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| Given an [[DEVS#Atomic DEVS|atomic DEVS]] model, simulation algorithms are methods to generate the model's legal behaviors which are trajectories not to reach to illegal states. (see [[Behavior of DEVS]]). [[Simulation_Algorithms_for_Atomic_DEVS#References|[Zeigler84]]] originally introduced the algorithms that handle time variables related to ''lifespan'' <math>t_s \in [0,\infty]</math> and ''elapsed time'' <math>t_e\in [0,\infty)</math> by introducing two other time variables, ''last event time'', <math>t_l\in [0,\infty)</math>, and ''next event time'' <math> t_n\in [0,\infty]</math> with the following relations:
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| <center><math> \, t_e = t - t_l </math></center>
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| and
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| <center><math>\, t_s = t_n - t_l </math></center>
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| where <math>t\in [0,\infty)</math> denotes the ''current time''. And the ''remaining time'',
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| <center><math>\,t_r=t_s-t_e</math></center> is equivalently computed as
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| <center><math>\, t_r = t_n - t</math></center>, apparently <math> t_r \in [0,\infty]</math>.
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| Since the behavior of a given atomic DEVS model can be defined in two different views depending on the total state and the external transition function (refer to [[Behavior of DEVS]]), the simulation algorithms are also introduced in two different views as below.
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| == Common parts ==
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| Regardless of two different views of total states, algorithms for initialization and internal transition cases are commonly defined as below.
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| DEVS-simulator
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| variables:
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| parent // parent coordinator
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| <math>t_l</math> // time of last event
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| <math>t_n</math> // time of next event
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| <math>A=(X,Y,S,ta, \delta_{ext}, \delta_{int}, \lambda) </math>// the associated [[DEVS#Atomic DEVS|Atomic DEVS]] model
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| when receive init-message(Time <math>t</math>)
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| <math> t_l \leftarrow t;</math>
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| <math> t_n \leftarrow t_l + ta(s); </math>
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| when receive star-message(Time <math>t</math>)
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| if <math> t \ne t_n </math> then
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| error: bad synchronization;
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| <math> y \leftarrow \lambda(s);</math>
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| send y-message(<math>y,t</math>) to parent;
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| <math> s \leftarrow \delta_{int}(s)</math>
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| <math> t_l \leftarrow t;</math>
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| <math> t_n \leftarrow t_l + ta(s); </math>
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| == View 1: total states = states * elapsed times ==
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| As addressed in [[Behavior of Atomic DEVS]], when DEVS receives an input event, right calling <math>\delta_{ext}</math>, the last event time,<math>t_l</math> is set by the current time,<math>t</math>, thus the elapsed time<math>t_e</math> becomes zero because <math>t_e = t - t_l</math>.
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| when receive x-message(<math>x \in X</math>, Time <math>t</math>)
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| if <math>( t_l \le t </math> and <math> t \le t_n )</math> == false then
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| error: bad synchronization;
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| <math> s \leftarrow \delta_{ext}(s,t-t_l, x)</math>
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| <math> t_l \leftarrow t;</math>
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| <math> t_n \leftarrow t_l + ta(s); </math>
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| ==View 2: total states = states * lifespans * elapsed times==
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| Notice that as addressed in [[Behavior of Atomic DEVS]], depending on the value of <math>b</math> return by <math> \delta_{ext}</math>, last event time,<math>t_l</math>, and next event time,<math>t_n</math>,consequently, elapsed time, <math>t_e</math>, and lifespan<math>t_n</math>, are updated (if <math>b=1</math>) or preserved (if <math>b=0</math>).
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| when receive x-message(<math>x \in X</math>, Time <math>t</math>)
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| if <math>( t_l \le t </math> and <math> t \le t_n )</math> == false then
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| error: bad synchronization;
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| <math> (s,b) \leftarrow \delta_{ext}(s, t-t_l, x)</math>
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| if <math> b = 1 </math> then
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| <math> t_l \leftarrow t;</math>
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| <math> t_n \leftarrow t_l + ta(s); </math>
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| ==See also==
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| * [[DEVS#Atomic DEVS|Atomic DEVS]]
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| * [[Behavior of atomic DEVS]]
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| * [[Simulation algorithms for coupled DEVS]]
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| == References ==
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| * [Zeigler84] {{cite book|author = Bernard Zeigler | year = 1984| title = Multifacetted Modeling and Discrete Event Simulation | publisher = Academic Press, London; Orlando | id = ISBN 978-0-12-778450-2 }}
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| * [ZKP00] {{cite book|author = 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}}
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| [[Category:Algorithms]]
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Hi there! :) My name is Ivan, I'm a student studying Modern Languages and Classics from Hutton Wandesley, United Kingdom.
Also visit my site: ореховая диета