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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
<meta charset="utf-8" />
<meta name="generator" content="Docutils 0.23: https://docutils.sourceforge.io/" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<style>body,footer,header{max-width:none!important;width:100%;padding:1px 2%;margin:0 auto;}</style><style>.step-hidden{opacity:0;}</style><title>CPU Scheduling - yoosofan</title>
<link rel="stylesheet" href="./assets/style.css" type="text/css" />
<style type="text/css">
/* Minimal style sheet for the HTML output of Docutils. */
/* */
/* :Author: Günter Milde, based on html4css1.css by David Goodger */
/* :Id: $Id: minimal.css 10018 2025-03-06 16:19:15Z milde $ */
/* :Copyright: © 2015, 2021 Günter Milde. */
/* :License: Released under the terms of the `2-Clause BSD license`_, */
/* in short: */
/* */
/* Copying and distribution of this file, with or without modification, */
/* are permitted in any medium without royalty provided the copyright */
/* notice and this notice are preserved. */
/* */
/* This file is offered as-is, without any warranty. */
/* */
/* .. _2-Clause BSD license: http://www.spdx.org/licenses/BSD-2-Clause */
/* This CSS3 stylesheet defines rules for Docutils elements without */
/* HTML equivalent. It is required to make the document semantics visible. */
/* */
/* .. _validates: http://jigsaw.w3.org/css-validator/validator$link */
/* titles */
p.topic-title,
p.admonition-title,
p.system-message-title {
font-weight: bold;
}
p.sidebar-title,
p.rubric {
font-weight: bold;
font-size: larger;
}
p.rubric {
color: maroon;
}
p.subtitle,
p.section-subtitle,
p.sidebar-subtitle {
font-weight: bold;
margin-top: -0.5em;
}
h1 + p.subtitle {
font-size: 1.6em;
}
a.toc-backref {
color: inherit;
text-decoration: none;
}
/* Warnings, Errors */
.system-messages h2,
.system-message-title,
pre.problematic,
span.problematic {
color: red;
}
/* Inline Literals */
.docutils.literal {
font-family: monospace;
white-space: pre-wrap;
}
/* do not wrap at hyphens and similar: */
.literal > span.pre { white-space: nowrap; }
/* keep line-breaks (\n) visible */
.pre-wrap { white-space: pre-wrap; }
/* Lists */
/* compact and simple lists: no margin between items */
.simple li, .simple ul, .simple ol, .simple > li p,
.compact li, .compact ul, .compact ol, .compact > li p,
dl.simple > dd, dl.compact > dd, dl.docinfo > dd {
margin-top: 0;
margin-bottom: 0;
}
/* Nested Paragraphs */
p:first-child { margin-top: 0; }
p:last-child { margin-bottom: 0; }
details > p:last-child { margin-bottom: 1em; }
/* Table of Contents */
.contents ul.auto-toc { /* section numbers present */
list-style-type: none;
}
/* Enumerated Lists */
ol.arabic { list-style: decimal }
ol.loweralpha { list-style: lower-alpha }
ol.upperalpha { list-style: upper-alpha }
ol.lowerroman { list-style: lower-roman }
ol.upperroman { list-style: upper-roman }
/* Definition Lists and Derivatives */
dt .classifier { font-style: italic }
dt .classifier:before {
font-style: normal;
margin: 0.5em;
content: ":";
}
/* Field Lists and similar */
/* bold field name, content starts on the same line */
dl.field-list,
dl.option-list,
dl.docinfo {
display: flow-root;
}
dl.field-list > dt,
dl.option-list > dt,
dl.docinfo > dt {
font-weight: bold;
clear: left;
float: left;
margin: 0;
padding: 0;
padding-right: 0.25em;
}
/* Offset for field content (corresponds to the --field-name-limit option) */
dl.field-list > dd,
dl.option-list > dd,
dl.docinfo > dd {
margin-left: 9em; /* ca. 14 chars in the test examples, fit all Docinfo fields */
}
/* start nested lists on new line */
dd > dl:first-child,
dd > ul:first-child,
dd > ol:first-child {
clear: left;
}
/* start field-body on a new line after long field names */
dl.field-list > dd > *:first-child,
dl.option-list > dd > *:first-child
{
display: inline-block;
width: 100%;
margin: 0;
}
/* Bibliographic Fields (docinfo) */
dl.docinfo pre.address {
font: inherit;
margin: 0;
}
dl.docinfo > dd.authors > p { margin: 0; }
/* Option Lists */
dl.option-list > dt { font-weight: normal; }
span.option { white-space: nowrap; }
/* Footnotes and Citations */
.footnote, .citation { margin: 1em 0; } /* default paragraph skip (Firefox) */
/* hanging indent */
.citation { padding-left: 2em; }
.footnote { padding-left: 1.7em; }
.footnote.superscript { padding-left: 1.0em; }
.citation > .label { margin-left: -2em; }
.footnote > .label { margin-left: -1.7em; }
.footnote.superscript > .label { margin-left: -1.0em; }
.footnote > .label + *,
.citation > .label + * {
display: inline-block;
margin-top: 0;
vertical-align: top;
}
.footnote > .backrefs + *,
.citation > .backrefs + * {
margin-top: 0;
}
.footnote > .label + p, .footnote > .backrefs + p,
.citation > .label + p, .citation > .backrefs + p {
display: inline;
vertical-align: inherit;
}
.backrefs { user-select: none; }
.backrefs > a { font-style: italic; }
/* superscript footnotes */
a[role="doc-noteref"].superscript,
.footnote.superscript > .label,
.footnote.superscript > .backrefs {
vertical-align: super;
font-size: smaller;
line-height: 1;
}
a[role="doc-noteref"].superscript > .fn-bracket,
.footnote.superscript > .label > .fn-bracket {
/* hide brackets in display but leave for copy/paste */
display: inline-block;
width: 0;
overflow: hidden;
}
[role="doc-noteref"].superscript + [role="doc-noteref"].superscript {
padding-left: 0.15em; /* separate consecutive footnote references */
/* TODO: unfortunately, "+" also selects with text between the references. */
}
/* Alignment */
.align-left {
text-align: left;
margin-right: auto;
}
.align-center {
text-align: center;
margin-left: auto;
margin-right: auto;
}
.align-right {
text-align: right;
margin-left: auto;
}
.align-top { vertical-align: top; }
.align-middle { vertical-align: middle; }
.align-bottom { vertical-align: bottom; }
/* reset inner alignment in figures and tables */
figure.align-left, figure.align-right,
table.align-left, table.align-center, table.align-right {
text-align: inherit;
}
/* Text Blocks */
.topic { margin: 1em 2em; }
.sidebar,
.admonition,
.system-message {
margin: 1em 2em;
border: thin solid;
padding: 0.5em 1em;
}
div.line-block { display: block; }
div.line-block div.line-block, pre { margin-left: 2em; }
/* Code line numbers: don't copy with drag-and-drop */
pre.code .ln { display: none; }
pre.code code:before {
content: attr(data-lineno);
font-size: small;
color: gray;
}
/* Tables */
table {
border-collapse: collapse;
}
td, th {
border: thin solid silver;
padding: 0 1ex;
}
.borderless td, .borderless th {
border: 0;
padding: 0;
padding-right: 0.5em /* separate table cells */
}
table > caption, figcaption {
text-align: left;
margin-top: 0.2em;
margin-bottom: 0.2em;
}
table.captionbelow {
caption-side: bottom;
}
/* MathML (see "math.css" for --math-output=HTML) */
math .boldsymbol { font-weight: bold; }
math.boxed, math .boxed {padding: 0.25em; border: thin solid; }
/* style table similar to AMS "align" or "aligned" environment: */
mtable.cases > mtr > mtd { text-align: left; }
mtable.ams-align > mtr > mtd { padding-left: 0; padding-right: 0; }
mtable.ams-align > mtr > mtd:nth-child(2n) { text-align: left; }
mtable.ams-align > mtr > mtd:nth-child(2n+1) { text-align: right; }
mtable.ams-align > mtr > mtd:nth-child(2n+3) { padding-left: 2em; }
.mathscr mi, mi.mathscr {
font-family: STIX, XITSMathJax_Script, rsfs10,
"Asana Math", Garamond, cursive;
}
/* Document Header and Footer */
header { border-bottom: 1px solid black; }
footer { border-top: 1px solid black; }
/* Images are block-level by default in Docutils */
/* New HTML5 block elements: set display for older browsers */
img, svg, header, footer, main, aside, nav, section, figure, video, details {
display: block;
}
svg { width: auto; height: auto; } /* enable scaling of SVG images */
/* inline images */
p img, p svg, p video,
h1 img, h2 img, h3 img, h4 img, h5 img, h6 img,
h1 svg, h2 svg, h3 svg, h4 svg, h5 svg, h6 svg {
display: inline;
}
</style>
<style type="text/css">
/* CSS31_ style sheet for the output of Docutils HTML writers. */
/* Rules for easy reading and pre-defined style variants. */
/* */
/* :Author: Günter Milde, based on html4css1.css by David Goodger */
/* :Id: $Id: plain.css 10079 2025-04-10 12:01:48Z milde $ */
/* :Copyright: © 2015 Günter Milde. */
/* :License: Released under the terms of the `2-Clause BSD license`_, */
/* in short: */
/* */
/* Copying and distribution of this file, with or without modification, */
/* are permitted in any medium without royalty provided the copyright */
/* notice and this notice are preserved. */
/* */
/* This file is offered as-is, without any warranty. */
/* */
/* .. _2-Clause BSD license: http://www.spdx.org/licenses/BSD-2-Clause */
/* .. _CSS3: https://www.w3.org/Style/CSS/ */
/* Document Structure */
/* ****************** */
/* "page layout" */
body {
margin: 0;
background-color: #dbdbdb;
--field-indent: 9em; /* default indent of fields in field lists */
}
main, footer, header {
line-height:1.6;
/* avoid long lines --> better reading */
/* optimum is 45…75 characters/line <http://webtypography.net/2.1.2> */
/* OTOH: lines should not be too short because of missing hyphenation, */
max-width: 50rem;
padding: 1px 2%; /* 1px on top avoids grey bar above title (mozilla) */
margin: auto;
}
main {
counter-reset: table figure;
background-color: white;
}
footer, header {
font-size: smaller;
padding: 0.5em 2%;
border: none;
}
/* Table of Contents */
ul.auto-toc > li > p {
padding-left: 1em;
text-indent: -1em;
}
nav.contents ul {
padding-left: 1em;
}
main > nav.contents ul ul ul ul:not(.auto-toc) {
list-style-type: '\2B29\ ';
}
main > nav.contents ul ul ul ul ul:not(.auto-toc) {
list-style-type: '\2B1D\ ';
}
/* Transitions */
hr.docutils {
width: 80%;
margin-top: 1em;
margin-bottom: 1em;
clear: both;
}
/* Paragraphs */
/* vertical space (parskip) */
p, ol, ul, dl, li,
.footnote, .citation,
div > math,
table {
margin-top: 0.5em;
margin-bottom: 0.5em;
}
h1, h2, h3, h4, h5, h6,
dd, details > p:last-child {
margin-bottom: 0.5em;
}
/* Lists */
/* ===== */
/* Definition Lists */
/* Indent lists nested in definition lists */
dd > ul:only-child, dd > ol:only-child { padding-left: 1em; }
/* Description Lists */
/* styled like in most dictionaries, encyclopedias etc. */
dl.description {
display: flow-root;
}
dl.description > dt {
font-weight: bold;
clear: left;
float: left;
margin: 0;
padding: 0;
padding-right: 0.3em;
}
dl.description > dd:after {
display: table;
content: "";
clear: left; /* clearfix for empty descriptions */
}
/* Field Lists */
dl.field-list > dd,
dl.docinfo > dd {
margin-left: var(--field-indent); /* adapted in media queries or HTML */
}
/* example for custom field-name width */
dl.field-list.narrow > dd {
--field-indent: 5em;
}
/* run-in: start field-body on same line after long field names */
dl.field-list.run-in > dd p {
display: block;
}
/* Bibliographic Fields */
/* generally, bibliographic fields use dl.docinfo */
/* but dedication and abstract are placed into divs */
div.abstract p.topic-title {
text-align: center;
}
div.dedication {
margin: 2em 5em;
text-align: center;
font-style: italic;
}
div.dedication p.topic-title {
font-style: normal;
}
/* disclosures */
details { padding-left: 1em; }
summary { margin-left: -1em; }
/* Text Blocks */
/* =========== */
/* Literal Blocks */
pre.literal-block, pre.doctest-block,
pre.math, pre.code {
font-family: monospace;
}
/* Block Quotes and Topics */
bockquote { margin: 1em 2em; }
blockquote p.attribution {
text-align: right;
margin-left: 20%;
}
/* Tables */
/* ====== */
/* th { vertical-align: bottom; } */
table tr { text-align: left; }
/* "booktabs" style (no vertical lines) */
table.booktabs {
border: 0;
border-top: 2px solid;
border-bottom: 2px solid;
border-collapse: collapse;
}
table.booktabs * {
border: 0;
}
table.booktabs th {
border-bottom: thin solid;
}
/* numbered tables (counter defined in div.document) */
table.numbered > caption:before {
counter-increment: table;
content: "Table " counter(table) ": ";
font-weight: bold;
}
/* Explicit Markup Blocks */
/* ====================== */
/* Footnotes and Citations */
/* ----------------------- */
/* line on the left */
.footnote-list {
border-left: solid thin;
padding-left: 0.25em;
}
/* Directives */
/* ---------- */
/* Body Elements */
/* ~~~~~~~~~~~~~ */
/* Images and Figures */
/* let content flow to the side of aligned images and figures */
figure.align-left,
img.align-left,
svg.align-left,
video.align-left,
div.align-left,
object.align-left {
clear: left;
float: left;
margin-right: 1em;
}
figure.align-right,
img.align-right,
svg.align-right,
video.align-right,
div.align-right,
object.align-right {
clear: right;
float: right;
margin-left: 1em;
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<body>
<section class="slide">
<h2>CPU Scheduling</h2>
<p>Ahmad Yoosofan</p>
<p><a class="reference external" href="https://yoosofan.github.io">https://yoosofan.github.io</a></p>
<p>University of Kashan</p>
<p><a class="reference external" href="https://yoosofan.github.io/slide/os.cpu.presentation.html">https://yoosofan.github.io/slide/os.cpu.presentation.html</a></p>
<p><a class="reference external" href="https://github.com/yoosofan/slide/blob/main/os.cpu.rst">https://github.com/yoosofan/slide/blob/main/os.cpu.rst</a></p>
<div class="slide-number">1</div></section>
<section class="slide t2c">
<h2>CPU Burst / Service Time</h2>
<div class="docutils container">
<ul class="simple">
<li><p>cpu utilization by multiprogramming</p></li>
<li><p>cpu - I/O cycle of a process</p></li>
<li><p>cpu : burst time, service time</p></li>
<li><p>I/O : or other blocking events like memory request</p></li>
</ul>
<p>Process behaviour</p>
<ol class="arabic simple">
<li><p>cpu bound</p></li>
<li><p>I/O bound</p></li>
</ol>
</div>
<img alt="os/img/cpu/burst.png" class="step-hidden" src="os/img/cpu/burst.png" />
<div class="slide-number">2</div></section>
<section class="slide t2c">
<h2>CPU Burst / Service Time</h2>
<div class="docutils container">
<ul class="simple">
<li><p>cpu utilization by multiprogramming</p></li>
<li><p>cpu - I/O cycle of a process</p></li>
<li><p>cpu : burst time, service time</p></li>
<li><p>I/O : or other blocking events like memory request</p></li>
</ul>
<p>Process behaviour</p>
<ol class="arabic simple">
<li><p>cpu bound</p></li>
<li><p>I/O bound</p></li>
</ol>
</div>
<img alt="os/img/cpu/burst.png" src="os/img/cpu/burst.png" />
<div class="slide-number">2</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="step-hidden docutils container">
<p class="step-hidden">Short Term Schedular</p>
<ul class="step-hidden simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p class="step-hidden">Time Unit Concept</p>
<ul class="step-hidden simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p class="step-hidden">Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p class="step-hidden">Short Term Schedular</p>
<ul class="step-hidden simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p class="step-hidden">Time Unit Concept</p>
<ul class="step-hidden simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p class="step-hidden">Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p>Short Term Schedular</p>
<ul class="step-hidden simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p class="step-hidden">Time Unit Concept</p>
<ul class="step-hidden simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p class="step-hidden">Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p>Short Term Schedular</p>
<ul class="simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p class="step-hidden">Time Unit Concept</p>
<ul class="step-hidden simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p class="step-hidden">Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p>Short Term Schedular</p>
<ul class="simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p>Time Unit Concept</p>
<ul class="step-hidden simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p class="step-hidden">Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p>Short Term Schedular</p>
<ul class="simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p>Time Unit Concept</p>
<ul class="simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p class="step-hidden">Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p>Short Term Schedular</p>
<ul class="simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p>Time Unit Concept</p>
<ul class="simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p>Scheduling type</p>
<ul class="step-hidden simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>CPU Schedular</h2>
<img alt="os/img/in/process_state_chart.png" height="389" src="os/img/in/process_state_chart.png" width="992" />
<div class="docutils container">
<p>Short Term Schedular</p>
<ul class="simple">
<li><p>ready queue</p></li>
<li><p>Dispatcher</p></li>
</ul>
<p>Time Unit Concept</p>
<ul class="simple">
<li><p>Millisecond</p></li>
<li><p>Nanosecond</p></li>
<li><p>?</p></li>
</ul>
<p>Scheduling type</p>
<ul class="simple">
<li><p>nonpreemptive</p></li>
<li><p>preemptive</p></li>
</ul>
</div>
<div class="slide-number">3</div></section>
<section class="slide t2c">
<h2>Processes Table</h2>
<table class="center">
<thead>
<tr><th class="head"><p>process</p></th>
<th class="head"><p>service(Burst) time</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
</math></p></td>
<td><p>3</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
</math></p></td>
<td><p>1</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>3</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
</tr>
</tbody>
</table>
<table class="center step-hidden">
<thead>
<tr><th class="head"><p>process</p></th>
<th class="head"><p>service time</p></th>
<th class="head"><p>arrival time</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
</math></p></td>
<td><p>3</p></td>
<td><p>0</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
<td><p>0</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
</math></p></td>
<td><p>1</p></td>
<td><p>3</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>3</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
<td><p>5</p></td>
</tr>
</tbody>
</table>
<table class="center step-hidden">
<thead>
<tr><th class="head"><p>prs</p></th>
<th class="head"><p>st</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
</math></p></td>
<td><p>3</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
</math></p></td>
<td><p>1</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>3</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
</tr>
</tbody>
</table>
<table class="center step-hidden">
<thead>
<tr><th class="head"><p>pcs</p></th>
<th class="head"><p>st</p></th>
<th class="head"><p>at</p></th>
</tr>
</thead>
<tbody>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
</math></p></td>
<td><p>3</p></td>
<td><p>0</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</math></p></td>
<td><p>2</p></td>
<td><p>0</p></td>
</tr>
<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>