inter-arrival times of the jobs arriving at the
dispatcher. These inter-arrival times have the following properties:
(a) Each ak is the product of two random numbers a1k and a2k, i.e ak = a1ka2k ∀k = 1,2,…
(b) The sequence a1k is exponentially distributed with a mean arrival rate λ requests/s.
© The sequence a2k is uniformly distributed in the interval [a2l,a2u].
Note: The easiest way to generate the inter-arrival times is to multiply an exponentially
distributed random number with the given rate and a uniformly distributed random number
in the given range. It would be more difficult to use the inverse transform method in this
case, though it is doable.
13 - The workload of a job is characterised by two attributes: the server group (i.e., Group 0 or
- that the job is to be sent to, and the service time of the job.
(a) The first step to determine which server group to send the job to. This decision is made
by a parameter p0 ∈ (0,1):
• Prob[a job is indicated by the user for a Group 0 server] = p0
• Prob[a job is indicated by the user for a Group 1 server] = 1 −p0
For example, if p0 is 0.8, then there is a probability of 0.8 that a job is indicated for a
Group 0 server and a probability of 0.2 for a Group 1 server. The server group for each
job is independently generated.
(b) Once the server group for a job has been generated, the next step is to generate its
service time. The service time distribution to be used depends on the server group.
i. If a job is indicated to go to a Group 0 server, its service time has the probability
density function (PDF) g0(t):
g0(t) =
where
0
η0
γ0 tη0+1
0
γ0 = α−η0
0
for 0 ≤ t ≤ α0
for α0 < t < β0
for t ≥ β0
−β−η0
0
(1)
Note that this probability density function has 3 parameters: α0, β0 and η0. You
can assume that β0 > α0 > 0 and η0 > 1.
ii. If a job is indicated to go to a Group 1 server, its service time has PDF:
0
g1(t) =
where
η1
γ1 tη1+1
for 0 ≤ t ≤ α1
for α1 < t
γ1 = α−η1
1
(2)
Note that this probability density function has 2 parameters: α1 and η1. You can
assume that α1 > 0 and η1 > 1.
5.1.2 The trace mode
When your simulation is working in the trace mode, it will read the list of inter-arrival times,
the list of service times and server groups from two separate ASCII files. We will explain the
format of these files in Sections 6.1.3 and 6.1.4.
An important requirement for the trace mode is that your program is required to simulate
until all jobs have departed from the system. You can refer to Table 2 for an illustration.
5.2 Determining the value of n0 that minimises a weighted mean re
sponse time
After writing your simulation program, your next step is to use your simulation program to de
termine the number of Group 0 servers n0 that minimises a weighted mean response time.
For this design problem, you will assume the following parameter values:
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• Total number of servers: n = 10
• The service time limit Tlimit for Group 0 servers is 3.3.
• For inter-arrival times: λ = 3.1, a2ℓ = 0.85, a2u = 1.21
• The probability p0 that a job is indicated for a Group 0 server is 0.74.
• The service time for a job which is indicated for Group 0: α0 = 0.5, β0 = 5.7, η0 = 1.9.
• The service time for a job which is indicated for Group 1: α1 = 2.7 and η1 = 2.5.
The aim of the design problem is to minimise the weighted response time:
w0T0 +w1T1
(3)
where T0 is the mean response time of the completed Group 0 jobs and T1 is the mean response
time of Group 1 jobs. The value of the weights w0 and w1 are fixed for this design problem, and
they are given by 0.83 and 0.059 respectively. As an example, if T0 = 1.86 and T1 = 56.7, then the
weighted mean response time is 0.83 × 1.86 + 0.059 × 56.7. The rationale behind choosing these
weights is explained in Remark 3.
The aim of the design problem is to find the value of n0 to minimise this weighted response
time. Note that we assume that there is at least a server in each group, therefore 1 ≤ n0 ≤ n−1.
In solving this design problem, you need to ensure that you use statistically sound methods
to compare systems. You will need to consider simulation controls such as length of simulation,
number of replications, transient removals and so on. You will need to justify in your report on
how you determine the value of n0.
Remark 3 For the parameters above, out of all the jobs that are not re-circulated, 73.65% are
Group 0 jobs within the time limit and 26.35% are Group 1 jobs. The average service time for
Group 0 jobs within the time limit is 0.887 and that for Group 1 jobs is 4.5. The weights w0
and w1 are computed, respectively, from 0.7365
0.887 and 0.2635
4.5 . So the weights take into account the
frequency of a class of jobs. We also use the inverse service time as a weight so that we are not
giving too much advantage to Class 1 jobs as they have large service time requirement.
6 Testing your simulation program
In order for us to test the correctness of your simulation program, we will run your program using
a number of test cases. The aim of this section is to describe the expected input/output file format
and how the testing will be performed.
Each test is specified by 4 configurations files. We will index the tests from 0. If 12 tests are
used, then the indices for the tests are 0, 1, 2, …, 11. The names of the configuration files are:
• For Test 0, the configuration files are mode_0.txt, para_0.txt, interarrival_0.txt and
service_0.txt. The files are similarly named for indices 1, 2, 3, …, 9.
• For Test 10, the configuration files are mode_10.txt, para_10.txt, interarrival_10.txt
and service_10.txt. The files are similarly named if the test index is a 2-digit number.
We will refer to these files using the generic names mode
the format of the configuration files in Section 6.1
.txt, para
.txt etc. We will describe
Each test should produce 2 output files whose format will be described in Section 6.2. We will
explain how testing will be conducted in Sections 6.3 and 6.5.
15
6.1 Configurationfileformat
Note thatTest0 is the sameasExample0discussed inSection4.1. Wewill use that test to
illustratethefileformat.
6.1.1 mode.txt
Thisfileistoindicatewhetherthesimulationshouldrunintherandomortracemode.Thefile
containsonestring,whichcaneitherberandomortrace.
6.1.2 para.txt
If thesimulationmodeistrace, thenthisfilehasthreelines. Thefirst lineisthevalueofn(=
totalnumberof servers), thesecondlinehasthevalueofn0 (=numberofGroup0servers)and
thethirdlinehasthevalueofTlimit. Ifthetest isExample0inSection4.1, thenthecontentsof
thisfileare:
3
1
3
Thesevaluesareinthesamplefilepara_0.txt.
If thesimulationmode israndom, thenthefilehas four lines. Themeaningof thefirstthree
linesisthesameasabove.Thelastlinecontainsthevalueoftime_end,whichistheendtimeof
thesimulation. Thecontentsof thesamplefilepara_4.txtareshownbelowwherethe last line
indicatesthatthesimulationshouldrununtil200.
5
2
3.1
200
Youcanassumethatwewill onlygiveyouvalidvalues. Youcanexpectntobeapositive
integergreater than2,n0≥1andTlimit>0. Fortime_end, it isastrictlypositive integeror
floatingpointnumber.
6.1.3 interarrival*.txt
Thecontentsof thefileinterarrival*.txtdependonthemodeof thetest. Ifmode istrace,
thenthefileinterarrival*.txtcontainstheinterarrivaltimesofthejobswithoneinterarrival
timeoccupyingone line. Youcanassume that the listof interarrival times isalwayspositive.
ForExample0 inSection4.1, thearrival timesare [2,10,11,12,14,15,19,20]whichmeans the
inter-arrivaltimesare[2,8,1,1,2,1,4,1].Forthisexample,theinter-arrivaltimeswillbespecified
byafile(seesamplefileinterarrival0.txt)whosecontentsare:
2.0000
8.0000
1.0000
1.0000
2.0000
1.0000
4.0000
1.0000
If themode israndom, thenthefileinterarrival*.txtcontainthreenumbers inone line.
Thesethreenumberscorrespondtotheparametersλ,a2ℓanda2u.Asanexample, thecontents
ofinterarrival4.txtare:
16
0.90.911.27
For thisexample, thevaluesofλ, a2ℓ anda2uarerespectively0.9, 0.91and1.27. Youcan
assumethatall theseparametervaluesarepositive.
6.1.4 service*.txt
Fortracemode, thefileservice*.txtcontains, foreachjob, its servicetimeandtheserver
groupforwhichthe jobisdestined. Asanillustration, theservicetimesandservergroups for
Example0inSection4.1willbespecifiedbyafile(seesamplefileservice0.txt)whosecontents
are:
5.00001
4.00000
9.00000
2.00000
8.00001
5.00000
3.00000
6.00001
Notethateachrowhas2entries, andtheycorrespondtotheservicetime(firstentry)andthe
servergroup(secondentry).Forexample,thefirstjobhasaservicetimeof5andisindicatedfora
Group1server.Youwillfindaone-to-onecorrespondencebetweenthecontentofservice0.txt
andthe informationinTable1. Youcanassumethatthefirstentryisapositivefloat,andthe
secondentryineachrowiseither0or1.
Forrandommode, thefileservice*.txtcontainsthree lines. Forexample, thecontentsof
service4.txtare:
0.7
1.23.62.1
2.84.1
Thenumberinthefirstlineisp0.Thethreenumbersinthesecondlineareα0,β0andη0.Finally,
thetwonumbersinthethirdlineareα1andη1.Youcanassumeall thesevaluesarevalid.
Youcanassumethatthedataweprovidefortracemodeareconsistentinthefollowingway:
thenumberof inter-arrival timesandthenumberof linesofservicetimesareequal.
6.2 Outputfileformat
Inorder totestyoursimulationprogram,weneedtwooutputfilespertest. Onefilecontains
twomeanresponsetimes.Theotherfilecontainsthearrivaltimes,departuretimesandjobclas
sificationinformationsimilartoColumns2–4inTable3.
Forrandommode, themeanresponse time shouldbecalculatedusingthose jobs thathave
permanentlydepartedthesystembytime_end. Inotherwords, forthosejobswhicharestill in
thequeueorarebeingprocessedintheserverattime_end,youdonot includethesejobswhen
calculatingthemeanresponsetime.
Note thatyoudonothave toconsider transient removal for themeanresponsebeforeyou
writetheresulttotheoutputfile. However,youshouldconsidertransientremovalwhenyoudo
yourdesign.
17
Twomeanresponsetimesshouldbewrittentoafilewhosefilenamehastheformmrt_.txt.
ForExample0inSection4.1, theexpectedcontentsofthisfileare:
5.50007.0000
where the twonumbers correspondtothemeanresponse timesof, respectively, thecompleted
Class0andClass1jobs.
Theotherfiledep_.txtcontainsthedeparturetypeandclassificationof the jobs. ForEx
ample1inSection4.2, theexpectedcontentsofthisfileare:
4.10007.20000
2.10007.30001
3.40007.50001
4.500010.60000
4.700011.70001
5.500012.20001
6.000013.10000
8.100015.70000
4.400016.1000r0
5.900020.2000r0
6.500020.30001
7.600024.3000r0
Notethefollowingrequirementsforthefile:
- Eachlinecontains3entries.
- Foreachline,thefirstentryisthearrivaltimeofthejobtothesystem(i.e.,asanewjob),
thesecondentryis itspermanentdeparturetimefromthesystemandthethirdentryisa
classificationofthejobinthesamewayasColumn4inTable3.Thepossibleclassifications
forajobare0,r0and1.Youshouldbeabletoreconcilethecontentsoftheabovefilewith
Example1inSection4.2. - Thejobsmustbeorderedaccordingtoascendingcompletiontimes.
- Ifthesimulationisinthetracemode,weexpectthesimulationtofinishafterall jobshave
beenprocessed.Therefore,thenumberof linesindep_*.txtshouldbeequaltothenumber
of jobs. - If thesimulationis intherandommode, thefileshouldcontainall thejobsthathavebeen
completedbytime_end.
Allmeanresponse times, arrival timesandcompletiontimes inmrt_.txtanddep_.txt
shouldbeprintedasfloatingpointnumberstoexactly4decimalplaces.Notethatyoursimulation
shouldbeperformedinfullfloatingpointprecisionandyoushouldonlydotheroundingwhen
youarewritingtheoutputfiles.
6.3 Thetestingframework
Whenyou submit your project, youmust include aLinuxbash shell scriptwith the name
run_test.shsothatwecanrunyourprogramontheCSEsystem. Thisshell script isrequired
becauseyouareallowedtouseacomputerlanguageofyourchoice.
Letusfirst recall that eachtest is specifiedby four configurationfilesandshouldproduce
twooutputfiles. Forexample, testnumber0isspecifiedbytheconfigurationfilesmode_0.txt,
interarrival_0.txt,service_0.txtandpara_0.txt;andtestnumber0isexpectedtoproduce
18
the output files mrt_0.txt and dep_0.txt.
We will use the following directory structure when we do testing.
the directory containing run
config/
output/
test.sh
Wewill put all the configuration files for all the tests in the sub-directory config/. You should
write all the output files to the sub-directory output/.
To run test number 0, we use the shell command:
./run_test.sh 0
The expected behaviour is that your simulation program will read in the configuration files for
test number 0 from config/, carry out the simulation and create the output files in output/.
Similarly, to run test number 1, we use the shell command:
./run_test.sh 1
This means that the shell script run_test.sh has one input argument which is the test number
to be used.
Let us for the time being assume that you use Python (Version 3) to write your simulation
program and you call your simulation program main.py. If the file main.py is in the same directory
as run_test.sh, then run_test.sh can be the following one-line shell script:
python3 main.py $1
The shell script will pass the test number (which is in the input argument $1) to your simula
tion program main.py. This also implies that your simulation program should accept one input
argument which is the test number.
Just in case you are not familiar with shell script, we have provided two sample files: run_test.sh
and main.py to illustrate the interaction between a shell script and a Python (Version 3) file. You
need to make sure run_test.sh is executable. (You can make the shell script run_test.sh exe
cutable by using the command “chmod u+x run_test.sh”.) If you run the command ./run_test.sh 2,
it will produce a file with the name dummy_2.txt in the directory output/. You can also try using
other input arguments for the sample shell script. You can use these sample files to help you to
develop your code.
If you use C, C++ or Java, then your run_test.sh should first compile the source code and
then run the executable. You should of course pass the test number to the executable as an input.
You can put your code in the same directory that contains run_test.sh or in a subdirectory
below it. For example, you may have a subdirectory src/ for your code like the following:
the directory containing run
test.sh
config/
output/
src/
6.4 Sample files
You should download the file sample
project
files.zip from the project page on the course
website. The zip archive has the following directory structure:
19
Base directory containing cf
config/
output/
ref/
Details on the zip-archive are:
output
with
ref.py, run
test.sh and main.py
• The sub-directory config/ contains configuration files that you can use for testing.– The files mode_0.txt, mode_1.txt, …, and mode_7.txt. Note that Tests 0–3 are for
trace mode while Tests 4–6 are for random mode.– The files para_.txt, interarrival_.txt and service_.txt for * from 0 to 6, as
the input to the simulation.– Note that Tests 0–2 are the same as Examples 0–2 in Section 4.
• The sub-directory output/ is empty. Your simulation program should place the output files
in this sub-dirrectory.
• The sub-directory ref/ contains the expected simulation results.– Thefiles mrt_ref.txt and depref.txt for * from 0 to 6, as the reference files for
the output. For Tests 0–3, you should be able to reproduce the results in mrtref.txt
and dep*_ref.txt. However, since Tests 4–6 are in random mode, you will not be
able to reproduce the results in the output files. They have been provided so that you
can check the expected format of the files.
• ThePython file cf_output_with_ref.py which illustrates how we will compare your output
against the reference output. This file takes in one input argument, which is the test number.
For example, if you want to check your simulation outputs for test 0, you use:
python3 cf_output_with_ref.py 0
Note the following:– The file cf_output_with_ref.py expects the directory structure shown earlier.– For trace mode, we will check your mean response times, the departure times and
classifications. Note that we are not looking for an exact match but rather whether
your results are within a valid tolerance. The tolerance for the trace mode is 10−3
which is fairly generous for numbers with 4 decimal places.– For random mode, we will only check the mean response times. You can see from the
sample file that we check whether the mean response time is within an interval. We
obtain this interval using the following method: (i) we first simulate the system many
times; (ii) we then use the simulation results to estimate the maximum and minimum
mean response times; (iii) we use the estimated maximum and minimum values to form
an interval; (iv) in order to provide some tolerance due to randomness, we enlarge this
interval further.– Note that we use a very generous tolerance so if your mean response time does not pass
the test, then it is highly likely that your simulation program is not correct.
• The files run_test.sh and main.py as mentioned in Section 6.3.
20
6.5 Carrying out your own testing on the CSE system
It is important for you to note the assumption on directory structure mentioned in Section 6.3.
You must ensure your shell script and program files are written with this assumption in mind.
Since we will be testing your work on the CSE system, we strongly advise you to carry out the
following on the CSE system before submission.
• Create a new folder in your CSE account and cd to that folder. We will refer to this directory
as the base directory.– Copy your shell script run_test.sh and program files to the base directory– Copy the config and ref directories, as well as their contents, to the base directory– Create an empty directory output
• Make sure your shell script is executable by using the command “chmod u+x run_test.sh”
• Run your shell script for each test one by one. Make sure that each run produces the
appropriate output files for that test in the output directory.
• Copy cf_output_with_ref.py to the base directory. Run it to compare your output against
the reference output.
These steps are the same as those that we will use for testing. It is important to know that
we will create an empty output/ directory before we run your code. This means your code does
NOThave to create the output/ directory.
The submission portal will make an attempt to run test number 0 with your submitted files,
see Section 7.3.
6.6 Getting started and base code
For this project, we do not require you to write your code from scratch. You are allowed to build
your project by using: (i) the sample code from COMP9334; or (ii) the code in the public domain
as long as it meets the requirements below.
If you intend to use Python 3 to write your simulation code, the best way to get started is to
use the M/M/m simulation code provided with the solution to Week 4B’s revision problem and
modify from there. Sample code for trace driven simulation is provided with the lecture in Week
4B.
There is also a lot of discrete event simulation code in Python 3, C, C++ and Java in the
public domain. You are allowed to use the public domain code as a basis for your project work as
long as it meets the following requirements: - The code has a clearly identifiable author
- The code has a date which is before the date that this project document is released.
- You provide us with an URL of the source code.
- You clearly state the changes that you have made on the original code to adapt it to the
specifications of this project.
If you use any public domain code in your project, your project report must include the in
formation to satisfy the above four requirements.
21
If you would like to use a certain public domain source but you are not sure whether it meets
our requirements, you can consult the lecturer on the forum using a private message.
If your project work is based on the COMP9334 sample code, then your report must state
that the COMP9334 sample code has been used and provide information to satisfy Requirement
4 above.
7 Project requirements
This is an individual project. You are expected to complete this project on your own.
7.1 Submission requirements
Your submission should include the following: - A written report
(a) Only soft copy is required.
(b) It must be in Acrobat pdf format.
© It must be called ”report.pdf”.
(d) The report must include the information required in Section 6.6. - Program source code:
(a) For doing simulation
(b) The shell script run_test.sh, see Section 6.3. - Any supporting materials, e.g. logs created by your simulation, scripts that you have written
to process the data etc.
The assessment will be based on your submission and running your code on the CSE system.
It is important that you submit the right version of the code and make sure that it runs on the
CSE system.
It is important that you write a clear and to-the-point report. You need to aware that you
are writing the report to the marker (the intended audience of the report) not for yourself. Your
report will be assessed primarily based on the quality of the work that you have done. You do
not have to include any background materials in your report. You only have to talk about how
you do the work and we have provided a set of assessment criteria in Section 7.2 to help you to
write your report. In order for you to demonstrate these criteria, your report should refer to your
programs, scripts, additional materials so that we are aware of them.
7.2 Assessment criteria
We will assess the quality of your project based on the following criteria: - The correctness of your simulation code. For this, we will:
(a) Test your code using test cases
(b) Look for evidence in your report that you have verified the correctness of the inter
arrival probability distribution, the probability of sending a job to Group 0 or Group
1, and service time distribution. You can include appropriate supporting materials to
demonstrate this in your submission.
22
© Look for evidence in your report that you have verified the correctness of your simulation
code. Although we have given you test cases, we have at no point claimed that those
test cases are sufficient to verify the correctness of your simulation output.
You can meet this assessment criterion by arguing that the test cases that we have
provided are sufficient and why. Alternative. you may derive test cases to test your
code and explain the rationale of your new test cases. You can include appropriate
supporting materials to demonstrate this in your submission. - Youwill need to demonstrate that your results are reproducible. You should provide evidence
of this in your report. - For the part on determining a suitable value of n0 that minimises the weighted mean response
time, we will look for the following in your report:
(a) Evidence of using statistically sound methods to analyse simulation results
(b) Explanation on how you choose your simulation and data processing parameters, e.g
lengths of your simulation, number of replications, end of transient etc.
The above marking criteria closely follow the messages that we have been promoting in our
lectures on discrete event simulation. You need to ensure that your simulation code is correct
and at the same time you need to consider the choice of simulation parameters and use statistical
sound method to compare systems. If you want to do well for the project, you must make sure
that you cover all the above aspects. Roughly half of the project marks go to Points 1 and 2
above, and roughly half of the project marks go to Point 3 above.
7.3 How to submit
You should “zip” your report, shell script, programs and supporting materials into a file called
“project.zip”. The submission system will only accept this filename. If you need to store directo
ries when zipping, you need to use the-r switch to preserve the relative path.
You should submit your work via the course website. Your submission cannot be more than
20MBytes in size.
You can submit multiple times before the deadline. A later submission overrides the earlier
submissions, so make sure you submit the correct file. We will only mark the last submission that
you make. Do not leave until the last moment to submit, as there may be technical or communi
cation error and you will not have time to rectify.
When you submit your files, the submission portal will unzip your project.zip and run a test
script. The script will search for your run_test.sh (using the shell command find .-name test.sh)
and executes sample test 0 if a unique run_test.sh is find. If the test script says that it cannot
f
ind your run_test.sh or it finds multiple files with the name run_test.sh, then you should
resubmit and you should ensure that there is exactly one run_test.sh file in your zip archive.
You can do this test after you have got the simulation part ready and before you attempt the
design. Since later submissions will overwrite the earlier ones, you can get this test done earlier.
8 Further project conditions - The total mark for this project is 30 marks.
- The submission deadline is 5:00pm Friday 19 April 2024. Submissions made after the dead
line will incur a penalty of 5% per day. The penalty is applied to the mark that you would
have received if the submission was not late. Late submissions will only be accepted until
5:00pm Wednesday 24 April 2024, after which no submissions will be accepted.
23 - If you use a computer program to perform any part of your work, you must submit the
program or you lose marks for that component. This requirement applies to computer
programs for simulation as well as those for statistical analysis. - Additional project conditions:
• Joint work is not permitted on this project.– This is an individual project. As stated in Section 6.6, you must identify the
source of the code that you have used, whether it comes from COMP9334 or public
domain.– Do not request help from anyone other than the teaching staff of COMP9344.– Do not post your project work or code to the course forum.– project submissions are routinely examined both automatically and manually for
work written by others.
Rationale: this project is designed to develop the individual skills needed to solve
problems. Using work/code written by, or taken from, other people will stop you
learning these skills. Other CSE courses focus on skills needed for working in a team.
• The use of AI generative tools, such as ChatGPT, is not permitted on this project.
Rationale: We have given you the permission to use public domain code as a basis to
develop your project, so it is not necessary for you to use ChatGPT. Our test with
ChatGPT found that it was not able to supply us with a piece of complete running
code for simulating a M/M/1 queue.
• Sharing, publishing, or distributing your project work is not permitted.– Do not provide or show your project work to any other person, other than the
teaching staff of COMP9334. For example, do not message your work to friends.– Do not publish your project code via the Internet. For example, do not place your
project in a public GitHub repository.
Rationale: by publishing or sharing your work, you are facilitating other students using
your work. If other students find your project work and submit part or all of it as their
own work, you may become involved in an academic integrity investigation.
• Sharing, publishing, or distributing your project work after the completion of COMP9334
is not permitted.– For example, do not place your project in a public GitHub repository after this
offering of COMP9334 is over.
Rationale: COMP9334 may reuse project themes covering similar concepts and content.
If students in future terms find your project work and submit part or all of it as their
own work, you may become involved in an academic integrity investigation.
References
[1] Mor Harchol-Balter and Ziv Scully. The Most Common Queueing Theory Questions Asked
by Computer Systems Practitioners.First International Workshop on Teaching Performance
Analysis of ComputerSystems (TeaPACS 2021) In conjunction with the IFIP Performance
2021 Conference. Milan, Italy, Nov 2021. DOI 10.1145/3543146.3543148
[2] Mor Harchol-Balter. Performance Modeling and Design of Computer Systems. Cambridge
University Press (2013).
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