|
|
| Line 1: |
Line 1: |
| {{multiple issues|
| |
| {{COI|date=November 2012}}
| |
| {{notability|date=November 2012}}
| |
| {{primary sources|date=November 2012}}
| |
| {{technical|date=November 2012}}
| |
| }}
| |
| Behaviors of a given [[DEVS]] model is a set of sequences of timed events including null events, called [[event segment]]s which make the model move one state to another within a set of legal states. To define this way, the concept of a set of illegal state as well a set of legal states are needed to be introduced.
| |
|
| |
|
| In addition, since the behaviors of a given DEVS model needs to define how the state transition change both when time is passed by and when an event occurs, it has been described by a much general formalism, called general system [[Behavior_of_DEVS#References|[ZPK00]]]. In this article, we use a sub-class of General System formalism, called [[timed event system]] instead.
| |
|
| |
|
| Depending on how to define the total state and its external state transition function of [[DEVS]], two ways to define the behavior of a [[DEVS]] model using [[Timed Event System]].
| | They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. If you adored this article and also you would like to receive more info about [http://rlpr.co/backup_plugin_178145 wordpress backup plugin] please visit our web-site. You may discover this probably the most time-consuming part of building a Word - Press MLM website. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. s ultimately easy to implement and virtually maintenance free. After activating, you will find their website link and get the activation code from their website. <br><br>These folders as well as files have to copied and the saved. If you wish to sell your services or products via internet using your website, you have to put together on the website the facility for trouble-free payment transfer between customers and the company. You are able to set them within your theme options and so they aid the search engine to get a suitable title and description for the pages that get indexed by Google. It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box. This can be done by using a popular layout format and your unique Word - Press design can be achieved in other elements of the blog. <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. When a business benefits from its own domain name and a tailor-made blog, the odds of ranking higher in the search engines and being visible to a greater number of people is more likely. 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. 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>It is the convenient service through which professionals either improve the position or keep the ranking intact. * Robust CRM to control and connect with your subscribers. A higher percentage of women are marrying at older ages,many are delaying childbearing until their careers are established, the divorce rate is high and many couples remarry and desire their own children. IVF ,fertility,infertility expert,surrogacy specialist in India at Rotundaivf. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. <br><br>Many developers design websites and give them to the clients, but still the client faces problems to handle the website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup. Working with a Word - Press blog and the appropriate cost-free Word - Press theme, you can get a professional internet site up and published in no time at all. 95, and they also supply studio press discount code for their clients, coming from 10% off to 25% off upon all theme deals. |
| Since [[Behavior of Coupled DEVS|behavior of a coupled DEVS]] model is defined as an [[DEVS#Atomic_DEVS|atomic DEVS]] model, behavior of coupled DEVS class is defined by timed event system.
| |
| | |
| == View 1: total states = states * elapsed times ==
| |
| Suppose that a [[DEVS]] model,
| |
| <math>\mathcal{M}=<X,Y,S,s_0,ta,\delta_{ext},\delta_{int},\lambda></math> has
| |
| | |
| # the external state transition <math> \delta_{ext}:Q \times X \rightarrow S</math>.
| |
| # the total state set <math>Q=\{(s,t_e)| s \in S, t_e \in (\mathbb{T} \cap [0, ta(s)])\}</math> where <math> t_e </math> denotes elapsed time since last event and <math> \mathbb{T}=[0,\infty)</math> denotes the set of non-negative real numbers, and
| |
| | |
| | |
| Then the [[DEVS]] model,
| |
| <math>\mathcal{M} </math> is a [[Timed Event System]] <math>\mathcal{G}=<Z,Q,Q_0,Q_A,\Delta> </math> where
| |
| <blockquote>
| |
| *The event set <math>Z=X \cup Y^\phi</math>.
| |
| *The state set <math>Q=Q_A \cup Q_N</math> where <math> Q_N=\{\bar{s} \not \in S \}</math>.
| |
| *The set of initial states <math> \,Q_0 = \{(s_0,0)\}</math>.
| |
| *The set of accepting states <math> Q_A = \mathcal{M}.Q.</math>
| |
| *The set of state trajectories <math> \Delta \subseteq Q \times \Omega_{Z,[t_l,t_u]}
| |
| \times Q</math> is defined for two different cases: <math> q \in Q_N </math> and <math> q \in Q_A </math>. For an non-accepting state <math> q \in Q_N </math>, there is no change together with any even segment <math>\omega \in \Omega_{Z,[t_l,t_u]}</math> so <math>(q,\omega,q) \in \Delta.</math>
| |
| | |
| For a total state <math> q=(s,t_e) \in Q_A</math> at time <math> t \in \mathbb{T} </math> and an [[event segment]] <math> \omega \in \Omega_{Z,[t_l,t_u]}</math> as follows. <br>
| |
| | |
| If [[Event Segment#Unit event segment|unit event segment]] <math> \omega</math> is the [[Event Segment#Null event segment|null event segment]], i.e. <math> \omega=\epsilon_{[t, t+dt]}</math>
| |
| <center> <math>\, (q, \omega, (s, t_e+dt)) \in \Delta.\,</math> </center>
| |
| | |
| If [[Event Segment#Unit event segment|unit event segment]] <math> \omega</math> is a [[Event Segment#Timed event|timed event]] <math> \omega=(x, t)</math> where the event is an input event <math> x \in X</math>, | |
| <center> <math>
| |
| (q, \omega, (\delta_{ext}(q,x), 0)) \in \Delta.
| |
| </math> </center>
| |
| | |
| If [[Event Segment#Unit event segment|unit event segment]] <math> \omega</math> is a [[Event Segment#Timed event|timed event]] <math> \omega=(y, t)</math> where the event is an output event or the unobservable event <math> y \in Y^\phi</math>,
| |
| <center> <math>
| |
| \begin{cases}
| |
| (q, \omega,(\delta_{int}(s), 0)) \in \Delta& \textrm{if } ~ t_e = ta(s), y = \lambda(s)\\
| |
| (q, \omega, \bar{s}) & \textrm{otherwise}.
| |
| \end{cases}
| |
| </math> </center>
| |
| | |
| </blockquote>
| |
| | |
| Computer algorithms to simulate this view of behavior are available at [[Simulation Algorithms for Atomic DEVS]].
| |
| | |
| ==View 2: total states = states * lifespans * elapsed times==
| |
| Suppose that a [[DEVS]] model,
| |
| <math>\mathcal{M}=<X,Y,S,s_0,ta,\delta_{ext},\delta_{int},\lambda></math> has
| |
| | |
| # the total state set <math>Q=\{(s,t_s, t_e)| s \in S, t_s\in \mathbb{T}^\infty, t_e \in (\mathbb{T} \cap [0, t_s])\}</math> where <math> t_s </math> denotes lifespan of state <math> s </math>, <math> t_e </math> denotes elapsed time since last <math>t_s </math>update, and <math> \mathbb{T}^\infty=[0,\infty) \cup \{ \infty \}</math> denotes the set of non-negative real numbers plus infinity,
| |
| # the external state transition is <math> \delta_{ext}:Q \times X \rightarrow S \times \{0,1\} </math>.
| |
| | |
| Then the [[DEVS]] <math>Q=\mathcal{D}</math> is a timed event system <math>\mathcal{G}=<Z,Q,Q_0,Q_A,\Delta> </math> where
| |
| <blockquote>
| |
| *The event set <math>Z=X \cup Y^\phi</math>.
| |
| *The state set <math>Q=Q_A \cup Q_N </math> where <math> Q_N=\{ \bar{s} \not \in S \}</math>.
| |
| *The set of initial states<math> \,Q_0 = \{(s_0,ta(s_0),0)\}</math>.
| |
| *The set of acceptance states <math> Q_A = \mathcal{M}.Q</math>.
| |
| *The set of state trajectories <math> \Delta \subseteq Q \times \Omega_{Z,[t_l,t_u]}
| |
| \times Q</math> is depending on two cases: <math>q \in Q_N </math> and <math>q \in Q_A </math>. For a non-accepting state <math> q \in Q_N </math>, there is no changes together with any segment <math>\omega \in \Omega_{Z,[t_l,t_u]}</math> so <math>(q,\omega,q) \in \Delta.</math>
| |
| | |
| For a total state <math> q=(s,t_s, t_e) \in Q_A</math> at time <math> t \in \mathbb{T} </math> and an [[event segment]] <math> \omega \in \Omega_{Z,[t_l,t_u]}</math> as follows. <br>
| |
| | |
| If [[Event Segment#Unit event segment|unit event segment]] <math> \omega</math> is the [[Event Segment#Null event segment|null event segment]], i.e. <math> \omega=\epsilon_{[t, t+dt]}</math>
| |
| <center> <math> (q, \omega, (s, t_s, t_e+dt)) \in \Delta.</math> </center>
| |
| | |
| If [[Event Segment#Unit event segment|unit event segment]] <math> \omega</math> is a [[Event Segment#Timed event|timed event]] <math> \omega=(x, t)</math> where the event is an input event <math> x \in X</math>,
| |
| <center> <math>
| |
| \begin{cases}
| |
| (q, \omega, (s', ta(s'), 0))\in \Delta& \textrm{if } ~\delta_{ext}(s,t_s,t_e,x)=(s',1),\\
| |
| (q, \omega, (s', t_s, t_e))\in \Delta& \textrm{otherwise, i.e. } ~\delta_{ext}(s,t_s,t_e,x)=(s',0).
| |
| \end{cases}
| |
| </math> </center>
| |
| | |
| If [[Event Segment#Unit event segment|unit event segment]] <math> \omega</math> is a [[Event Segment#Timed event|timed event]] <math> \omega=(y, t)</math> where the event is an output event or the unobservable event <math> y \in Y^\phi</math>,
| |
| <center> <math>
| |
| \begin{cases}
| |
| (q, \omega, (s', ta(s'),0)) \in \Delta& \textrm{if } ~t_e = t_s, y = \lambda(s), \delta_{int}(s)=s',\\
| |
| (q, \omega, \bar{s} )\in \Delta& \textrm{otherwise}.
| |
| \end{cases}
| |
| </math> </center>
| |
| | |
| </blockquote>
| |
| Computer algorithms to simulate this view of behavior are available at [[Simulation Algorithms for Atomic DEVS]].
| |
| | |
| == Comparison of View1 and View2 ==
| |
| === Features of View1 ===
| |
| View1 has been introduced by Zeigler [[Behavior_of_DEVS#References|[Zeigler84]]] in which given a total state <math> q=(s,t_e) \in Q </math> and <center><math>\, ta(s)=\sigma </math> </center>
| |
| where <math> \sigma </math> is the remaining time [[Behavior_of_DEVS#References|[Zeigler84]]] [[Behavior_of_DEVS#References|[ZPK00]]]. In other words, the set of partial states is indeed <math>S=\{(d,\sigma)| d \in S', \sigma \in \mathbb{T}^\infty \} </math> where <math> S'</math> is a state set.
| |
| | |
| When a DEVS model receives an input event <math> x \in X</math>, View1 resets the elapsed time <math> t_e </math> by zero, if the DEVS model needs to ignore <math> x </math> in terms of the lifespan control, modellers have to update the remaining time
| |
| <center> <math>\, \sigma = \sigma - t_e</math> </center>
| |
| in the external state transition function <math> \delta_{ext} </math> that is the responsibility of the modellers.
| |
| | |
| Since the number of possible values of <math> \sigma </math> is the same as the number of possible input events coming to the DEVS model, that is unlimited. As a result, the number of states <math> s=(d, \sigma) \in S </math> is also unlimited that is the reason why View2 has been proposed.
| |
| | |
| If we don't care the finite-vertex reachability graph of a DEVS model, View1 has an advantage of simplicity for treating the elapsed time <math> t_e=0</math> every time any input event arrives into the DEVS model. But disadvantage might be modelers of DEVS should know how to manage <math>\sigma</math> as above, which is not explicitly explained in <math>\delta_{ext} </math> itself but in <math>\Delta</math>.
| |
| | |
| === Features of View2 ===
| |
| View2 has been introduced by Hwang and Zeigler[[Behavior_of_DEVS#References|[HZ06]]][[Behavior_of_DEVS#References|[HZ07]]] in which given a total state <math> q=(s, t_s, t_e) \in Q </math>, the remaining time, <math> \sigma</math> is computed as
| |
| | |
| <center> <math>\, \sigma = t_s - t_e.
| |
| </math> </center>
| |
| | |
| When a DEVS model receives an input event <math> x \in X</math>, View2 resets the elapsed time <math> t_e </math> by zero only if <math> \delta_{ext}(q,x)=(s',1)</math>. If the DEVS model needs to ignore <math> x </math> in terms of the lifespan control, modellers can use <math> \delta_{ext}(q,x)=(s',0) </math>.
| |
|
| |
| Unlike View1, since the remaining time <math> \sigma </math> is not component of <math> S </math> in nature, if the number of states, i.e. <math> |S| </math> is finite, we can draw a finite-vertex (as well as edge) state-transition diagram [[Behavior_of_DEVS#References|[HZ06]]][[Behavior_of_DEVS#References|[HZ07]]]. As a result, we can abstract behavior of such a DEVS-class network, for example [[SP-DEVS]] and [[FD-DEVS]], as a finite-vertex graph, called reachability graph [[Behavior_of_DEVS#References|[HZ06]]][[Behavior_of_DEVS#References|[HZ07]]].
| |
| | |
| ==See also==
| |
| *[[DEVS]]
| |
| | |
| *[[Behavior of Coupled DEVS]]
| |
| | |
| *[[Simulation Algorithms for Atomic DEVS]]
| |
| | |
| *[[Simulation Algorithms for Coupled DEVS]]
| |
| | |
| == References ==
| |
| * [Zeigler76] {{cite book|author = [[Bernard P. Zeigler|Bernard Zeigler]] | year = 1976| title = Theory of Modeling and Simulation| publisher = Wiley Interscience, New York | id = |edition=first}}
| |
| * [Zeigler84] {{cite book|author = [[Bernard P. Zeigler|Bernard Zeigler]] | year = 1984| title = Multifacetted Modeling and Discrete Event Simulation | publisher = Academic Press, London; Orlando | id = ISBN 978-0-12-778450-2 }}
| |
| * [ZKP00] {{cite book|author = [[Bernard P. Zeigler|Bernard Zeigler]], Tag Gon Kim, Herbert Praehofer| year = 2000| title = Theory of Modeling and Simulation| publisher = Academic Press, New York | id= ISBN 978-0-12-778455-7 |edition=second}}
| |
| * [HZ06] M. H. Hwang and [[Bernard P. Zeigler|Bernard Zeigler]], ``A Reachable Graph of Finite and Deterministic DEVS Networks``, ''Proceedings of 2006 DEVS Symposium'', pp48-56, Huntsville, Alabama, USA, (Available at http://www.acims.arizona.edu and http://moonho.hwang.googlepages.com/publications)
| |
| * [HZ07] M.H. Hwang and [[Bernard P. Zeigler|Bernard Zeigler]], ``Reachability Graph of Finite & Deterministic DEVS``, IEEE Transactions on Automation Science and Engineering, Volume 6, Issue 3, 2009, pp.454–467, http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=5153598&arnumber=5071137&count=19&index=7
| |
| | |
| [[Category:Automata theory]]
| |
| [[Category:Formal specification languages]]
| |
They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. If you adored this article and also you would like to receive more info about wordpress backup plugin please visit our web-site. You may discover this probably the most time-consuming part of building a Word - Press MLM website. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. s ultimately easy to implement and virtually maintenance free. After activating, you will find their website link and get the activation code from their website.
These folders as well as files have to copied and the saved. If you wish to sell your services or products via internet using your website, you have to put together on the website the facility for trouble-free payment transfer between customers and the company. You are able to set them within your theme options and so they aid the search engine to get a suitable title and description for the pages that get indexed by Google. It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box. This can be done by using a popular layout format and your unique Word - Press design can be achieved in other elements of the blog.
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. When a business benefits from its own domain name and a tailor-made blog, the odds of ranking higher in the search engines and being visible to a greater number of people is more likely. 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. 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.
It is the convenient service through which professionals either improve the position or keep the ranking intact. * Robust CRM to control and connect with your subscribers. A higher percentage of women are marrying at older ages,many are delaying childbearing until their careers are established, the divorce rate is high and many couples remarry and desire their own children. IVF ,fertility,infertility expert,surrogacy specialist in India at Rotundaivf. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route.
Many developers design websites and give them to the clients, but still the client faces problems to handle the website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup. Working with a Word - Press blog and the appropriate cost-free Word - Press theme, you can get a professional internet site up and published in no time at all. 95, and they also supply studio press discount code for their clients, coming from 10% off to 25% off upon all theme deals.