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COMP9334 Priority queueing for multi-phase jobs
创建日期：2024-05-22 15:13:27
标签： COMP9334
Priority queueing for multi-phase jobs

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COMP9334 Project, Term 1, 2023:

Priority queueing for multi-phase jobs
Due Date: 5:00pm Friday 21 April 2023
Version 1.00
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 1.00. Issued on 20 March 2023.
1 Introduction and learning objectives
When you were learning about operational analysis earlier in the term, we talked about jobs that
require multiple visits to the CPU (or servers) to receive their service. In this project, you will
use simulation to study how priority queueing can be used to improve the performance of a multi-
server system that works on jobs that require multiple visits to the servers.
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
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/
1
Server 1
Server n
Jobs
arriving
externally
Dispatcher
•
•
•
High priority queue ↓
Low priority queue ↑
Jobs that do not require
further processing depart
the system permanently
Jobs that do not require
further processing depart
the system permanently
Jobs requiring further
processing are sent back
to the dispatcher
Jobs requiring further
processing are sent back
to the dispatcher
Jobs requiring further
processing,
i.e., recirculated jobs
Figure 1: The system for this project.
3 Multi-server system configuration and job characteristics
for this project
The configuration of the system that you will use in this project is shown in Figure 1. The sys-
tem consists of a dispatcher and n servers where n > 1. The dispatcher has two queues: a high
priority queue and a low priority queue. You can assume that both queues have infinite queueing
slots. You have not learnt about priority queues yet but the following description will explain how
priority queues are used.
We will use the word job to refer to a request that requires service from this system. A job
may require one or more visits to the servers in order to get all its work completed. These visits of
a job take place one after another with a possible time gap between two consecutive visits. Jobs
in this system do not use parallel processing so each job does not use more than one server at a time.
We will now explain how this system handles a new job. When a new job (i.e., an external
arrival) arrives at the system, the dispatcher will send the job to any one of the idle servers if
there is at least one idle server. If all the servers are busy, the dispatcher will place this job at the
end of the high priority queue.
After a job has completed a visit to the server, the job either requires or does not require further
visits to the servers. If the job does not require further visits to the servers, then the job will depart
from the system permanently. If the job requires further visits to the servers, then the job will be
sent back to the dispatcher. We will use the term re-circulated jobs to refer to those jobs that are
sent back to the dispatcher from the servers because these jobs require further visits to the servers.
2
A job that arrives at the dispatcher can either be a new job or a re-circulated job, see Figure
1. We have already explained how the dispatcher handles new jobs. We will start to describe how
the dispatcher handles the re-circulated jobs. Since the dispatcher handles all re-circulated jobs
in the same way, the procedure therefore applies to a generic re-circulated job. We first need to
define some notation. First, when a re-circulated job arrives at the dispatcher, the job can have
completed 1, 2, 3 or more visits to the servers. We will use c to denote the number of completed
server visits when a re-circulated job arrives at the dispatcher. Second, the dispatcher uses a
threshold h, which is an integer bigger than or equal to 1, to decide on whether an arriving re-
circulated job should be considered a high or low priority job. Now we have defined the notation,
we can state the rule that the dispatcher uses: When a re-circulated job arrives at the dispatcher,
the dispatcher will classify this job as low priority if its value of c is greater than or equal to h;
otherwise the job is a high priority job. Let us consider an example.
Example 1 In this example, we assume the threshold h has a value of 2. Let us consider a job
which requires altogether 3 server visits before it will permanently depart from the system. So, this
job will re-circulate to the dispatcher two times: once with a value of c = 1 and the other with
c = 2.
• When this job re-circulates to the dispatcher the first time, its value of c will be 1. Since c ≥ h
does not hold, the dispatcher will consider this job as a high priority job on this occasion.
• The second time that this job re-circulates to the dispatcher, its value of c will be 2. Since
c ≥ h holds, the dispatcher will consider this job as a low priority job on this occasion.
We have now explained how the dispatcher classifies an arriving re-circulated job into either a
high or low priority job. We have yet to explain the detailed working of the dispatcher. We will
do that together with the description of how departures are handled. This is because the arrival
of a re-circulated job at a dispatcher follows the job’s earlier departure from a server, see Figure
1. The following steps describe how a job, which has completed a server visit, will be handled.
For ease of referral, we will use the term tagged job to refer to this job that has just completed
its server visit.
• The tagged job is considered to be a permanent departure if the number of complete visits
that it has already made is equal to the total number of visits that this job requires. If the
tagged job is not a permanent departure, then it will be re-circulated to the dispatcher. The
server that was working on the tagged job would send a message to the dispatcher to inform
it that it is available to serve another job.
• If the tagged job is a re-circulated job, then it will be sent to the dispatcher which will
classify it into either a high or low priority job using the values of c and h as described
earlier. The dispatcher will then place the tagged job at the end of the appropriate queue.
• The dispatcher is aware that a server has just completed a visit of a job and is available to
process another job. The dispatcher executes the following:
– If the high priority queue is non-empty, then the job at the head of the high priority
queue will be sent to the available server for processing.
– If the high priority queue is empty and the low priority queue is non-empty, then the job
at the head of the low priority queue will be sent to the available server for processing.
– If both high and low priority queues are empty, then the dispatcher does not need to
do anything. The server that has just been made available will go idle.
We remark that the above description means that the dispatcher uses the non-preemptive queue-
ing discipline. We will be discussing queueing disciplines in Week 7 and you can read about it on
p. 500 of [1]. However, the above description should be enough for you to get your project going
3
now even before we discuss priority queues in Week 7.
We make the following assumptions on the system in Figure 1. First, it takes the dispatcher
negligible time to process a job, 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 re-circulated job to the dispatcher and 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 re-circulated 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 threshold h can be used to
influence the system’s mean response time. So, a design problem that you will consider in this
project is to determine the value of the threshold h to minimise the mean response time of the
system. You can read in [1] how priority queueing can be used to reduce the mean response time
of computer systems.
Remark 1 This project is inspired by a recent work [2] which studies how priority queueing can be
used to improve the performance of a multi-server system that provide service to multi-phase jobs.
A multi-phase job also requires multiple visit to the servers in order to get its work done. However,
the multi-phase job in [2] will sometimes require only the service of a server but sometimes it may
require a number of servers in parallel. In order to make this project more do-able, we have
simplified many of the settings in [2]. For example, we do not use preemptive queueing, processor
sharing and parallel servers.
4 Examples
We will now present two 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 1: number of servers n = 2 and threshold h = 1
In this example, we assume the there are n = 2 servers in the system and the threshold h for
determining whether a re-circulated job is of low or high priority is 1.
In this example, each job requires one or two visits to the servers before it permanently departs
from the system. Table 1 shows, for each job, its arrival time and the service times for its visits. If
there is only one service time in the third column in Table 1, then it means the job only requires
one server visit. If there are two service times, then the job requires two server visits. For example,
Job 1 in Table 1 requires two visits where the first and second visits require, respectively, 3 and
10 time units of service times. As another example, Job 3 requires only one visit and the service
time required for that visit is 6 time units.
In this example, a job will be identified with using the tuple (i, c/r) where i is the job’s index
(see the first column of Table 1), c is the number of complete servers visits made by the job and
r is the total number of server visits required by the job. For example,
• The job (1, 0/2) refers to the job with index 1. We know from Table 1 that Job 1 requires
2 visits to the servers and this is indicated by “/2”. The notation “0/2” says that this job
4
Job index Arrival time Service times of the job’s server visits
1 0.9 3, 10
2 1.5 2, 1
3 2.2 6
4 3.3 2
5 8.0 1, 4
Table 1: Data for Example 1.
has done zero complete visits to the servers. When Job 1 re-circulates to the dispatcher for
the first time, its tuple becomes (1, 1/2).
• The job (5, 1/2) refers to Job 5 which requires altogether 2 visits to the servers. The notation
“1/2” says that this job has done one complete visit to the servers out of the two required
visits.
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 the
completion of a visit at a server. Note that we have not included the arrival of a re-circulated job
to the dispatcher as an event. This is because the arrival of a re-circulated job at the dispatcher
is immediately after the completion of a server visit. So the simulation will handle the arrival of
re-circulated job at the dispatcher and its associated server completion together.
We will illustrate how the simulation of the system works using “on-paper simulation”. The
quantities that you need to keep track of are:
• Next arrival time is the time that the next new 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 completion time is the time at which the job will complete its current server
visit. If the server is idle, the next completion time is set to ∞. Note that there is a
next completion time for each server.
– The time 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.
– A list of the service times for the future server visits of this job. Note that we enclose
the list of service times within a pair of square brackets [ ].
– The job’s tuple.
For example, the job information “3.5, 1.5, [1], (2,0/2)” indicates that current visit will be
completed at time 3.5 and this job arrived at the system at time 1.5. The “0/2” indicates
that the job has not completed any server visits so the current visit is the job’s first visit to
the server. The “[1]” indicates that the job needs one more visit in the future and this visit
will require a service time of 1. Note that if the job has no more future visits to make, then
we will use [ ] to indicate that.
• The contents of the high and low priority queues. Each job in the queue is identified by 3
fields: the job’s tuple, the job’s arrival time to the system, a list of the job’s service times
for its future server visits. For example, we write a job in a queue as
5
[(1,1/2), 0.9, [10] ]
which means the job (1,1/2) arrived at the system at time 0.9, has 1 visit completed and its
future visit to the server will require a service time of 10.
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 completion of a visit at a server, we will simply refer
to these two events as Arrival and Completion in the “Event type” column (i.e., second column)
in Table 2.
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PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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