Hardy Cross method - Revision history

en>Mehalf at 07:11, 30 September 2014

2014-09-30T07:11:22Z

← Older revision		Revision as of 09:11, 30 September 2014
Line 1:		Line 1:
	In [[queueing theory]], a discipline within the mathematical [[probability theory\|theory of probability]], the '''Gordon–Newell theorem''' is an extension of [[Jackson's theorem (queueing theory)\|Jackson's theorem]] from open queueing networks to closed queueing networks of exponential servers where customers cannot leave the network.<ref>{{cite doi\|10.1287/opre.15.2.254}}</ref> Jackson's theorem cannot be applied to closed networks because the queue length at a node in the closed network is limited by the population of the network. The Gordon–Newell theorem calculates the open network solution and then eliminates the infeasible states by renormalizing the probabilities. Calculation of the [[normalizing constant]] makes the treatment more awkward as the whole state space must be enumerated. [[Buzen's algorithm]] or [[mean value analysis]] can be used to calculate the normalizing constant more efficiently.<ref>{{cite doi\|10.1145/362342.362345}}</ref>		== deti Nike Free Run Dámské ==

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	~~A network of ''m'' interconnected queues is known as~~ a ~~'''Gordon–Newell network'''<ref>{{cite jstor\|1426680}}~~<~~/ref~~> ~~or '''closed Jackson network'''~~<~~ref~~>~~{{cite doi\|10~~.~~1016~~/j.~~ijpe~~.~~2007~~.10.~~013}}~~<~~/ref~~> ~~if it meets the following conditions:~~		<li>[http://pcbbbs.net/read.php?tid=468/read.php?tid=468 http://pcbbbs.net/read.php?tid=468/read.php?tid=468]</li>

	~~# the network is closed~~ (~~no customers can enter or leave the network~~),		<li>[http://www.stgkyb.net/news/html/?80427.html http://www.stgkyb.net/news/html/?80427.html]</li>
	~~# all service times are exponentially distributed and the service discipline at all queues is~~ [~~[FCFS]~~],
	~~# a customer completing service at queue ''i'' will move to queue ''j'' with probability~~ <~~math~~>~~P_{ij}~~<~~/math~~>, ~~with the~~ <~~math~~>~~P_{ij}~~<~~/math~~> ~~such that~~ <~~math~~>~~\scriptstyle{\sum_{j =1}^m P_{ij} = 1}~~</~~math>~~,		<li>[http://mlab.test.quonic.net/wiki/povedal-addedcalifornia-nike-air-max http://mlab.test.quonic.net/wiki/povedal-addedcalifornia-nike-air-max]</li>
	~~# the utilization of all of the queues is less than one~~.
			<li>[http://lab.nqnwebs.com/lavoz_bak/spip.php?article5818/ http://lab.nqnwebs.com/lavoz_bak/spip.php?article5818/]</li>
	~~==Theorem==~~
			<li>[http://gamesvisit.com/activity/p/342723/ http://gamesvisit.com/activity/p/342723/]</li>
	In a ~~closed Gordon–Newell network of ''m'' queues~~, ~~with~~ a ~~total population of ''K'' individuals~~, ~~write~~ <~~math~~>~~\scriptstyle{(k_1~~,~~k_2~~,~~\ldots~~,~~k_m)}~~<~~/math~~> ~~(where ''k''<sub>''i''</sub> is the length of queue ''i'') for the state of the network and ''S''(''K'', ''m'') for the state space~~
			</ul>
	:<~~math~~>~~S(K,m)~~ = ~~\left\{ \mathbf{k} \in \mathbb{Z}^m \text{ such that } \sum_{i~~=~~1}^m k_i~~ = ~~K \text{ and } k_i \geq 0\quad \forall i\right\}~~.</~~math~~>

	~~Then the equilibrium state probability distribution exists and is given by~~

	:<~~math~~>~~\pi (k_1,k_2,\ldots,k_m) = \frac{1}{G(K)} \prod_{i=1}^m \left( \frac{e_i}{\mu_i} \right)^{k_i}~~</~~math~~>

	~~where service times at queue ''i'' are exponentially distributed with parameter ''μ~~<~~sub~~>i</~~sub>''~~. ~~The normalizing constant ''G''(''K'') is given by~~

	:~~<math>G(K) = \sum_{\mathbf{k} \in S(K,m)} \prod_{i=1}^{m} \left( \frac{e_i}{\mu_i} \right)^{k_i} ,~~</~~math~~>

	~~and ''e''~~<~~sub~~>~~''i''<~~/~~sub> is the visit ratio, calculated by solving the simultaneous equations~~

	:~~<math>e_i = \sum_{j=1}^m e_j p_{ji} \text{ for }1 \leq i \leq m~~. \, </~~math~~>

	~~==See also==~~
	*[~~[BCMP network]]~~

	~~==References==~~
	~~{{Reflist}}~~

	~~{{Queueing theory}}~~

	~~{{DEFAULTSORT~~:~~Gordon-Newell theorem}}~~
	~~[[Category~~:~~Stochastic processes]~~]
	~~[[Category:Probability theorems]]~~
	~~[[Category:Queueing theory]]~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-20T17:07:33Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 19:07, 20 January 2014
Line 1:		Line 1:
	~~by Nas~~, is ~~very fitting and~~ the ~~film agrees with it~~. ~~If you have any queries pertaining to exactly where and how to use [http:~~/~~/urlon~~.~~com~~.br/~~wordpress_backup_870920 backup plugin], you can contact us~~ at ~~our own web site. It~~ is ~~very easy to customize plugins according to~~ the ~~needs~~ of ~~a particular business~~. ~~These templates are professionally designed~~ and ~~are also Adsense ready~~. ~~If you are using videos on your site then this is~~ the ~~plugin to use~~. It's ~~as simple as hiring a Wordpress plugin developer~~ or ~~learning how~~ to ~~create what is needed~~. <br><br>~~Creating~~ a ~~website from scratch can be such~~ a ~~pain~~. ~~When you write a new post~~, ~~you'll see a small bar that goes across~~ the ~~text input area. This plugin~~ is a ~~must have for anyone who is serious about using Word - Press. You can up your site~~'~~s rank~~ with the ~~search engines by simply taking a bit of time with your site. The biggest advantage of using a coupon or deal plugin is~~ that ~~it gives your readers the coupons and deals within minutes of them becoming available.~~ <br><br>~~But before choosing any one~~ of ~~these, let's compare between~~ the ~~two~~. ~~Word - Press has different exciting features including~~ a ~~plug-in architecture~~ with a ~~templating system. We can active Akismet from wp-admin~~ > ~~Plugins~~ > ~~Installed Plugins. The animation can be quite subtle these as snow falling gently or some twinkling start in~~ the ~~track record which are essentially not distracting but as an alternative gives some viewing enjoyment~~ for the ~~visitor~~ of the ~~internet site. Converting HTML to Word - Press theme~~ for ~~your website can allow you to enjoy~~ the ~~varied Word - Press features~~ that ~~aid in consistent growth your online business~~. <br><br>~~Numerous bloggers are utilizing Word - Press and with good reason. And~~, ~~make no mistake~~,~~India~~'~~s Fertility Clinics and IVF specialists~~ are ~~amongst the best in the world,and have been for some time~~. ~~Next you~~'~~ll go~~ by ~~way of to your simple Word - Press site. So~~, ~~we have to add our social media sharing buttons in website. Now all you have to do is log into your Word - Press site making use of the very same username~~ and ~~password that you initially had in your previous site.~~ <br><br>~~Millions of individuals and organizations are now successfully using this tool throughout~~ the ~~world. s ability to use different themes and skins known as Word - Press Templates or Themes. You can select color of your choice~~, ~~graphics of your favorite, skins, photos, pages, etc. Word - Press is an open source content management system which is easy to use and offers many user friendly features. You can check out~~ the ~~statistics of page of views~~ for ~~your web pages using free tools that are available on the internet~~.		In [[queueing theory]], a discipline within the mathematical [[probability theory\|theory of probability]], the '''Gordon–Newell theorem''' is an extension of [[Jackson's theorem (queueing theory)\|Jackson's theorem]] from open queueing networks to closed queueing networks of exponential servers where customers cannot leave the network.<ref>{{cite doi\|10.1287/opre.15.2.254}}</ref> Jackson's theorem cannot be applied to closed networks because the queue length at a node in the closed network is limited by the population of the network. The Gordon–Newell theorem calculates the open network solution and then eliminates the infeasible states by renormalizing the probabilities. Calculation of the [[normalizing constant]] makes the treatment more awkward as the whole state space must be enumerated. [[Buzen's algorithm]] or [[mean value analysis]] can be used to calculate the normalizing constant more efficiently.<ref>{{cite doi\|10.1145/362342.362345}}</ref>

			==Definition of a Gordon–Newell network==

			A network of ''m'' interconnected queues is known as a '''Gordon–Newell network'''<ref>{{cite jstor\|1426680}}</ref> or '''closed Jackson network'''<ref>{{cite doi\|10.1016/j.ijpe.2007.10.013}}</ref> if it meets the following conditions:

			# the network is closed (no customers can enter or leave the network),
			# all service times are exponentially distributed and the service discipline at all queues is [[FCFS]],
			# a customer completing service at queue ''i'' will move to queue ''j'' with probability <math>P_{ij}</math>, with the <math>P_{ij}</math> such that <math>\scriptstyle{\sum_{j =1}^m P_{ij} = 1}</math>,
			# the utilization of all of the queues is less than one.

			==Theorem==

			In a closed Gordon–Newell network of ''m'' queues, with a total population of ''K'' individuals, write <math>\scriptstyle{(k_1,k_2,\ldots,k_m)}</math> (where ''k''<sub>''i''</sub> is the length of queue ''i'') for the state of the network and ''S''(''K'', ''m'') for the state space

			:<math>S(K,m) = \left\{ \mathbf{k} \in \mathbb{Z}^m \text{ such that } \sum_{i=1}^m k_i = K \text{ and } k_i \geq 0\quad \forall i\right\}.</math>

			Then the equilibrium state probability distribution exists and is given by

			:<math>\pi (k_1,k_2,\ldots,k_m) = \frac{1}{G(K)} \prod_{i=1}^m \left( \frac{e_i}{\mu_i} \right)^{k_i}</math>

			where service times at queue ''i'' are exponentially distributed with parameter ''μ<sub>i</sub>''. The normalizing constant ''G''(''K'') is given by

			:<math>G(K) = \sum_{\mathbf{k} \in S(K,m)} \prod_{i=1}^{m} \left( \frac{e_i}{\mu_i} \right)^{k_i} ,</math>

			and ''e''<sub>''i''</sub> is the visit ratio, calculated by solving the simultaneous equations

			:<math>e_i = \sum_{j=1}^m e_j p_{ji} \text{ for }1 \leq i \leq m. \, </math>

			==See also==
			*[[BCMP network]]

			==References==
			{{Reflist}}

			{{Queueing theory}}

			{{DEFAULTSORT:Gordon-Newell theorem}}
			[[Category:Stochastic processes]]
			[[Category:Probability theorems]]
			[[Category:Queueing theory]]

en>Mecanismo: added a reference to the moment distribution method, which is the hardy cross method applied to structural mechanics

2012-06-04T14:59:03Z

added a reference to the moment distribution method, which is the hardy cross method applied to structural mechanics

New page

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