Topological game: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Kryuuri
en>Michael Hardy
fixing a surprisingly large number of punctuation errors per WP:MOS
 
Line 1: Line 1:
In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], a '''BCMP network''' is a class of [[queueing theory|queueing network]] for which a [[product-form solution|product-form equilibrium distribution]] exists. It is named after the authors of the paper where the network was first described: Baskett, [[K. Mani Chandy|Chandy]], Muntz and Palacios. The theorem is a significant extension to a [[Jackson network]] allowing virtually arbitrary customer routing and service time distributions, subject to particular service disciplines.<ref>{{Cite journal | last = Baskett | first = F. | author-link = | last2 = Chandy | first2 = K. Mani | author2-link = K. Mani Chandy | last3 = Muntz | first3 = R.R. | last4 = Palacios | first4 = F.G. | title = Open, closed and mixed networks of queues with different classes of customers | journal = Journal of the ACM | volume = 22 | issue = 2 | pages = 248&ndash;260 | year = 1975 | doi = 10.1145/321879.321887 }}</ref>
The main advantage of using the blog is that anyone can use the Word - Press blog and customize the elements in the theme regardless to limited knowledge about internet and website development. You can either install Word - Press yourself or use free services offered on the web today. This is a service where people write articles using a specific keyword you have given them. s and intelligently including a substantial amount of key words in the title tags, image links, etc. This particular wordpress plugin is essential for not only having the capability where you improve your position, but to enhance your organic searches for your website. <br><br>You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. Which is perfect for building a mobile site for business use. Now, I want to anxiety that not every single query will be answered. 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>Digital photography is a innovative effort, if you removethe stress to catch every position and viewpoint of a place, you free yourself up to be more innovative and your outcomes will be much better. The following piece of content is meant to make your choice easier and reassure you that the decision to go ahead with this conversion is requited with rich benefits:. Possibly the most downloaded Word - Press plugin, the Google XML Sitemaps plugin but not only automatically creates a site map linking to everyone your pages and posts, it also notifies Google, Bing, Yahoo, and Ask.  If you loved this informative article and you wish to receive more information relating to [http://a.thedeltalog.com/delta/index.php?task=profile&id=546251 wordpress backup plugin] kindly visit our web page. Nonetheless, with stylish Facebook themes obtainable on the Globe Broad Internet, half of your enterprise is done previously. Websites using this content based strategy are always given top scores by Google. <br><br>Word - Press has plenty of SEO benefits over Joomla and Drupal. And, that is all the opposition events with nationalistic agenda in favor of the individuals of Pakistan marching collectively in the battle in opposition to radicalism. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. See a product, take a picture, and it gives you an Amazon price for that product, or related products. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. with posts or testimonials updated as they are uploaded to a particular section of the website. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.
 
The paper is well known, and the theorem was described in 1990 as "one of the seminal achievements in queueing theory in the last 20 years" by [[J. Michael Harrison]] and Ruth Williams.<ref>{{cite journal | last = Harrison | first = J.M. | authorlink = J. Michael Harrison | last2 = Williams | first2 = R.J. | title = On the Quasireversibility of a Multiclass Brownian Service Station | journal = The Annals of Probability | volume = 18 | issue = 3 | pages = 1249&ndash;1268 | publisher = Institute of Mathematical Statistics | year = 1990 | jstor = 2244425 | doi = 10.1214/aop/1176990745 }}</ref>
 
==Definition of a BCMP network==
 
A network of ''m'' interconnected queues is known as a '''BCMP network''' if each of the queues is of one of the following four types:
 
# [[First-come, first-served|FCFS]] discipline where all customers have the same [[Exponential distribution|negative exponential]] service time distribution. The service rate can be state dependent, so write <math>\scriptstyle{\mu_j}</math> for the service rate when the queue length is ''j''.
# Processor sharing queues
# Infinite server queues
# [[LIFO (computing)|LCFS]] with pre-emptive resume (work is not lost)
 
In the final three cases, service time distributions must have [[rational function|rational]] [[Laplace transform]]s. This means the Laplace transform must be of the form<ref>{{cite web|url=http://cnx.org/content/m10853/latest/|title=BCMP Theorem|first=Bart|last=Sinclair|publisher=Connexions|accessdate=2011-08-14}}</ref>
:<math>L(s) = \frac{N(s)}{D(s)}.</math>
 
Also, the following conditions must be met.
 
# external arrivals to node ''i'' (if any) form a [[Poisson process]],
# a customer completing service at queue ''i'' will either move to some new queue ''j'' with (fixed) probability <math>P_{ij}</math> or leave the system with probability <math>1-\sum_{j=1}^{m}P_{ij}</math>, which is non-zero for some subset of the queues.
 
==Theorem==
 
For a BCMP network of ''m'' queues which is open, closed or mixed in which each queue is of type 1, 2, 3 or 4, the equilibrium state probabilities are given by
 
:<math>\pi(x_1,x_2,\ldots,x_m) = C \pi_1(x_1) \pi_2(x_2) \cdots \pi_m(x_m),</math>
 
where ''C'' is a normalizing constant chosen to make the equilibrium state probabilities sum to 1 and <math>\scriptstyle{\pi_i(\cdot)}</math> represents the equilibrium distribution for queue ''i''.
 
===Proof===
 
The original proof of the theorem was given by checking the [[independent balance equation]]s were satisfied.
 
[[Peter G. Harrison]] offered an alternative proof<ref>{{cite doi|10.1017/CBO9781139226424.029}}</ref> by considering reversed processes.<ref>{{cite doi|10.1016/j.laa.2004.02.020}}</ref>
 
==References==
 
{{Reflist}}
 
{{Queueing theory}}
 
{{DEFAULTSORT:Bcmp Network}}
[[Category:Stochastic processes]]
[[Category:Queueing theory]]
 
 
{{probability-stub}}

Latest revision as of 00:03, 13 July 2014

The main advantage of using the blog is that anyone can use the Word - Press blog and customize the elements in the theme regardless to limited knowledge about internet and website development. You can either install Word - Press yourself or use free services offered on the web today. This is a service where people write articles using a specific keyword you have given them. s and intelligently including a substantial amount of key words in the title tags, image links, etc. This particular wordpress plugin is essential for not only having the capability where you improve your position, but to enhance your organic searches for your website.

You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. Which is perfect for building a mobile site for business use. Now, I want to anxiety that not every single query will be answered. 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.

Digital photography is a innovative effort, if you removethe stress to catch every position and viewpoint of a place, you free yourself up to be more innovative and your outcomes will be much better. The following piece of content is meant to make your choice easier and reassure you that the decision to go ahead with this conversion is requited with rich benefits:. Possibly the most downloaded Word - Press plugin, the Google XML Sitemaps plugin but not only automatically creates a site map linking to everyone your pages and posts, it also notifies Google, Bing, Yahoo, and Ask. If you loved this informative article and you wish to receive more information relating to wordpress backup plugin kindly visit our web page. Nonetheless, with stylish Facebook themes obtainable on the Globe Broad Internet, half of your enterprise is done previously. Websites using this content based strategy are always given top scores by Google.

Word - Press has plenty of SEO benefits over Joomla and Drupal. And, that is all the opposition events with nationalistic agenda in favor of the individuals of Pakistan marching collectively in the battle in opposition to radicalism. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. See a product, take a picture, and it gives you an Amazon price for that product, or related products.

Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. with posts or testimonials updated as they are uploaded to a particular section of the website. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.