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In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], an '''M/D/c queue''' represents the queue length in a system having ''c'' servers, where arrivals are determined by a [[Poisson process]] and job service times are fixed (deterministic). The model name is written in [[Kendall's notation]].<ref>{{cite doi|10.1214/aoms/1177728975}}</ref> [[Agner Krarup Erlang]] first published on this model in 1909, starting the subject of [[queueing theory]].<ref>{{cite doi|10.1007/s11134-009-9147-4}}</ref><ref>{{cite journal | title = The theory of probabilities and telephone conversations | journal = Nyt Tidsskrift for Matematik B | volume = 20 | pages = 33–39 | url = http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf | year = 1909}}</ref> The model is an extension of the [[M/D/1 queue]] which has only a single server.
<html prefix="mw: http://mediawiki.org/rdf/"><head prefix="schema: http://schema.org/"><meta charset="UTF-8"><meta property="mw:articleNamespace" content="0"><meta property="schema:CreativeWork/version" content="559856801"><meta property="schema:CreativeWork/version/parent" content="559856706"><meta property="schema:CreativeWork/dateModified" content="2013-06-14T10:51:56.000Z"><meta property="schema:CreativeWork/contributor/username" content="//en.wikipedia.org/wiki/User:Gareth Jones"><meta property="schema:CreativeWork/contributor" content="//en.wikipedia.org/wiki/Special:UserById/313335"><meta property="mw:revisionSHA1" content="19239dbadc887c8b075ede25da4eefafd9f1b1dc"><meta property="schema:CreativeWork/comment" content="link m/d/1 queue in lead"><title>M/D/c queue</title><base href="//en.wikipedia.org/wiki/M/D/c_queue"></head><body><p data-parsoid='{"dsr":[0,882,0,0]}'>In <a rel="mw:WikiLink" href="../../Queueing_theory" data-parsoid='{"a":{"href":"../../Queueing_theory"},"sa":{"href":"queueing theory"},"stx":"simple","dsr":[3,22,2,2]}'>queueing theory</a>, a discipline within the mathematical <a rel="mw:WikiLink" href="../../Probability_theory" data-parsoid='{"a":{"href":"../../Probability_theory"},"sa":{"href":"probability theory"},"stx":"piped","dsr":[61,105,21,2]}'>theory of probability</a>, an <b data-parsoid='{"dsr":[110,127,3,3]}'>M/D/c queue</b> represents the queue length in a system having <i data-parsoid='{"dsr":[175,180,2,2]}'>c</i> servers, where arrivals are determined by a <a rel="mw:WikiLink" href="../../Poisson_process" data-parsoid='{"a":{"href":"../../Poisson_process"},"sa":{"href":"Poisson process"},"stx":"simple","dsr":[225,244,2,2]}'>Poisson process</a> and job service times are fixed (deterministic). The model name is written in <a rel="mw:WikiLink" href="../../Kendall's_notation" data-parsoid='{"a":{"href":"../../Kendall&#39;s_notation"},"sa":{"href":"Kendall&#39;s notation"},"stx":"simple","dsr":[323,345,2,2]}'>Kendall's notation</a>.<span about="#mwt4" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;{{cite doi|10.1214/aoms/1177728975}}&amp;quot;,&amp;quot;dsr&amp;quot;:[351,387,null,null]}\" about=\"#mwt7\" typeof=\"mw:Transclusion\" data-mw=\"{&amp;quot;target&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;cite doi&amp;quot;,&amp;quot;href&amp;quot;:&amp;quot;../../Template:Cite_doi&amp;quot;},&amp;quot;params&amp;quot;:{&amp;quot;1&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;10.1214/aoms/1177728975&amp;quot;}}}\"><a rel=\"mw:WikiLink\" href=\"../../David_George_Kendall\" data-parsoid=\"{&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;../../David_George_Kendall&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;David George Kendall&amp;quot;},&amp;quot;stx&amp;quot;:&amp;quot;piped&amp;quot;}\">Kendall, D. G.</a> (1953). \"Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain\". <i data-parsoid=\"{}\">The Annals of Mathematical Statistics</i> <b data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\">24</b> (3): 338. <a rel=\"mw:WikiLink\" href=\"../../Digital_object_identifier\" data-parsoid=\"{&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;../../Digital_object_identifier&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;Digital object identifier&amp;quot;},&amp;quot;stx&amp;quot;:&amp;quot;piped&amp;quot;}\">doi</a>:<a rel=\"mw:ExtLink\" href=\"http://dx.doi.org/10.1214%2Faoms%2F1177728975\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:342,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;http://dx.doi.org/10.1214%2Faoms%2F1177728975&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;e model name is written in [[Kendall&#39;s notati&amp;quot;}}\">10.1214/aoms/1177728975</a>. <a rel=\"mw:WikiLink\" href=\"../../JSTOR\" data-parsoid=\"{&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;../../JSTOR&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;JSTOR&amp;quot;},&amp;quot;stx&amp;quot;:&amp;quot;piped&amp;quot;}\">JSTOR</a><span typeof=\"mw:Entity\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;&amp;amp;nbsp;&amp;quot;,&amp;quot;srcContent&amp;quot;:&amp;quot;&amp;nbsp;&amp;quot;}\">&amp;nbsp;</span><a rel=\"mw:ExtLink\" href=\"http://www.jstor.org/stable/2236285\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:426,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;http://www.jstor.org/stable/2236285&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;ef> [[Agner Krarup Erlang]] first p&amp;quot;}}\">2236285</a>.</span><span title=\"ctx_ver=Z39.88-2004&amp;amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;amp;rft.atitle=Stochastic+Processes+Occurring+in+the+Theory+of+Queues+and+their+Analysis+by+the+Method+of+the+Imbedded+Markov+Chain&amp;amp;rft.aufirst=D.+G.&amp;amp;rft.au=Kendall%2C+D.+G.&amp;amp;rft.aulast=Kendall&amp;amp;rft.date=1953&amp;amp;rft.genre=article&amp;amp;rft_id=info%3Adoi%2F10.1214%2Faoms%2F1177728975&amp;amp;rft.issue=3&amp;amp;rft.jstor=2236285&amp;amp;rft.jtitle=The+Annals+of+Mathematical+Statistics&amp;amp;rft.pages=338&amp;amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;amp;rft.volume=24\" class=\"Z3988\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt7\"><span style=\"display:none;\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\"><span typeof=\"mw:Entity\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;&amp;amp;nbsp;&amp;quot;,&amp;quot;srcContent&amp;quot;:&amp;quot;&amp;nbsp;&amp;quot;}\">&amp;nbsp;</span></span></span><span class=\"plainlinks noprint\" style=\"font-size:smaller\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt7\"> <a rel=\"mw:ExtLink\" href=\"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1214.2Faoms.2F1177728975&amp;amp;action=edit&amp;amp;editintro=Template:Cite_doi/editintro2\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:1215,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1214.2Faoms.2F1177728975&amp;amp;action=edit&amp;amp;editintro=Template:Cite_doi/editintro2&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;urrently in service. \\n\\n* Arrivals occur at rate λ according to a [[Poisson process]] and move the process from state &#39;&#39;i&#39;&#39; to &#39;&#39;i&#39;&#39;&amp;amp;n&amp;quot;}}\">edit</a></span>"},"attrs":{}}' id="cite_ref-1-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"<ref>{{cite doi|10.1214/aoms/1177728975}}</ref>","dsr":[346,393,5,6]}'><a href="#cite_note-1">[1]</a></span> <a rel="mw:WikiLink" href="../../Agner_Krarup_Erlang" data-parsoid='{"a":{"href":"../../Agner_Krarup_Erlang"},"sa":{"href":"Agner Krarup Erlang"},"stx":"simple","dsr":[394,417,2,2]}'>Agner Krarup Erlang</a> first published on this model in 1909, starting the subject of <a rel="mw:WikiLink" href="../../Queueing_theory" data-parsoid='{"a":{"href":"../../Queueing_theory"},"sa":{"href":"queueing theory"},"stx":"simple","dsr":[481,500,2,2]}'>queueing theory</a>.<span about="#mwt5" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;{{cite doi|10.1007/s11134-009-9147-4}}&amp;quot;,&amp;quot;dsr&amp;quot;:[506,544,null,null]}\" about=\"#mwt8\" typeof=\"mw:Transclusion\" data-mw=\"{&amp;quot;target&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;cite doi&amp;quot;,&amp;quot;href&amp;quot;:&amp;quot;../../Template:Cite_doi&amp;quot;},&amp;quot;params&amp;quot;:{&amp;quot;1&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;10.1007/s11134-009-9147-4&amp;quot;}}}\"><a rel=\"mw:WikiLink\" href=\"../../John_Kingman\" data-parsoid=\"{&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;../../John_Kingman&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;John Kingman&amp;quot;},&amp;quot;stx&amp;quot;:&amp;quot;piped&amp;quot;}\">Kingman, J. F. C.</a> (2009). \"The first Erlang century—and the next\". <i data-parsoid=\"{}\">Queueing Systems</i> <b data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\">63</b>: 3–4. <a rel=\"mw:WikiLink\" href=\"../../Digital_object_identifier\" data-parsoid=\"{&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;../../Digital_object_identifier&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;Digital object identifier&amp;quot;},&amp;quot;stx&amp;quot;:&amp;quot;piped&amp;quot;}\">doi</a>:<a rel=\"mw:ExtLink\" href=\"http://dx.doi.org/10.1007%2Fs11134-009-9147-4\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:233,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;http://dx.doi.org/10.1007%2Fs11134-009-9147-4&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;s, where arrivals are determined by a [[Poiss&amp;quot;}}\">10.1007/s11134-009-9147-4</a>.</span><span title=\"ctx_ver=Z39.88-2004&amp;amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;amp;rft.atitle=The+first+Erlang+century%E2%80%94and+the+next&amp;amp;rft.aufirst=J.+F.+C.&amp;amp;rft.au=Kingman%2C+J.+F.+C.&amp;amp;rft.aulast=Kingman&amp;amp;rft.date=2009&amp;amp;rft.genre=article&amp;amp;rft_id=info%3Adoi%2F10.1007%2Fs11134-009-9147-4&amp;amp;rft.jtitle=Queueing+Systems&amp;amp;rft.pages=3%E2%80%934&amp;amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;amp;rft.volume=63\" class=\"Z3988\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt8\"><span style=\"display:none;\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\"><span typeof=\"mw:Entity\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;&amp;amp;nbsp;&amp;quot;,&amp;quot;srcContent&amp;quot;:&amp;quot;&amp;nbsp;&amp;quot;}\">&amp;nbsp;</span></span></span><span class=\"plainlinks noprint\" style=\"font-size:smaller\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt8\"> <a rel=\"mw:ExtLink\" href=\"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1007.2Fs11134-009-9147-4&amp;amp;action=edit&amp;amp;editintro=Template:Cite_doi/editintro2\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:932,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1007.2Fs11134-009-9147-4&amp;amp;action=edit&amp;amp;editintro=Template:Cite_doi/editintro2&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;ef> The model is an extension of the [[M/D/1 queue]] which has only a single server.\\n\\n==Model definition==\\n\\nAn M/D/&#39;&#39;c&#39;&#39; queue is a s&amp;quot;}}\">edit</a></span>"},"attrs":{}}' id="cite_ref-2-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"<ref>{{cite doi|10.1007/s11134-009-9147-4}}</ref>","dsr":[501,550,5,6]}'><a href="#cite_note-2">[2]</a></span><span about="#mwt6" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;{{cite journal | title = The theory of probabilities and telephone conversations | journal = Nyt Tidsskrift for Matematik B | volume = 20 | pages = 33–39 | url = http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf | year = 1909}}&amp;quot;,&amp;quot;dsr&amp;quot;:[555,795,null,null]}\" about=\"#mwt9\" typeof=\"mw:Transclusion\" data-mw=\"{&amp;quot;target&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;cite journal &amp;quot;,&amp;quot;href&amp;quot;:&amp;quot;../../Template:Cite_journal&amp;quot;},&amp;quot;params&amp;quot;:{&amp;quot; title &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;The theory of probabilities and telephone conversations &amp;quot;},&amp;quot; journal &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;Nyt Tidsskrift for Matematik B &amp;quot;},&amp;quot; volume &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;20 &amp;quot;},&amp;quot; pages &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;33–39 &amp;quot;},&amp;quot; url &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf &amp;quot;},&amp;quot; year &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;1909&amp;quot;}}}\"><a rel=\"mw:ExtLink\" href=\"http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:95,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;line within the mathematical [[probability theory|theory of pr&amp;quot;}}\">\"The theory of probabilities and telephone conversations\"</a>. <i data-parsoid=\"{}\">Nyt Tidsskrift for Matematik B</i> <b data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\">20</b>: 33–39. 1909.</span><span title=\"ctx_ver=Z39.88-2004&amp;amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;amp;rft.atitle=The+theory+of+probabilities+and+telephone+conversations&amp;amp;rft.date=1909&amp;amp;rft.genre=article&amp;amp;rft_id=http%3A%2F%2Foldwww.com.dtu.dk%2Fteletraffic%2Ferlangbook%2Fpps131-137.pdf&amp;amp;rft.jtitle=Nyt+Tidsskrift+for+Matematik+B&amp;amp;rft.pages=33%E2%80%9339&amp;amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;amp;rft.volume=20\" class=\"Z3988\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt9\"><span style=\"display:none;\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\"><span typeof=\"mw:Entity\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;&amp;amp;nbsp;&amp;quot;,&amp;quot;srcContent&amp;quot;:&amp;quot;&amp;nbsp;&amp;quot;}\">&amp;nbsp;</span></span></span>"},"attrs":{}}' id="cite_ref-3-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"<ref>{{cite journal | title = The theory of probabilities and telephone conversations | journal = Nyt Tidsskrift for Matematik B | volume = 20 | pages = 33–39 | url = http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf | year = 1909}}</ref>","dsr":[550,801,5,6]}'><a href="#cite_note-3">[3]</a></span> The model is an extension of the <a rel="mw:WikiLink" href="../../M/D/1_queue" data-parsoid='{"a":{"href":"../../M/D/1_queue"},"sa":{"href":"M/D/1 queue"},"stx":"simple","dsr":[835,850,2,2]}'>M/D/1 queue</a> which has only a single server.</p>
 
<h2 data-parsoid=='{"dsr":[884,904,2,2]}'>Model definition==</h2>
 
<p data-parsoid='{"dsr":[906,1102,0,0]}'>An M/D/<i data-parsoid='{"dsr":[913,918,2,2]}'>c''</i> queue is a stochastic process whose [[<a rel="mw:WikiLink" href="../../State_space" data-parsoid='{"a":{"href":"../../State_space"},"sa":{"href":"state space"},"stx":"simple","dsr":[955,970,2,2]]}'>state space</a> is the set {0,1,2,3,...} where the value corresponds to the number of customers in the system, including any currently in service. </p>
 
<ul data-parsoid='{"dsr":[1104,1649,0,0]}'><li data-parsoid='{"dsr":[1104,1227,1,0]}'> Arrivals occur at rate λ according to a <a rel="mw:WikiLink" href="../../Poisson_process" data-parsoid='{"a":{"href":"../../Poisson_process"},"sa":{"href":"Poisson process"},"stx":"simple","dsr":[1146,1165,2,2]}'>Poisson process</a> and move the process from state <i data-parsoid='{"dsr":[1198,1203,2,2]}'>i</i> to <i data-parsoid='{"dsr":[1207,1212,2,2]}'>i</i><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1212,1218,null,null]}'>&nbsp;</span>+<span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1219,1225,null,null]}'>&nbsp;</span>1.</li>
* Arrivals occur at rate λ according to a [[Poisson process]] and move the process from state ''i'' to ''i''&nbsp;+&nbsp;1.
<li data-parsoid='{"dsr":[1228,1317,1,0]}'> Service times are deterministic time <i data-parsoid='{"dsr":[1267,1272,2,2]}'>D</i> (serving at rate <i data-parsoid='{"dsr":[1290,1295,2,2]}'>μ</i><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1295,1301,null,null]}'>&nbsp;</span>=<span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1302,1308,null,null]}'>&nbsp;</span>1/<i data-parsoid='{"dsr":[1310,1315,2,2]}'>D</i>).</li>
* Service times are deterministic time ''D'' (serving at rate ''μ''&nbsp;=&nbsp;1/''D'').
*<li data-parsoid='{"dsr":[1318,1551,1,0]}'c> <i data-parsoid='{"dsr":[1320,1325,2,2]}'>c</i> servers serve customers from the front of the queue, according to a [[<a rel="mw:WikiLink" href="../../First-come,_first-served" data-parsoid='{"a":{"href":"../../First-come,_first-served"},"sa":{"href":"first-come, first-served"},"stx":"simple","dsr":[1394,1422,2,2]]}'>first-come, first-served</a> discipline. When the service is complete the customer leaves the queue and the number of customers in the system reduces by one.</li>
*<li data-parsoid='{"dsr":[1552,1649,1,0]}'> The buffer is of infinite size, so there is no limit on the number of customers it can contain.</li></ul>
 
<h2 data-parsoid=='{"dsr":[1651,1680,2,2]}'>Waiting time distribution==</h2>
 
<p data-parsoid='{"dsr":[1682,1892,0,0]}'>Erlang showed that when <i data-parsoid='{"dsr":[1706,1711,2,2]}'>ρ</i><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1711,1717,null,null]}'>&nbsp;</span>=<span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1718,1724,null,null]}'>&nbsp;</span><i data-parsoid='{"dsr":[1724,1729,2,2]}'>λ</i><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1729,1735,null,null]}'>&nbsp;</span><i data-parsoid='{"dsr":[1735,1740,2,2]}'>D</i>/<i data-parsoid='{"dsr":[1741,1746,2,2]}'>c</i><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1746,1752,null,null]}'>&nbsp;</span>&lt;<span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;","dsr":[1753,1759,null,null]}'>&nbsp;</span>1, the waiting time distribution has distribution F(<i data-parsoid='{"dsr":[1811,1816,2,2]}'>y</i>) given by<span about="#mwt11" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;{{cite doi|10.1016/S0167-6377(01)00108-0}}&amp;quot;,&amp;quot;dsr&amp;quot;:[1844,1886,null,null]}\" about=\"#mwt12\" typeof=\"mw:Transclusion\" data-mw=\"{&amp;quot;target&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;cite doi&amp;quot;,&amp;quot;href&amp;quot;:&amp;quot;../../Template:Cite_doi&amp;quot;},&amp;quot;params&amp;quot;:{&amp;quot;1&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;10.1016/S0167-6377(01)00108-0&amp;quot;}}}\">Franx, G. J. (2001). \"A simple solution for the M/D/c waiting time distribution\". <i data-parsoid=\"{}\">Operations Research Letters</i> <b data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\">29</b> (5): 221–229. <a rel=\"mw:WikiLink\" href=\"../../Digital_object_identifier\" data-parsoid=\"{&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;../../Digital_object_identifier&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;Digital object identifier&amp;quot;},&amp;quot;stx&amp;quot;:&amp;quot;piped&amp;quot;}\">doi</a>:<a rel=\"mw:ExtLink\" href=\"http://dx.doi.org/10.1016%2FS0167-6377%2801%2900108-0\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:258,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;http://dx.doi.org/10.1016%2FS0167-6377%2801%2900108-0&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot; are determined by a [[Poisson process]] and job serv&amp;quot;}}\">10.1016/S0167-6377(01)00108-0</a>.</span><span title=\"ctx_ver=Z39.88-2004&amp;amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;amp;rft.atitle=A+simple+solution+for+the+M%2FD%2Fc+waiting+time+distribution&amp;amp;rft.aufirst=G.+J.&amp;amp;rft.au=Franx%2C+G.+J.&amp;amp;rft.aulast=Franx&amp;amp;rft.date=2001&amp;amp;rft.genre=article&amp;amp;rft_id=info%3Adoi%2F10.1016%2FS0167-6377%2801%2900108-0&amp;amp;rft.issue=5&amp;amp;rft.jtitle=Operations+Research+Letters&amp;amp;rft.pages=221%E2%80%93229&amp;amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;amp;rft.volume=29\" class=\"Z3988\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt12\"><span style=\"display:none;\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\"><span typeof=\"mw:Entity\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;&amp;amp;nbsp;&amp;quot;,&amp;quot;srcContent&amp;quot;:&amp;quot;&amp;nbsp;&amp;quot;}\">&amp;nbsp;</span></span></span><span class=\"plainlinks noprint\" style=\"font-size:smaller\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt12\"> <a rel=\"mw:ExtLink\" href=\"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1016.2FS0167-6377.2801.2900108-0&amp;amp;action=edit&amp;amp;editintro=Template:Cite_doi/editintro2\" data-parsoid=\"{&amp;quot;targetOff&amp;quot;:1010,&amp;quot;a&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1016.2FS0167-6377.2801.2900108-0&amp;amp;action=edit&amp;amp;editintro=Template:Cite_doi/editintro2&amp;quot;},&amp;quot;sa&amp;quot;:{&amp;quot;href&amp;quot;:&amp;quot;single server.\\n\\n==Model definition==\\n\\nAn M/D/&#39;&#39;c&#39;&#39; queue is a stochastic process whose [[state space]] is the set {0,1,2,3,...} where the val&amp;quot;}}\">edit</a></span>"},"attrs":{"name":"franx"}}' id="cite_ref-franx-4-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"<ref name=\"franx\">{{cite doi|10.1016/S0167-6377(01)00108-0}}</ref>","dsr":[1826,1892,18,6]}'><a href="#cite_note-franx-4">[4]</a></span></p>
Erlang showed that when ''ρ''&nbsp;=&nbsp;''λ''&nbsp;''D''/''c''&nbsp;<&nbsp;1, the waiting time distribution has distribution F(''y'') given by<ref name="franx">{{cite doi|10.1016/S0167-6377(01)00108-0}}</ref>
 
<dl data-parsoid='{"dsr":[1894,2035,0,0]}'><dd data-parsoid='{"dsr":[1894,2035,1,0]}'><dl data-parsoid='{"dsr":[1895,2035,0,0]}'><dd data-parsoid='{"dsr":[1895,2035,1,0]}'><img class="tex" alt="F(y) = \int_0^\infty F(x+y-D)\frac{\lambda^c x^{c-1}}{(c-1)!} e^{-\lambda x} \text{d} x, \quad y \geq 0 \quad c \in \mathbb N." src="//upload.wikimedia.org/math/d/0/f/d0f83f237a48a605b1eca5df7a08fd3b.png" typeof="mw:Extension/math" data-parsoid='{"src":"<math>F(y) = \\int_0^\\infty F(x+y-D)\\frac{\\lambda^c x^{c-1}}{(c-1)!} e^{-\\lambda x} \\text{d} x, \\quad y \\geq 0 \\quad c \\in \\mathbb N.</math>","dsr":[1896,2035,null,null]}' data-mw='{"name":"math","attrs":{},"body":{"extsrc":"F(y) = \\int_0^\\infty F(x+y-D)\\frac{\\lambda^c x^{c-1}}{(c-1)!} e^{-\\lambda x} \\text{d} x, \\quad y \\geq 0 \\quad c \\in \\mathbb N."}}' about="mwt14"></dd></dl></dd></dl>
::<math>F(y) = \int_0^\infty F(x+y-D)\frac{\lambda^c x^{c-1}}{(c-1)!} e^{-\lambda x} \text{d} x, \quad y \geq 0 \quad c \in \mathbb N.</math>
 
<p data-parsoid='{"dsr":[2037,2370,0,0]}'>Crommelin showed that, writing <i data-parsoid='{"dsr":[2068,2073,2,2]}'>P''<sub/i><sub data-parsoid='{"stx":"html","dsr":[2073,2089,5,6]}'n><i data-parsoid='{"dsr":[2078,2083,2,2]}'>n</i></sub> for the stationary probability of a system with <i data-parsoid='{"dsr":[2138,2143,2,2]}'>n''</i> or fewer customers,
<span about="#mwt16" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;{{cite journal | first = C.D. | last = Crommelin | title = Delay probability formulas when the holding times are constant | journal = P.O. Electr. Engr. J.| volume = 25| year=1932| pages= 41–50}}&amp;quot;,&amp;quot;dsr&amp;quot;:[2169,2364,null,null]}\" about=\"#mwt17\" typeof=\"mw:Transclusion\" data-mw=\"{&amp;quot;target&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;cite journal &amp;quot;,&amp;quot;href&amp;quot;:&amp;quot;../../Template:Cite_journal&amp;quot;},&amp;quot;params&amp;quot;:{&amp;quot; first &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;C.D. &amp;quot;},&amp;quot; last &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;Crommelin &amp;quot;},&amp;quot; title &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;Delay probability formulas when the holding times are constant &amp;quot;},&amp;quot; journal &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;P.O. Electr. Engr. J.&amp;quot;},&amp;quot; volume &amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;25&amp;quot;},&amp;quot; year&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;1932&amp;quot;},&amp;quot; pages&amp;quot;:{&amp;quot;wt&amp;quot;:&amp;quot;41–50&amp;quot;}}}\">Crommelin, C.D. (1932). \"Delay probability formulas when the holding times are constant\". <i data-parsoid=\"{}\">P.O. Electr. Engr. J.</i> <b data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\">25</b>: 41–50.</span><span title=\"ctx_ver=Z39.88-2004&amp;amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;amp;rft.atitle=Delay+probability+formulas+when+the+holding+times+are+constant&amp;amp;rft.au=Crommelin%2C+C.D.&amp;amp;rft.aufirst=C.D.&amp;amp;rft.aulast=Crommelin&amp;amp;rft.date=1932&amp;amp;rft.genre=article&amp;amp;rft.jtitle=P.O.+Electr.+Engr.+J.&amp;amp;rft.pages=41%E2%80%9350&amp;amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;amp;rft.volume=25\" class=\"Z3988\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\" about=\"#mwt17\"><span style=\"display:none;\" data-parsoid=\"{&amp;quot;stx&amp;quot;:&amp;quot;html&amp;quot;}\"><span typeof=\"mw:Entity\" data-parsoid=\"{&amp;quot;src&amp;quot;:&amp;quot;&amp;amp;nbsp;&amp;quot;,&amp;quot;srcContent&amp;quot;:&amp;quot;&amp;nbsp;&amp;quot;}\">&amp;nbsp;</span></span></span>"},"attrs":{}}' id="cite_ref-5-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"<ref>{{cite journal | first = C.D. | last = Crommelin | title = Delay probability formulas when the holding times are constant | journal = P.O. Electr. Engr. J.| volume = 25| year=1932| pages= 41–50}}</ref>","dsr":[2164,2370,5,6]}'><a href="#cite_note-5">[5]</a></span></p>
<ref>{{cite journal | first = C.D. | last = Crommelin | title = Delay probability formulas when the holding times are constant | journal = P.O. Electr. Engr. J.| volume = 25| year=1932| pages= 41–50}}</ref>
 
<dl data-parsoid='{"dsr":[2372,2537,0,0]}'><dd data-parsoid='{"dsr":[2372,2537,1,0]}'><dl data-parsoid='{"dsr":[2373,2537,0,0]}'><dd data-parsoid='{"dsr":[2373,2537,1,0]}'><img class="tex" alt="\mathbb P(W \leq x) = \sum_{n=0}^{c-1} P_n \sum_{k=1}^m \frac{(-\lambda(x-kD))^{(k+1)c-1-n}}{((K+1)c-1-n)!}e^{\lambda(x-kD)}, \quad mD \leq x <(m+1)D." src="//upload.wikimedia.org/math/4/7/f/47f7699996b1ee30a74a04950eab1ebe.png" typeof="mw:Extension/math" data-parsoid='{"src":"<math>\\mathbb P(W \\leq x) = \\sum_{n=0}^{c-1} P_n \\sum_{k=1}^m \\frac{(-\\lambda(x-kD))^{(k+1)c-1-n}}{((K+1)c-1-n)!}e^{\\lambda(x-kD)}, \\quad mD \\leq x <(m+1)D.</math>","dsr":[2374,2537,null,null]}' data-mw='{"name":"math","attrs":{},"body":{"extsrc":"\\mathbb P(W \\leq x) = \\sum_{n=0}^{c-1} P_n \\sum_{k=1}^m \\frac{(-\\lambda(x-kD))^{(k+1)c-1-n}}{((K+1)c-1-n)!}e^{\\lambda(x-kD)}, \\quad mD \\leq x <(m+1)D."}}' about="mwt19"></dd></dl></dd></dl>
::<math>\mathbb P(W \leq x) = \sum_{n=0}^{c-1} P_n \sum_{k=1}^m \frac{(-\lambda(x-kD))^{(k+1)c-1-n}}{((K+1)c-1-n)!}e^{\lambda(x-kD)}, \quad mD \leq x <(m+1)D.</math>
 
<h2 data-parsoid='{"dsr":[2539,2553,2,2]}'>References</h2>
==References==
<div class="reflist " style=" list-style-type: decimal;" data-parsoid='{"src":"{{Reflist}}","dsr":[2554,2600,null,null]}' about="mwt21" typeof="mw:Transclusion" data-mw='{"target":{"wt":"Reflist","href":"../../Template:Reflist"},"params":{}}'>
{{Reflist}}
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F. C.</a> (2009). "The first Erlang century—and the next". <i data-parsoid="{}">Queueing Systems</i> <b data-parsoid='{"stx":"html"}'>63</b>: 3–4. <a rel="mw:WikiLink" href="../../Digital_object_identifier" data-parsoid='{"a":{"href":"../../Digital_object_identifier"},"sa":{"href":"Digital object identifier"},"stx":"piped"}'>doi</a>:<a rel="mw:ExtLink" href="http://dx.doi.org/10.1007%2Fs11134-009-9147-4" data-parsoid='{"targetOff":233,"a":{"href":"http://dx.doi.org/10.1007%2Fs11134-009-9147-4"},"sa":{"href":"s, where arrivals are determined by a [[Poiss"}}'>10.1007/s11134-009-9147-4</a>.</span><span title="ctx_ver=Z39.88-2004&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;rft.atitle=The+first+Erlang+century%E2%80%94and+the+next&amp;rft.aufirst=J.+F.+C.&amp;rft.au=Kingman%2C+J.+F.+C.&amp;rft.aulast=Kingman&amp;rft.date=2009&amp;rft.genre=article&amp;rft_id=info%3Adoi%2F10.1007%2Fs11134-009-9147-4&amp;rft.jtitle=Queueing+Systems&amp;rft.pages=3%E2%80%934&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.volume=63" class="Z3988" data-parsoid='{"stx":"html"}' about="#mwt8"><span style="display:none;" data-parsoid='{"stx":"html"}'><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;"}'>&nbsp;</span></span></span><span class="plainlinks noprint" style="font-size:smaller" data-parsoid='{"stx":"html"}' about="#mwt8"> <a rel="mw:ExtLink" href="//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1007.2Fs11134-009-9147-4&amp;action=edit&amp;editintro=Template:Cite_doi/editintro2" data-parsoid='{"targetOff":932,"a":{"href":"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1007.2Fs11134-009-9147-4&amp;action=edit&amp;editintro=Template:Cite_doi/editintro2"},"sa":{"href":"ef>\n\n==Model definition==\n\nAn M/D/&#39;&#39;c&#39;&#39; queue is a stochastic process whose [[state space]] is the set {0,1,2,3,...} where the value "}}'>edit</a></span></span></li><li about="#cite_note-3" id="cite_note-3"><span rel="mw:referencedBy"><a href="#cite_ref-3-0">↑</a></span> <span><span class="citation journal" data-parsoid='{"src":"{{cite journal | title = The theory of probabilities and telephone conversations | journal = Nyt Tidsskrift for Matematik B | volume = 20 | pages = 33–39 | url = http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf | year = 1909}}","dsr":[555,795,null,null]}' about="#mwt9" typeof="mw:Transclusion" data-mw='{"target":{"wt":"cite journal ","href":"../../Template:Cite_journal"},"params":{" title ":{"wt":"The theory of probabilities and telephone conversations "}," journal ":{"wt":"Nyt Tidsskrift for Matematik B "}," volume ":{"wt":"20 "}," pages ":{"wt":"33–39 "}," url ":{"wt":"http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf "}," year ":{"wt":"1909"}}}'><a rel="mw:ExtLink" href="http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf" data-parsoid='{"targetOff":95,"a":{"href":"http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf"},"sa":{"href":"line within the mathematical [[probability theory|theory of pr"}}'>"The theory of probabilities and telephone conversations"</a>. <i data-parsoid="{}">Nyt Tidsskrift for Matematik B</i> <b data-parsoid='{"stx":"html"}'>20</b>: 33–39. 1909.</span><span title="ctx_ver=Z39.88-2004&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;rft.atitle=The+theory+of+probabilities+and+telephone+conversations&amp;rft.date=1909&amp;rft.genre=article&amp;rft_id=http%3A%2F%2Foldwww.com.dtu.dk%2Fteletraffic%2Ferlangbook%2Fpps131-137.pdf&amp;rft.jtitle=Nyt+Tidsskrift+for+Matematik+B&amp;rft.pages=33%E2%80%9339&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.volume=20" class="Z3988" data-parsoid='{"stx":"html"}' about="#mwt9"><span style="display:none;" data-parsoid='{"stx":"html"}'><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;"}'>&nbsp;</span></span></span></span></li><li about="#cite_note-franx-4" id="cite_note-franx-4"><span rel="mw:referencedBy"><a href="#cite_ref-franx-4-0">↑</a></span> <span><span class="citation journal" data-parsoid='{"src":"{{cite doi|10.1016/S0167-6377(01)00108-0}}","dsr":[1763,1805,null,null]}' about="#mwt12" typeof="mw:Transclusion" data-mw='{"target":{"wt":"cite doi","href":"../../Template:Cite_doi"},"params":{"1":{"wt":"10.1016/S0167-6377(01)00108-0"}}}'>Franx, G. J. (2001). "A simple solution for the M/D/c waiting time distribution". <i data-parsoid="{}">Operations Research Letters</i> <b data-parsoid='{"stx":"html"}'>29</b> (5): 221–229. <a rel="mw:WikiLink" href="../../Digital_object_identifier" data-parsoid='{"a":{"href":"../../Digital_object_identifier"},"sa":{"href":"Digital object identifier"},"stx":"piped"}'>doi</a>:<a rel="mw:ExtLink" href="http://dx.doi.org/10.1016%2FS0167-6377%2801%2900108-0" data-parsoid='{"targetOff":258,"a":{"href":"http://dx.doi.org/10.1016%2FS0167-6377%2801%2900108-0"},"sa":{"href":" are determined by a [[Poisson process]] and job serv"}}'>10.1016/S0167-6377(01)00108-0</a>.</span><span title="ctx_ver=Z39.88-2004&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;rft.atitle=A+simple+solution+for+the+M%2FD%2Fc+waiting+time+distribution&amp;rft.aufirst=G.+J.&amp;rft.au=Franx%2C+G.+J.&amp;rft.aulast=Franx&amp;rft.date=2001&amp;rft.genre=article&amp;rft_id=info%3Adoi%2F10.1016%2FS0167-6377%2801%2900108-0&amp;rft.issue=5&amp;rft.jtitle=Operations+Research+Letters&amp;rft.pages=221%E2%80%93229&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.volume=29" class="Z3988" data-parsoid='{"stx":"html"}' about="#mwt12"><span style="display:none;" data-parsoid='{"stx":"html"}'><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;"}'>&nbsp;</span></span></span><span class="plainlinks noprint" style="font-size:smaller" data-parsoid='{"stx":"html"}' about="#mwt12"> <a rel="mw:ExtLink" href="//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1016.2FS0167-6377.2801.2900108-0&amp;action=edit&amp;editintro=Template:Cite_doi/editintro2" data-parsoid='{"targetOff":1010,"a":{"href":"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1016.2FS0167-6377.2801.2900108-0&amp;action=edit&amp;editintro=Template:Cite_doi/editintro2"},"sa":{"href":"whose [[state space]] is the set {0,1,2,3,...} where the value corresponds to the number of customers in the system, including any currently "}}'>edit</a></span></span></li><li about="#cite_note-5" id="cite_note-5"><span rel="mw:referencedBy"><a href="#cite_ref-5-0">↑</a></span> <span><span class="citation journal" data-parsoid='{"src":"{{cite journal | first = C.D. | last = Crommelin | title = Delay probability formulas when the holding times are constant | journal = P.O. Electr. Engr. J.| volume = 25| year=1932| pages= 41–50}}","dsr":[2088,2283,null,null]}' about="#mwt16" typeof="mw:Transclusion" data-mw='{"target":{"wt":"cite journal ","href":"../../Template:Cite_journal"},"params":{" first ":{"wt":"C.D. "}," last ":{"wt":"Crommelin "}," title ":{"wt":"Delay probability formulas when the holding times are constant "}," journal ":{"wt":"P.O. Electr. Engr. J."}," volume ":{"wt":"25"}," year":{"wt":"1932"}," pages":{"wt":"41–50"}}}'>Crommelin, C.D. (1932). "Delay probability formulas when the holding times are constant". <i data-parsoid="{}">P.O. Electr. Engr. J.</i> <b data-parsoid='{"stx":"html"}'>25</b>: 41–50.</span><span title="ctx_ver=Z39.88-2004&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AM%2FD%2Fc+queue&amp;rft.atitle=Delay+probability+formulas+when+the+holding+times+are+constant&amp;rft.au=Crommelin%2C+C.D.&amp;rft.aufirst=C.D.&amp;rft.aulast=Crommelin&amp;rft.date=1932&amp;rft.genre=article&amp;rft.jtitle=P.O.+Electr.+Engr.+J.&amp;rft.pages=41%E2%80%9350&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.volume=25" class="Z3988" data-parsoid='{"stx":"html"}' about="#mwt16"><span style="display:none;" data-parsoid='{"stx":"html"}'><span typeof="mw:Entity" data-parsoid='{"src":"&amp;nbsp;","srcContent":"&nbsp;"}'>&nbsp;</span></span></span></span></li></ol></div>
 
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{{Queueing theory}}
<a rel="mw:WikiLink" href="../../Queueing_theory" data-parsoid='{"a":{"href":"../../Queueing_theory"},"sa":{"href":"Queueing theory"},"stx":"simple"}'>Queueing theory</a></div></th></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Single queueing nodes</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
{{Stochastic processes}}
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../D/M/1_queue" data-parsoid='{"a":{"href":"../../D/M/1_queue"},"sa":{"href":"D/M/1 queue"},"stx":"simple"}'>D/M/1 queue</a></li>
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<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Layered_queueing_network" data-parsoid='{"a":{"href":"../../Layered_queueing_network"},"sa":{"href":"Layered queueing network"},"stx":"simple"}'>Layered queueing network</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><td class="navbox-abovebelow" colspan="2" data-parsoid='{"stx":"html"}'><div data-parsoid='{"stx":"html"}'><span typeof="mw:Image" data-mw='{"caption":" Category "}' data-parsoid='{"optList":[{"ck":"caption","ak":" Category "},{"ck":"width","ak":"16px"},{"ck":"link","ak":"link="}],"cacheKey":"[[File:Folder Hexagonal Icon.svg | Category |16px|link=]]","img":{"h":31,"w":36,"wdset":true}}'><span data-parsoid="{}"><img resource="../../File:Folder_Hexagonal_Icon.svg" src="http://upload.wikimedia.org/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/16px-Folder_Hexagonal_Icon.svg.png" height="14" width="16" data-parsoid='{"a":{"resource":"../../File:Folder_Hexagonal_Icon.svg"},"sa":{"resource":"File:Folder Hexagonal Icon.svg "}}'></span></span> <a rel="mw:WikiLink" href="../../Category:Queueing_theory" data-parsoid='{"a":{"href":"../../Category:Queueing_theory"},"sa":{"href":":Category:Queueing theory"},"stx":"piped"}'>Category</a></div></td></tr></tbody></table></td></tr></tbody></table>
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<a rel="mw:WikiLink" href="../../Stochastic_process" data-parsoid='{"a":{"href":"../../Stochastic_process"},"sa":{"href":"Stochastic process"},"stx":"simple","tail":"es"}'>Stochastic processes</a></div></th></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'><a rel="mw:WikiLink" href="../../Discrete-time_stochastic_process" data-parsoid='{"a":{"href":"../../Discrete-time_stochastic_process"},"sa":{"href":"Discrete-time stochastic process"},"stx":"piped"}'>Discrete time</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Bernoulli_process" data-parsoid='{"a":{"href":"../../Bernoulli_process"},"sa":{"href":"Bernoulli process"},"stx":"simple"}'>Bernoulli process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Branching_process" data-parsoid='{"a":{"href":"../../Branching_process"},"sa":{"href":"Branching process"},"stx":"simple"}'>Branching process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Chinese_restaurant_process" data-parsoid='{"a":{"href":"../../Chinese_restaurant_process"},"sa":{"href":"Chinese restaurant process"},"stx":"simple"}'>Chinese restaurant process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Galton–Watson_process" data-parsoid='{"a":{"href":"../../Galton–Watson_process"},"sa":{"href":"Galton–Watson process"},"stx":"simple"}'>Galton–Watson process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Independent_and_identically_distributed_random_variables" data-parsoid='{"a":{"href":"../../Independent_and_identically_distributed_random_variables"},"sa":{"href":"Independent and identically distributed random variables"},"stx":"simple"}'>Independent and identically distributed random variables</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Markov_chain" data-parsoid='{"a":{"href":"../../Markov_chain"},"sa":{"href":"Markov chain"},"stx":"simple"}'>Markov chain</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Moran_process" data-parsoid='{"a":{"href":"../../Moran_process"},"sa":{"href":"Moran process"},"stx":"simple"}'>Moran process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Random_walk" data-parsoid='{"a":{"href":"../../Random_walk"},"sa":{"href":"Random walk"},"stx":"simple"}'>Random walk</a>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Loop-erased_random_walk" data-parsoid='{"a":{"href":"../../Loop-erased_random_walk"},"sa":{"href":"Loop-erased random walk"},"stx":"piped"}'>Loop-erased</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Self-avoiding_walk" data-parsoid='{"a":{"href":"../../Self-avoiding_walk"},"sa":{"href":"Self-avoiding walk"},"stx":"piped"}'>Self-avoiding</a></li></ul></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'><a rel="mw:WikiLink" href="../../Continuous-time_stochastic_process" data-parsoid='{"a":{"href":"../../Continuous-time_stochastic_process"},"sa":{"href":"Continuous-time stochastic process"},"stx":"piped"}'>Continuous time</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Bessel_process" data-parsoid='{"a":{"href":"../../Bessel_process"},"sa":{"href":"Bessel process"},"stx":"simple"}'>Bessel process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Birth–death_process" data-parsoid='{"a":{"href":"../../Birth–death_process"},"sa":{"href":"Birth–death process"},"stx":"simple"}'>Birth–death process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Wiener_process" data-parsoid='{"a":{"href":"../../Wiener_process"},"sa":{"href":"Wiener process"},"stx":"piped"}'>Brownian motion</a>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Brownian_bridge" data-parsoid='{"a":{"href":"../../Brownian_bridge"},"sa":{"href":"Brownian bridge"},"stx":"piped"}'>Bridge</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Brownian_excursion" data-parsoid='{"a":{"href":"../../Brownian_excursion"},"sa":{"href":"Brownian excursion"},"stx":"piped"}'>Excursion</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Fractional_Brownian_motion" data-parsoid='{"a":{"href":"../../Fractional_Brownian_motion"},"sa":{"href":"Fractional Brownian motion"},"stx":"piped"}'>Fractional</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Geometric_Brownian_motion" data-parsoid='{"a":{"href":"../../Geometric_Brownian_motion"},"sa":{"href":"Geometric Brownian motion"},"stx":"piped"}'>Geometric</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Brownian_meander" data-parsoid='{"a":{"href":"../../Brownian_meander"},"sa":{"href":"Brownian meander"},"stx":"piped"}'>Meander</a></li></ul></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Cauchy_process" data-parsoid='{"a":{"href":"../../Cauchy_process"},"sa":{"href":"Cauchy process"},"stx":"simple"}'>Cauchy process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Contact_process_(mathematics)" data-parsoid='{"a":{"href":"../../Contact_process_(mathematics)"},"sa":{"href":"Contact process (mathematics)"},"stx":"piped"}'>Contact process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Cox_process" data-parsoid='{"a":{"href":"../../Cox_process"},"sa":{"href":"Cox process"},"stx":"simple"}'>Cox process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Diffusion_process" data-parsoid='{"a":{"href":"../../Diffusion_process"},"sa":{"href":"Diffusion process"},"stx":"simple"}'>Diffusion process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Empirical_process" data-parsoid='{"a":{"href":"../../Empirical_process"},"sa":{"href":"Empirical process"},"stx":"simple"}'>Empirical process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Feller_process" data-parsoid='{"a":{"href":"../../Feller_process"},"sa":{"href":"Feller process"},"stx":"simple"}'>Feller process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Fleming–Viot_process" data-parsoid='{"a":{"href":"../../Fleming–Viot_process"},"sa":{"href":"Fleming–Viot process"},"stx":"simple"}'>Fleming–Viot process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Gamma_process" data-parsoid='{"a":{"href":"../../Gamma_process"},"sa":{"href":"Gamma process"},"stx":"simple"}'>Gamma process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Hunt_process" data-parsoid='{"a":{"href":"../../Hunt_process"},"sa":{"href":"Hunt process"},"stx":"simple"}'>Hunt process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Interacting_particle_system" data-parsoid='{"a":{"href":"../../Interacting_particle_system"},"sa":{"href":"Interacting particle system"},"stx":"simple","tail":"s"}'>Interacting particle systems</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Itō_diffusion" data-parsoid='{"a":{"href":"../../Itō_diffusion"},"sa":{"href":"Itō diffusion"},"stx":"simple"}'>Itō diffusion</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Itō_process" data-parsoid='{"a":{"href":"../../Itō_process"},"sa":{"href":"Itō process"},"stx":"simple"}'>Itō process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Jump_diffusion" data-parsoid='{"a":{"href":"../../Jump_diffusion"},"sa":{"href":"Jump diffusion"},"stx":"simple"}'>Jump diffusion</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Jump_process" data-parsoid='{"a":{"href":"../../Jump_process"},"sa":{"href":"Jump process"},"stx":"simple"}'>Jump process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Lévy_process" data-parsoid='{"a":{"href":"../../Lévy_process"},"sa":{"href":"Lévy process"},"stx":"simple"}'>Lévy process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Local_time_(mathematics)" data-parsoid='{"a":{"href":"../../Local_time_(mathematics)"},"sa":{"href":"Local time (mathematics)"},"stx":"piped"}'>Local time</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Markov_additive_process" data-parsoid='{"a":{"href":"../../Markov_additive_process"},"sa":{"href":"Markov additive process"},"stx":"simple"}'>Markov additive process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../McKean–Vlasov_process" data-parsoid='{"a":{"href":"../../McKean–Vlasov_process"},"sa":{"href":"McKean–Vlasov process"},"stx":"simple"}'>McKean–Vlasov process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Ornstein–Uhlenbeck_process" data-parsoid='{"a":{"href":"../../Ornstein–Uhlenbeck_process"},"sa":{"href":"Ornstein–Uhlenbeck process"},"stx":"simple"}'>Ornstein–Uhlenbeck process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Poisson_process" data-parsoid='{"a":{"href":"../../Poisson_process"},"sa":{"href":"Poisson process"},"stx":"simple"}'>Poisson process</a>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Compound_Poisson_process" data-parsoid='{"a":{"href":"../../Compound_Poisson_process"},"sa":{"href":"Compound Poisson process"},"stx":"piped"}'>Compound</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Non-homogeneous_Poisson_process" data-parsoid='{"a":{"href":"../../Non-homogeneous_Poisson_process"},"sa":{"href":"Non-homogeneous Poisson process"},"stx":"piped"}'>Non-homogeneous</a></li></ul></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Schramm–Loewner_evolution" data-parsoid='{"a":{"href":"../../Schramm–Loewner_evolution"},"sa":{"href":"Schramm–Loewner evolution"},"stx":"simple"}'>Schramm–Loewner evolution</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Semimartingale" data-parsoid='{"a":{"href":"../../Semimartingale"},"sa":{"href":"Semimartingale"},"stx":"simple"}'>Semimartingale</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Sigma-martingale" data-parsoid='{"a":{"href":"../../Sigma-martingale"},"sa":{"href":"Sigma-martingale"},"stx":"simple"}'>Sigma-martingale</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Stable_process" data-parsoid='{"a":{"href":"../../Stable_process"},"sa":{"href":"Stable process"},"stx":"simple"}'>Stable process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Superprocess" data-parsoid='{"a":{"href":"../../Superprocess"},"sa":{"href":"Superprocess"},"stx":"simple"}'>Superprocess</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Telegraph_process" data-parsoid='{"a":{"href":"../../Telegraph_process"},"sa":{"href":"Telegraph process"},"stx":"simple"}'>Telegraph process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Variance_gamma_process" data-parsoid='{"a":{"href":"../../Variance_gamma_process"},"sa":{"href":"Variance gamma process"},"stx":"simple"}'>Variance gamma process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Wiener_process" data-parsoid='{"a":{"href":"../../Wiener_process"},"sa":{"href":"Wiener process"},"stx":"simple"}'>Wiener process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Wiener_sausage" data-parsoid='{"a":{"href":"../../Wiener_sausage"},"sa":{"href":"Wiener sausage"},"stx":"simple"}'>Wiener sausage</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Both</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Branching_process" data-parsoid='{"a":{"href":"../../Branching_process"},"sa":{"href":"Branching process"},"stx":"simple"}'>Branching process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Gaussian_process" data-parsoid='{"a":{"href":"../../Gaussian_process"},"sa":{"href":"Gaussian process"},"stx":"simple"}'>Gaussian process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Hidden_Markov_model" data-parsoid='{"a":{"href":"../../Hidden_Markov_model"},"sa":{"href":"Hidden Markov model"},"stx":"piped"}'>Hidden Markov model (HMM)</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Markov_process" data-parsoid='{"a":{"href":"../../Markov_process"},"sa":{"href":"Markov process"},"stx":"simple"}'>Markov process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Martingale_(probability_theory)" data-parsoid='{"a":{"href":"../../Martingale_(probability_theory)"},"sa":{"href":"Martingale (probability theory)"},"stx":"piped"}'>Martingale</a>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Martingale_difference_sequence" data-parsoid='{"a":{"href":"../../Martingale_difference_sequence"},"sa":{"href":"Martingale difference sequence"},"stx":"piped"}'>Differences</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Local_martingale" data-parsoid='{"a":{"href":"../../Local_martingale"},"sa":{"href":"Local martingale"},"stx":"piped"}'>Local</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Submartingale" data-parsoid='{"a":{"href":"../../Submartingale"},"sa":{"href":"Submartingale"},"stx":"piped"}'>Sub-</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Supermartingale" data-parsoid='{"a":{"href":"../../Supermartingale"},"sa":{"href":"Supermartingale"},"stx":"piped"}'>Super-</a></li></ul></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Random_dynamical_system" data-parsoid='{"a":{"href":"../../Random_dynamical_system"},"sa":{"href":"Random dynamical system"},"stx":"simple"}'>Random dynamical system</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Regenerative_process" data-parsoid='{"a":{"href":"../../Regenerative_process"},"sa":{"href":"Regenerative process"},"stx":"simple"}'>Regenerative process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Renewal_process" data-parsoid='{"a":{"href":"../../Renewal_process"},"sa":{"href":"Renewal process"},"stx":"simple"}'>Renewal process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../White_noise" data-parsoid='{"a":{"href":"../../White_noise"},"sa":{"href":"White noise"},"stx":"simple"}'>White noise</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Fields and other</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Dirichlet_process" data-parsoid='{"a":{"href":"../../Dirichlet_process"},"sa":{"href":"Dirichlet process"},"stx":"simple"}'>Dirichlet process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Gaussian_random_field" data-parsoid='{"a":{"href":"../../Gaussian_random_field"},"sa":{"href":"Gaussian random field"},"stx":"simple"}'>Gaussian random field</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Gibbs_measure" data-parsoid='{"a":{"href":"../../Gibbs_measure"},"sa":{"href":"Gibbs measure"},"stx":"simple"}'>Gibbs measure</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Hopfield_model" data-parsoid='{"a":{"href":"../../Hopfield_model"},"sa":{"href":"Hopfield model"},"stx":"simple"}'>Hopfield model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Ising_model" data-parsoid='{"a":{"href":"../../Ising_model"},"sa":{"href":"Ising model"},"stx":"simple"}'>Ising model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Markov_random_field" data-parsoid='{"a":{"href":"../../Markov_random_field"},"sa":{"href":"Markov random field"},"stx":"simple"}'>Markov random field</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Percolation_theory" data-parsoid='{"a":{"href":"../../Percolation_theory"},"sa":{"href":"Percolation theory"},"stx":"piped"}'>Percolation</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Pitman–Yor_process" data-parsoid='{"a":{"href":"../../Pitman–Yor_process"},"sa":{"href":"Pitman–Yor process"},"stx":"simple"}'>Pitman–Yor process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Point_process" data-parsoid='{"a":{"href":"../../Point_process"},"sa":{"href":"Point process"},"stx":"simple"}'>Point process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Potts_model" data-parsoid='{"a":{"href":"../../Potts_model"},"sa":{"href":"Potts model"},"stx":"simple"}'>Potts model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Random_field" data-parsoid='{"a":{"href":"../../Random_field"},"sa":{"href":"Random field"},"stx":"simple"}'>Random field</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Random_graph" data-parsoid='{"a":{"href":"../../Random_graph"},"sa":{"href":"Random graph"},"stx":"simple"}'>Random graph</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'><a rel="mw:WikiLink" href="../../Time_series" data-parsoid='{"a":{"href":"../../Time_series"},"sa":{"href":"Time series"},"stx":"piped"}'>Time series models</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Autoregressive_conditional_heteroskedasticity" data-parsoid='{"a":{"href":"../../Autoregressive_conditional_heteroskedasticity"},"sa":{"href":"Autoregressive conditional heteroskedasticity"},"stx":"piped"}'>Autoregressive conditional heteroskedasticity (ARCH) model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Autoregressive_integrated_moving_average" data-parsoid='{"a":{"href":"../../Autoregressive_integrated_moving_average"},"sa":{"href":"Autoregressive integrated moving average"},"stx":"piped"}'>Autoregressive integrated moving average (ARIMA) model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Autoregressive_model" data-parsoid='{"a":{"href":"../../Autoregressive_model"},"sa":{"href":"Autoregressive model"},"stx":"piped"}'>Autoregressive (AR) model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Autoregressive–moving-average_model" data-parsoid='{"a":{"href":"../../Autoregressive–moving-average_model"},"sa":{"href":"Autoregressive–moving-average model"},"stx":"piped"}'>Autoregressive–moving-average (ARMA) model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../GARCH" data-parsoid='{"a":{"href":"../../GARCH"},"sa":{"href":"GARCH"},"stx":"piped"}'>Generalized autoregressive conditional heteroskedasticity (GARCH) model</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Moving-average_model" data-parsoid='{"a":{"href":"../../Moving-average_model"},"sa":{"href":"Moving-average model"},"stx":"piped"}'>Moving-average (MA) model</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Financial models</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Black–Derman–Toy_model" data-parsoid='{"a":{"href":"../../Black–Derman–Toy_model"},"sa":{"href":"Black–Derman–Toy model"},"stx":"piped"}'>Black–Derman–Toy</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Black–Karasinski_model" data-parsoid='{"a":{"href":"../../Black–Karasinski_model"},"sa":{"href":"Black–Karasinski model"},"stx":"piped"}'>Black–Karasinski</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Black–Scholes_model" data-parsoid='{"a":{"href":"../../Black–Scholes_model"},"sa":{"href":"Black–Scholes model"},"stx":"piped"}'>Black–Scholes–Samuelson</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Chen_model" data-parsoid='{"a":{"href":"../../Chen_model"},"sa":{"href":"Chen model"},"stx":"piped"}'>Chen</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Constant_elasticity_of_variance_model" data-parsoid='{"a":{"href":"../../Constant_elasticity_of_variance_model"},"sa":{"href":"Constant elasticity of variance model"},"stx":"piped"}'>Constant elasticity of variance (CEV)</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Cox–Ingersoll–Ross_model" data-parsoid='{"a":{"href":"../../Cox–Ingersoll–Ross_model"},"sa":{"href":"Cox–Ingersoll–Ross model"},"stx":"piped"}'>Cox–Ingersoll–Ross (CIR)</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Garman–Kohlhagen_model" data-parsoid='{"a":{"href":"../../Garman–Kohlhagen_model"},"sa":{"href":"Garman–Kohlhagen model"},"stx":"piped"}'>Garman–Kohlhagen</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Heath–Jarrow–Morton_framework" data-parsoid='{"a":{"href":"../../Heath–Jarrow–Morton_framework"},"sa":{"href":"Heath–Jarrow–Morton framework"},"stx":"piped"}'>Heath–Jarrow–Morton (HJM)</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Heston_model" data-parsoid='{"a":{"href":"../../Heston_model"},"sa":{"href":"Heston model"},"stx":"piped"}'>Heston</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Ho–Lee_model" data-parsoid='{"a":{"href":"../../Ho–Lee_model"},"sa":{"href":"Ho–Lee model"},"stx":"piped"}'>Ho–Lee</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Hull–White_model" data-parsoid='{"a":{"href":"../../Hull–White_model"},"sa":{"href":"Hull–White model"},"stx":"piped"}'>Hull–White</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../LIBOR_market_model" data-parsoid='{"a":{"href":"../../LIBOR_market_model"},"sa":{"href":"LIBOR market model"},"stx":"piped"}'>LIBOR market</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../SABR_volatility_model" data-parsoid='{"a":{"href":"../../SABR_volatility_model"},"sa":{"href":"SABR volatility model"},"stx":"piped"}'>SABR volatility</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Vasicek_model" data-parsoid='{"a":{"href":"../../Vasicek_model"},"sa":{"href":"Vasicek model"},"stx":"piped"}'>Vašícek</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'><a rel="mw:WikiLink" href="../../Actuarial_mathematics" data-parsoid='{"a":{"href":"../../Actuarial_mathematics"},"sa":{"href":"Actuarial mathematics"},"stx":"piped"}'>Actuarial models</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Bühlmann_model" data-parsoid='{"a":{"href":"../../Bühlmann_model"},"sa":{"href":"Bühlmann model"},"stx":"piped"}'>Bühlmann</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Cramér–Lundberg_model" data-parsoid='{"a":{"href":"../../Cramér–Lundberg_model"},"sa":{"href":"Cramér–Lundberg model"},"stx":"piped"}'>Cramér–Lundberg</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Risk_process" data-parsoid='{"a":{"href":"../../Risk_process"},"sa":{"href":"Risk process"},"stx":"simple"}'>Risk process</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Sparre–Anderson_model" data-parsoid='{"a":{"href":"../../Sparre–Anderson_model"},"sa":{"href":"Sparre–Anderson model"},"stx":"piped"}'>Sparre–Anderson</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'><a rel="mw:WikiLink" href="../../Queueing_model" data-parsoid='{"a":{"href":"../../Queueing_model"},"sa":{"href":"Queueing model"},"stx":"simple","tail":"s"}'>Queueing models</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Bulk_queue" data-parsoid='{"a":{"href":"../../Bulk_queue"},"sa":{"href":"Bulk queue"},"stx":"piped"}'>Bulk</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Fluid_queue" data-parsoid='{"a":{"href":"../../Fluid_queue"},"sa":{"href":"Fluid queue"},"stx":"piped"}'>Fluid</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../G-network" data-parsoid='{"a":{"href":"../../G-network"},"sa":{"href":"G-network"},"stx":"piped"}'>Generalized queueing network</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../M/G/1_queue" data-parsoid='{"a":{"href":"../../M/G/1_queue"},"sa":{"href":"M/G/1 queue"},"stx":"piped"}'>M/G/1</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../M/M/1_queue" data-parsoid='{"a":{"href":"../../M/M/1_queue"},"sa":{"href":"M/M/1 queue"},"stx":"piped"}'>M/M/1</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../M/M/c_queue" data-parsoid='{"a":{"href":"../../M/M/c_queue"},"sa":{"href":"M/M/c queue"},"stx":"piped"}'>M/M/c</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Properties</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Càdlàg" data-parsoid='{"a":{"href":"../../Càdlàg"},"sa":{"href":"Càdlàg"},"stx":"piped"}'>Càdlàg paths</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Continuous_stochastic_process" data-parsoid='{"a":{"href":"../../Continuous_stochastic_process"},"sa":{"href":"Continuous stochastic process"},"stx":"piped"}'>Continuous</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Sample-continuous_process" data-parsoid='{"a":{"href":"../../Sample-continuous_process"},"sa":{"href":"Sample-continuous process"},"stx":"piped"}'>Continuous paths</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Ergodicity" data-parsoid='{"a":{"href":"../../Ergodicity"},"sa":{"href":"Ergodicity"},"stx":"piped"}'>Ergodic</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Exchangeable_random_variables" data-parsoid='{"a":{"href":"../../Exchangeable_random_variables"},"sa":{"href":"Exchangeable random variables"},"stx":"piped"}'>Exchangeable</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Feller-continuous_process" data-parsoid='{"a":{"href":"../../Feller-continuous_process"},"sa":{"href":"Feller-continuous process"},"stx":"piped"}'>Feller-continuous</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Gauss–Markov_process" data-parsoid='{"a":{"href":"../../Gauss–Markov_process"},"sa":{"href":"Gauss–Markov process"},"stx":"piped"}'>Gauss–Markov</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Markov_property" data-parsoid='{"a":{"href":"../../Markov_property"},"sa":{"href":"Markov property"},"stx":"piped"}'>Markov</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Mixing_(mathematics)" data-parsoid='{"a":{"href":"../../Mixing_(mathematics)"},"sa":{"href":"Mixing (mathematics)"},"stx":"piped"}'>Mixing</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Piecewise_deterministic_Markov_process" data-parsoid='{"a":{"href":"../../Piecewise_deterministic_Markov_process"},"sa":{"href":"Piecewise deterministic Markov process"},"stx":"piped"}'>Piecewise deterministic</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Predictable_process" data-parsoid='{"a":{"href":"../../Predictable_process"},"sa":{"href":"Predictable process"},"stx":"piped"}'>Predictable</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Progressively_measurable_process" data-parsoid='{"a":{"href":"../../Progressively_measurable_process"},"sa":{"href":"Progressively measurable process"},"stx":"piped"}'>Progressively measurable</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Self-similar_process" data-parsoid='{"a":{"href":"../../Self-similar_process"},"sa":{"href":"Self-similar process"},"stx":"piped"}'>Self-similar</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Stationary_process" data-parsoid='{"a":{"href":"../../Stationary_process"},"sa":{"href":"Stationary process"},"stx":"piped"}'>Stationary</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Time_reversibility" data-parsoid='{"a":{"href":"../../Time_reversibility"},"sa":{"href":"Time reversibility"},"stx":"piped"}'>Time-reversible</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Limit theorems</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Central_limit_theorem" data-parsoid='{"a":{"href":"../../Central_limit_theorem"},"sa":{"href":"Central limit theorem"},"stx":"simple"}'>Central limit theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Donsker's_theorem" data-parsoid='{"a":{"href":"../../Donsker&#39;s_theorem"},"sa":{"href":"Donsker&#39;s theorem"},"stx":"simple"}'>Donsker's theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Doob's_martingale_convergence_theorems" data-parsoid='{"a":{"href":"../../Doob&#39;s_martingale_convergence_theorems"},"sa":{"href":"Doob&#39;s martingale convergence theorems"},"stx":"simple"}'>Doob's martingale convergence theorems</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Ergodic_theorem" data-parsoid='{"a":{"href":"../../Ergodic_theorem"},"sa":{"href":"Ergodic theorem"},"stx":"simple"}'>Ergodic theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Fisher–Tippett–Gnedenko_theorem" data-parsoid='{"a":{"href":"../../Fisher–Tippett–Gnedenko_theorem"},"sa":{"href":"Fisher–Tippett–Gnedenko theorem"},"stx":"simple"}'>Fisher–Tippett–Gnedenko theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Large_deviation_principle" data-parsoid='{"a":{"href":"../../Large_deviation_principle"},"sa":{"href":"Large deviation principle"},"stx":"simple"}'>Large deviation principle</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Law_of_large_numbers" data-parsoid='{"a":{"href":"../../Law_of_large_numbers"},"sa":{"href":"Law of large numbers"},"stx":"piped"}'>Law of large numbers (weak/strong)</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Law_of_the_iterated_logarithm" data-parsoid='{"a":{"href":"../../Law_of_the_iterated_logarithm"},"sa":{"href":"Law of the iterated logarithm"},"stx":"simple"}'>Law of the iterated logarithm</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Maximal_ergodic_theorem" data-parsoid='{"a":{"href":"../../Maximal_ergodic_theorem"},"sa":{"href":"Maximal ergodic theorem"},"stx":"simple"}'>Maximal ergodic theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Sanov's_theorem" data-parsoid='{"a":{"href":"../../Sanov&#39;s_theorem"},"sa":{"href":"Sanov&#39;s theorem"},"stx":"simple"}'>Sanov's theorem</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'><a rel="mw:WikiLink" href="../../List_of_inequalities#Probability_theory_and_statistics" data-parsoid='{"a":{"href":"../../List_of_inequalities#Probability_theory_and_statistics"},"sa":{"href":"List of inequalities#Probability theory and statistics"},"stx":"piped"}'>Inequalities</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Burkholder–Davis–Gundy_inequalities" data-parsoid='{"a":{"href":"../../Burkholder–Davis–Gundy_inequalities"},"sa":{"href":"Burkholder–Davis–Gundy inequalities"},"stx":"piped"}'>Burkholder–Davis–Gundy</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Doob's_martingale_inequality" data-parsoid='{"a":{"href":"../../Doob&#39;s_martingale_inequality"},"sa":{"href":"Doob&#39;s martingale inequality"},"stx":"piped"}'>Doob's martingale</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Kunita–Watanabe_inequality" data-parsoid='{"a":{"href":"../../Kunita–Watanabe_inequality"},"sa":{"href":"Kunita–Watanabe inequality"},"stx":"piped"}'>Kunita–Watanabe</a></li></ul></div></td></tr><tr style="height:2px;" data-parsoid='{"stx":"html"}'><td data-parsoid='{"stx":"html"}'></td></tr><tr data-parsoid='{"stx":"html"}'><th scope="row" class="navbox-group" data-parsoid='{"stx":"html"}'>Tools</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;" data-parsoid='{"stx":"html"}'><div style="padding:0em 0.25em;" data-parsoid='{"stx":"html"}'>
<ul data-parsoid="{}"><li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Cameron–Martin_formula" data-parsoid='{"a":{"href":"../../Cameron–Martin_formula"},"sa":{"href":"Cameron–Martin formula"},"stx":"simple"}'>Cameron–Martin formula</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Convergence_of_random_variables" data-parsoid='{"a":{"href":"../../Convergence_of_random_variables"},"sa":{"href":"Convergence of random variables"},"stx":"simple"}'>Convergence of random variables</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Doléans-Dade_exponential" data-parsoid='{"a":{"href":"../../Doléans-Dade_exponential"},"sa":{"href":"Doléans-Dade exponential"},"stx":"simple"}'>Doléans-Dade exponential</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Doob_decomposition_theorem" data-parsoid='{"a":{"href":"../../Doob_decomposition_theorem"},"sa":{"href":"Doob decomposition theorem"},"stx":"simple"}'>Doob decomposition theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Doob–Meyer_decomposition_theorem" data-parsoid='{"a":{"href":"../../Doob–Meyer_decomposition_theorem"},"sa":{"href":"Doob–Meyer decomposition theorem"},"stx":"simple"}'>Doob–Meyer decomposition theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Doob's_optional_stopping_theorem" data-parsoid='{"a":{"href":"../../Doob&#39;s_optional_stopping_theorem"},"sa":{"href":"Doob&#39;s optional stopping theorem"},"stx":"simple"}'>Doob's optional stopping theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Dynkin's_formula" data-parsoid='{"a":{"href":"../../Dynkin&#39;s_formula"},"sa":{"href":"Dynkin&#39;s formula"},"stx":"simple"}'>Dynkin's formula</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Feynman–Kac_formula" data-parsoid='{"a":{"href":"../../Feynman–Kac_formula"},"sa":{"href":"Feynman–Kac formula"},"stx":"simple"}'>Feynman–Kac formula</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Filtration_(mathematics)#Measure_theory" data-parsoid='{"a":{"href":"../../Filtration_(mathematics)#Measure_theory"},"sa":{"href":"Filtration (mathematics)#Measure theory"},"stx":"piped"}'>Filtration</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Girsanov_theorem" data-parsoid='{"a":{"href":"../../Girsanov_theorem"},"sa":{"href":"Girsanov theorem"},"stx":"simple"}'>Girsanov theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Infinitesimal_generator_(stochastic_processes)" data-parsoid='{"a":{"href":"../../Infinitesimal_generator_(stochastic_processes)"},"sa":{"href":"Infinitesimal generator (stochastic processes)"},"stx":"piped"}'>Infinitesimal generator</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Itō_integral" data-parsoid='{"a":{"href":"../../Itō_integral"},"sa":{"href":"Itō integral"},"stx":"simple"}'>Itō integral</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Itō's_lemma" data-parsoid='{"a":{"href":"../../Itō&#39;s_lemma"},"sa":{"href":"Itō&#39;s lemma"},"stx":"simple"}'>Itō's lemma</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Kolmogorov_continuity_theorem" data-parsoid='{"a":{"href":"../../Kolmogorov_continuity_theorem"},"sa":{"href":"Kolmogorov continuity theorem"},"stx":"simple"}'>Kolmogorov continuity theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Kolmogorov_extension_theorem" data-parsoid='{"a":{"href":"../../Kolmogorov_extension_theorem"},"sa":{"href":"Kolmogorov extension theorem"},"stx":"simple"}'>Kolmogorov extension theorem</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Lévy–Prokhorov_metric" data-parsoid='{"a":{"href":"../../Lévy–Prokhorov_metric"},"sa":{"href":"Lévy–Prokhorov metric"},"stx":"simple"}'>Lévy–Prokhorov metric</a></li>
<li data-parsoid="{}"> <a rel="mw:WikiLink" href="../../Malliavin_calculus" data-parsoid='{"a":{"href":"../../Malliavin_calculus"},"sa":{"href":"Malliavin calculus"},"stx":"simple"}'>Malliavin calculus</a></li>
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