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COMP9334 Computing clusters
Creation date：2024-06-14 14:07:43
Belonging category：计算机computer science
Computing clusters

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COMP9334 Project

Computing clusters
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.
• 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:
1. To use discrete event simulation to simulate a computer system
2. To use simulation to solve a design problem
3. 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
Server n - 1
New jobs
submitted
by users
Dispatcher ••
•Queue 0 ↓
Queue 1 ↑
Jobs that have completed
their processing will
depart the system
permanently
Jobs that are killed are
sent back
to the dispatcher
Jobs killed by servers in
Group 0
Server n0
Server n0 - 1
•
•
•
Jobs that have completed
their processing will
depart the system
permanently
Group 0 →
Group 1 →
Figure 1: The multi-server system for this project.
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. 
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
1. 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.
Case category
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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EARN 5 FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 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MGMTMFE 405 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 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ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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