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 M/D/c queue represents the queue length in a system having c 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's_notation"},"sa":{"href":"Kendall'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=\"{"src":"Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1214/aoms/1177728975, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1214/aoms/1177728975 instead.","dsr":[351,387,null,null]}\" about=\"#mwt7\" typeof=\"mw:Transclusion\" data-mw=\"{"target":{"wt":"cite doi","href":"../../Template:Cite_doi"},"params":{"1":{"wt":"10.1214/aoms/1177728975"}}}\"><a rel=\"mw:WikiLink\" href=\"../../David_George_Kendall\" data-parsoid=\"{"a":{"href":"../../David_George_Kendall"},"sa":{"href":"David George Kendall"},"stx":"piped"}\">Kendall, D. G.</a> (1953). \"Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain\". The Annals of Mathematical Statistics24 (3): 338. <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/10.1214%2Faoms%2F1177728975\" data-parsoid=\"{"targetOff":342,"a":{"href":"http://dx.doi.org/10.1214%2Faoms%2F1177728975"},"sa":{"href":"e model name is written in [[Kendall's notati"}}\">10.1214/aoms/1177728975</a>. <a rel=\"mw:WikiLink\" href=\"../../JSTOR\" data-parsoid=\"{"a":{"href":"../../JSTOR"},"sa":{"href":"JSTOR"},"stx":"piped"}\">JSTOR</a> <a rel=\"mw:ExtLink\" href=\"http://www.jstor.org/stable/2236285\" data-parsoid=\"{"targetOff":426,"a":{"href":"http://www.jstor.org/stable/2236285"},"sa":{"href":"ef> Agner Krarup Erlang first p"}}\">2236285</a>. <a rel=\"mw:ExtLink\" href=\"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1214.2Faoms.2F1177728975&action=edit&editintro=Template:Cite_doi/editintro2\" data-parsoid=\"{"targetOff":1215,"a":{"href":"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1214.2Faoms.2F1177728975&action=edit&editintro=Template:Cite_doi/editintro2"},"sa":{"href":"urrently in service. \\n\\n* Arrivals occur at rate λ according to a Poisson process and move the process from state ''i'' to ''i''&n"}}\">edit</a>"},"attrs":{}}' id="cite_ref-1-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"[1]","dsr":[346,393,5,6]}'><a href="#cite_note-1">[1]</a> <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=\"{"src":"Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/s11134-009-9147-4, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1007/s11134-009-9147-4 instead.","dsr":[506,544,null,null]}\" about=\"#mwt8\" typeof=\"mw:Transclusion\" data-mw=\"{"target":{"wt":"cite doi","href":"../../Template:Cite_doi"},"params":{"1":{"wt":"10.1007/s11134-009-9147-4"}}}\"><a rel=\"mw:WikiLink\" href=\"../../John_Kingman\" data-parsoid=\"{"a":{"href":"../../John_Kingman"},"sa":{"href":"John Kingman"},"stx":"piped"}\">Kingman, J. F. C.</a> (2009). \"The first Erlang century—and the next\". Queueing Systems63: 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>. <a rel=\"mw:ExtLink\" href=\"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1007.2Fs11134-009-9147-4&action=edit&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&action=edit&editintro=Template:Cite_doi/editintro2"},"sa":{"href":"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/''c'' queue is a s"}}\">edit</a>"},"attrs":{}}' id="cite_ref-2-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"[2]","dsr":[501,550,5,6]}'><a href="#cite_note-2">[2]</a><span about="#mwt6" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{"src":""The theory of probabilities and telephone conversations"(PDF). Nyt Tidsskrift for Matematik B. 20: 33–39. 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>. Nyt Tidsskrift for Matematik B20: 33–39. 1909. "},"attrs":{}}' id="cite_ref-3-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"[3]","dsr":[550,801,5,6]}'><a href="#cite_note-3">[3]</a> 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.
Model definition
An M/D/c 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.
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 to i+1.
Service times are deterministic time D (serving at rate μ=1/D).
c 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.
The buffer is of infinite size, so there is no limit on the number of customers it can contain.
Waiting time distribution
Erlang showed that when ρ=λD/c<1, the waiting time distribution has distribution F(y) given by<span about="#mwt11" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{"src":"Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1016/S0167-6377(01)00108-0, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1016/S0167-6377(01)00108-0 instead.","dsr":[1844,1886,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\". Operations Research Letters29 (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>. <a rel=\"mw:ExtLink\" href=\"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1016.2FS0167-6377.2801.2900108-0&action=edit&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&action=edit&editintro=Template:Cite_doi/editintro2"},"sa":{"href":"single server.\\n\\n==Model definition==\\n\\nAn M/D/''c'' queue is a stochastic process whose state space is the set {0,1,2,3,...} where the val"}}\">edit</a>"},"attrs":{"name":"franx"}}' id="cite_ref-franx-4-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"[4]","dsr":[1826,1892,18,6]}'><a href="#cite_note-franx-4">[4]</a>
<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="/media/math/d/0/f/d0f83f237a48a605b1eca5df7a08fd3b.png" typeof="mw:Extension/math" data-parsoid='{"src":"Failed to parse (syntax error): {\displaystyle 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.}
","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">
Crommelin showed that, writing Pn for the stationary probability of a system with n or fewer customers,
<span about="#mwt16" class="reference" data-mw='{"name":"ref","body":{"html":"<span class=\"citation journal\" data-parsoid=\"{"src":"Crommelin, C.D. (1932). "Delay probability formulas when the holding times are constant". P.O. Electr. Engr. J. 25: 41–50.","dsr":[2169,2364,null,null]}\" about=\"#mwt17\" 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\". P.O. Electr. Engr. J.25: 41–50. "},"attrs":{}}' id="cite_ref-5-0" rel="dc:references" typeof="mw:Extension/ref" data-parsoid='{"src":"[5]","dsr":[2164,2370,5,6]}'><a href="#cite_note-5">[5]</a>
^Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1214/aoms/1177728975, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1214/aoms/1177728975 instead.
^Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/s11134-009-9147-4, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1007/s11134-009-9147-4 instead.
^Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1016/S0167-6377(01)00108-0, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1016/S0167-6377(01)00108-0 instead.
^Crommelin, C.D. (1932). "Delay probability formulas when the holding times are constant". P.O. Electr. Engr. J. 25: 41–50.
<a href="#cite_ref-1-0">↑</a><span class="citation journal" data-parsoid='{"src":"Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1214/aoms/1177728975, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1214/aoms/1177728975 instead.","dsr":[351,387,null,null]}' about="#mwt7" typeof="mw:Transclusion" data-mw='{"target":{"wt":"cite doi","href":"../../Template:Cite_doi"},"params":{"1":{"wt":"10.1214/aoms/1177728975"}}}'><a rel="mw:WikiLink" href="../../David_George_Kendall" data-parsoid='{"a":{"href":"../../David_George_Kendall"},"sa":{"href":"David George Kendall"},"stx":"piped"}'>Kendall, D. G.</a> (1953). "Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain". The Annals of Mathematical Statistics24 (3): 338. <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/10.1214%2Faoms%2F1177728975" data-parsoid='{"targetOff":342,"a":{"href":"http://dx.doi.org/10.1214%2Faoms%2F1177728975"},"sa":{"href":"e model name is written in [[Kendall's notati"}}'>10.1214/aoms/1177728975</a>. <a rel="mw:WikiLink" href="../../JSTOR" data-parsoid='{"a":{"href":"../../JSTOR"},"sa":{"href":"JSTOR"},"stx":"piped"}'>JSTOR</a><a rel="mw:ExtLink" href="http://www.jstor.org/stable/2236285" data-parsoid='{"targetOff":426,"a":{"href":"http://www.jstor.org/stable/2236285"},"sa":{"href":"ef> Agner Krarup Erlang first p"}}'>2236285</a>. <a rel="mw:ExtLink" href="/w/index.php?title=Template:Cite_doi/10.1214.2Faoms.2F1177728975&action=edit&editintro=Template:Cite_doi/editintro2" data-parsoid='{"targetOff":1215,"a":{"href":"//en.wikipedia.org/w/index.php?title=Template:Cite_doi/10.1214.2Faoms.2F1177728975&action=edit&editintro=Template:Cite_doi/editintro2"},"sa":{"href":"s]] and move the process from state ''i'' to ''i'' + 1.\n* Service times are deterministic time ''D'' (serving at rate ''μ''"}}'>edit</a>
<a href="#cite_ref-2-0">↑</a><span class="citation journal" data-parsoid='{"src":"Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/s11134-009-9147-4, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1007/s11134-009-9147-4 instead.","dsr":[506,544,null,null]}' about="#mwt8" typeof="mw:Transclusion" data-mw='{"target":{"wt":"cite doi","href":"../../Template:Cite_doi"},"params":{"1":{"wt":"10.1007/s11134-009-9147-4"}}}'><a rel="mw:WikiLink" href="../../John_Kingman" data-parsoid='{"a":{"href":"../../John_Kingman"},"sa":{"href":"John Kingman"},"stx":"piped"}'>Kingman, J. F. C.</a> (2009). "The first Erlang century—and the next". Queueing Systems63: 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>. <a rel="mw:ExtLink" href="/w/index.php?title=Template:Cite_doi/10.1007.2Fs11134-009-9147-4&action=edit&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&action=edit&editintro=Template:Cite_doi/editintro2"},"sa":{"href":"ef>\n\n==Model definition==\n\nAn M/D/''c'' queue is a stochastic process whose state space is the set {0,1,2,3,...} where the value "}}'>edit</a>
<a href="#cite_ref-3-0">↑</a><span class="citation journal" data-parsoid='{"src":""The theory of probabilities and telephone conversations"(PDF). Nyt Tidsskrift for Matematik B. 20: 33–39. 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>. Nyt Tidsskrift for Matematik B20: 33–39. 1909.
<a href="#cite_ref-franx-4-0">↑</a><span class="citation journal" data-parsoid='{"src":"Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1016/S0167-6377(01)00108-0, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1016/S0167-6377(01)00108-0 instead.","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". Operations Research Letters29 (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>. <a rel="mw:ExtLink" href="/w/index.php?title=Template:Cite_doi/10.1016.2FS0167-6377.2801.2900108-0&action=edit&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&action=edit&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>
<a href="#cite_ref-5-0">↑</a><span class="citation journal" data-parsoid='{"src":"Crommelin, C.D. (1932). "Delay probability formulas when the holding times are constant". P.O. Electr. Engr. J. 25: 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". P.O. Electr. Engr. J.25: 41–50.
<a rel="mw:WikiLink" href="../../Mean_value_analysis" data-parsoid='{"a":{"href":"../../Mean_value_analysis"},"sa":{"href":"Mean value analysis"},"stx":"simple"}'>Mean value analysis</a>
<a rel="mw:WikiLink" href="../../Flow-equivalent_server_method" data-parsoid='{"a":{"href":"../../Flow-equivalent_server_method"},"sa":{"href":"Flow-equivalent server method"},"stx":"simple"}'>Flow-equivalent server method</a>
<a rel="mw:WikiLink" href="../../Mean_field_theory" data-parsoid='{"a":{"href":"../../Mean_field_theory"},"sa":{"href":"Mean field theory"},"stx":"simple"}'>Mean field theory</a>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<a rel="mw:WikiLink" href="../../Extreme_value_theory" data-parsoid='{"a":{"href":"../../Extreme_value_theory"},"sa":{"href":"Extreme value theory"},"stx":"piped"}'>Extreme value theory (EVT)</a>
<a rel="mw:WikiLink" href="../../Time_series_analysis" data-parsoid='{"a":{"href":"../../Time_series_analysis"},"sa":{"href":"Time series analysis"},"stx":"simple"}'>Time series analysis</a>
<a rel="mw:WikiLink" href="../../List_of_stochastic_processes_topics" data-parsoid='{"a":{"href":"../../List_of_stochastic_processes_topics"},"sa":{"href":"List of stochastic processes topics"},"stx":"piped"}'>List of topics</a>
