1719:
1158:
1714:{\displaystyle {\begin{aligned}X&=\{?{\textit {receive}}\}\\Y&=\{!{\textit {send}}\}\\S&=\{(d,\sigma )|d\in \{{\textit {Wait}},{\textit {Send}}\},\sigma \in \mathbb {T} ^{\infty }\}\\s_{0}&=({\textit {Send}},0.1)\\ta(s)&=\sigma {\text{ for all }}s\in S\\\delta _{ext}((({\textit {Wait}},\sigma ),t_{e}),?{\textit {receive}})&=({\textit {Send}},0.1)\\\delta _{int}({\textit {Send}},\sigma )&=({\textit {Wait}},\infty )\\\delta _{int}({\textit {Wait}},\sigma )&=({\textit {Send}},0.1)\\\lambda ({\textit {Send}},\sigma )&=!{\textit {send}}\\\lambda ({\textit {Wait}},\sigma )&=\phi \end{aligned}}}
3557:
170:
132:
journal in 1987. Since then, many extended formalism from DEVS have been introduced with their own purposes: DESS/DEVS for combined continuous and discrete event systems, P-DEVS for parallel DESs, G-DEVS for piecewise continuous state trajectory modeling of DESs, RT-DEVS for realtime DESs, Cell-DEVS
3458:
of DEVS is to control all models to have the identical current time. However, for an efficient execution, the algorithm makes the current time jump to the most urgent time when an event is scheduled to execute its internal state transition as well as its output generation.
144:
Due to the modular and hierarchical modeling views, as well as its simulation-based analysis capability, the DEVS formalism and its variations have been used in many application of engineering (such as hardware design, hardware/software codesign,
2450:
182:
DEVS defines system behavior as well as system structure. System behavior in DEVS formalism is described using input and output events as well as states. For example, for the ping-pong player of Fig. 1, the input event is
466:
4350:
Hessam S. Sarjoughian; Vignesh
Elamvazhuthi (2009). "CoSMoS: A Visual Environment for Component-Based Modeling, Experimental Design, and Simulation". Proceedings of the International Conference on Simulation Tools and
1150:
2731:
2129:
3070:
3925:
3463:
is to transmit a triggering message which can be either an input or output event along the associated couplings which are defined in a coupled DEVS model. For more detailed information, the reader can refer to
820:
3876:
3511:
has been applied for analysis of DEVS models. It is proven that infinite states of a given DEVS model (especially a coupled DEVS model ) can be abstracted by behaviorally isomorphic finite structure, called a
2528:
67:
2356:
133:
for cellular DESs, Fuzzy-DEVS for fuzzy DESs, Dynamic
Structuring DEVS for DESs changing their coupling structures dynamically, and so on. In addition to its extensions, there are some subclasses such as
4271:
Giambiasi N., Escude B. Ghosh S. “Generalized
Discrete Event Simulation of Dynamic Systems”, in: Issue 4 of SCS Transactions: Recent Advances in DEVS Methodology-part II, Vol. 18, pp. 216–229, dec
3182:
637:
3480:
By introducing a quantization method which abstracts a continuous segment as a piecewise const segment, DEVS can simulate behaviors of continuous state systems which are described by networks of
694:
3587:
Numerous extensions of the classic DEVS formalism have been developed in the last decades. Among them formalisms which allow to have changing model structures while the simulation time evolves.
1163:
4051:
953:
4137:
908:
2588:
1002:
2869:
345:
3484:. This research has been initiated by Zeigler in 1990s and many properties have been clarified by Prof. Kofman in 2000s and Dr. Nutaro. In 2006, Prof. Cellier who is the author of
3983:
82:
formalism, which is a finite state automaton where the outputs are determined by the current state alone (and do not depend directly on the input). The extension was done by
1028:
3398:
3349:
303:
102:
Since the lifespan of each state is a real number (more precisely, non-negative real) or infinity, it is distinguished from discrete time systems, sequential machines, and
2289:
2908:
1976:
587:
2827:
2246:
3673:
3646:
4414:
Gregory
Zacharewicz, Claudia Frydman, and Norbert Giambiasi (2008) G-DEVS/HLA Environment for Distributed Simulations of Workflows, SIMULATION May 2008 84: 197–213,
4009:
3428:
3309:
3236:
2789:
2760:
1947:
1802:
1776:
4168:
3283:
1901:
1849:
851:
62:
4071:
3256:
3210:
2207:
2181:
2155:
1921:
1869:
1822:
1750:
544:
518:
492:
2367:
33:, is a modular and hierarchical formalism for modeling and analyzing general systems that can be discrete event systems which might be described by
364:
1051:
1038:
event. This function defines how a state of the system generates an output event (when the elapsed time reaches to the lifetime of the state);
1997:
The coupled DEVS defines which sub-components belong to it and how they are connected with each other. A coupled DEVS model is defined as an 8-
3507:
As an alternative analysis method against the sampling-based simulation method, an exhaustive generating behavior approach, generally called
2607:
2005:
3530:. As a result, based on the reachability graph, (1) dead-lock and live-lock freeness as qualitative properties are decidable with SP-DEVS
2913:
3881:
703:
3812:
2461:
4195:
2296:
4535:
3075:
3779:
3739:
3469:
3438:
4511:
4463:
4405:
4386:
4340:
4262:
4243:
3734:
3465:
1986:
598:
648:
914:
which defines how a state of the system changes internally (when the elapsed time reaches to the lifetime of the state);
4321:
4444:
4284:
4014:
3351:. In both cases (1) and (2), a triggering event is transmitted to all influencees which are defined by coupling sets
919:
115:
53:
DEVS is a formalism for modeling and analysis of discrete event systems (DESs). The DEVS formalism was invented by
4076:
868:
106:, in which time is determined by a tick time multiplied by non-negative integers. Moreover, the lifespan can be a
4530:
3481:
3539:; and (2) min/max processing time bounds as a quantitative property are decidable with SP-DEVS so far by 2012.
2539:
962:
2832:
268:
4218:
4473:
Bernard
Zeigler (1987). "Hierarchical, modular discrete-event modelling in an object-oriented environment".
3454:
The simulation algorithm of DEVS models considers two issues: time synchronization and message propagation.
4306:
Proceedings of the 2012 Symposium on Theory of
Modeling and Simulation - DEVS Integrative M&S Symposium
3930:
4290:
M.H. Hwang and B. P. Zeigler, "A Modular
Verification Framework using Finite and Deterministic DEVS",
4184:
1007:
4369:
4188:
3354:
3314:
3729:
3434:
111:
2255:
4194:<We need any reference for this argument>. He was then working for a company spun off from
3724:
3496:
in which
Chapters 11 and 12 cover how DEVS simulates continuous state systems. Dr. Nutaro's book
2874:
1952:
559:
2794:
2218:
75:
34:
3658:
3631:
3437:. Computer algorithms to implement the behavior of a given coupled DEVS mode are available at
1985:. Computer algorithms to implement the behavior of a given Atomic DEVS model are available at
4356:
4297:
M.H. Hwang and B.P. Zeigler, "Reachability Graph of Finite and
Deterministic DEVS Networks",
3782:: SDL, a formal complete and unambiguous language to graphically represent simulation models.
146:
58:
38:
3988:
3403:
3288:
3215:
2765:
2736:
1926:
1781:
1755:
4275:
M.H. Hwang, "Tutorial: Verification of Real-time System Based on
Schedule-Preserved DEVS",
4210:
4146:
3757:
3568:
3261:
1874:
1827:
829:
20:
8:
4490:
4214:
4199:
4056:
3709:
3241:
3195:
2192:
2166:
2140:
1906:
1854:
1807:
1735:
529:
503:
477:
54:
42:
4507:
4459:
4440:
4401:
4382:
4336:
4317:
4280:
4258:
4239:
4494:
4482:
4415:
4171:
3516:
when the given DEVS model is a sub-class of DEVS such as Schedule-Preserving DEVS (
2445:{\displaystyle C_{yx}\subseteq \bigcup _{i\in D}Y_{i}\times \bigcup _{i\in D}X_{i}}
1982:
4183:
the use of quantized values in order to simulate continuous systems by means of a
3192:
Simply speaking, like the behavior of the atomic DEVS class, a coupled DEVS model
3751:
3596:, dynDEVS, Fuzzy-DEVS, GK-DEVS, ml-DEVS, Symbolic DEVS, Real-Time DEVS, rho-DEVS
1981:
For formal behavior description of given an Atomic DEVS model, refer to the page
107:
71:
4187:
method was empirically tried out a few years sooner - in the early 1990s - by a
4486:
4304:
M.H. Hwang, "Qualitative verification of finite and real-time DEVS networks",
4524:
4419:
4333:
Building Software for Simulation: Theory, Algorithms, and Applications in C++
3704:
461:{\displaystyle M=<X,Y,S,s_{0},ta,\delta _{ext},\delta _{int},\lambda >}
150:
103:
79:
125:
Zeigler proposed a hierarchical algorithm for DEVS model simulation in 1984
4501:
4395:
3769:
1145:{\displaystyle <X,Y,S,s_{0},ta,\delta _{ext},\delta _{int},\lambda >}
2594:
which defines how to select the event from the set of simultaneous events;
4349:
3556:
3499:, covers the discrete event simulation of continuous state systems too.
3433:
For formal definition of behavior of the coupled DEVS, you can refer to
4207:
3773:
219:
state lasts until the player receives the ball that is the input event
211:
state takes 0.1 seconds to send back the ball that is the output event
119:
700:
which defines how an input event changes a state of the system, where
141:
have been researched for achieving decidability of system properties.
3763:
2726:{\displaystyle N=<X,Y,D,\{M_{i}\},C_{xx},C_{yx},C_{yy},Select>}
2124:{\displaystyle N=<X,Y,D,\{M_{i}\},C_{xx},C_{yx},C_{yy},Select>}
158:
3798:
automata were the mathematical models of Dr. Zeigler's Ph.D. thesis
3065:{\displaystyle C_{yx}=\{(A.!send,B.?receive),(B.!send,A.?receive)\}}
2604:
The ping-pong game of Fig. 1 can be modeled as a coupled DEVS model
41:, and hybrid continuous state and discrete event systems. DEVS is a
4191:
3920:{\displaystyle Q=S\times \mathbb {T} ^{\infty }\times \mathbb {T} }
3776:
process in which the future will be determined by the current state
815:{\displaystyle Q=\{(s,t_{e})|s\in S,t_{e}\in (\mathbb {T} \cap )\}}
169:
4314:
Netcentric System of Systems Engineering with DEVS Unified Process
4311:
4170:. For more how to understand this function, refer to the article,
3871:{\displaystyle \delta _{ext}:Q\times X\rightarrow S\times \{0,1\}}
3760:: a state transition machine with finite sets of events and states
2523:{\displaystyle C_{yy}:\bigcup _{i\in D}Y_{i}\rightarrow Y^{\phi }}
226:
The structure of ping-pong game is to connect two players: Player
4379:
Discrete-Event Modeling and Simulation: A Practitioner's Approach
4252:
3719:
3715:
3652:
3625:
3617:
3613:
3609:
3605:
3521:
3517:
154:
138:
134:
3311:
executes its internal state transition and generates its output
118:. The state transition and output functions of DEVS can also be
4398:
Discrete-Event Modeling and Simulation: Theory and Applications
1732:
Simply speaking, there are two cases that an atomic DEVS model
110:; for example the lifespan of a given state can be distributed
3766:: a graphical representation of state and transition relations
3604:
There are some sub-classes known as Schedule-Preserving DEVS (
2351:{\displaystyle C_{xx}\subseteq X\times \bigcup _{i\in D}X_{i}}
1048:
The atomic DEVS model for player A of Fig. 1 is given Player=
1998:
356:
61:. DEVS was introduced to the public in Zeigler's first book,
347:
that is the set of non-negative real numbers plus infinity.
3177:{\displaystyle C_{yy}(A.!send)=\phi ,C_{yy}(B.!send)=\phi }
2291:
can be either an atomic DEVS model or a coupled DEVS model.
92:
providing a hierarchical concept with an operation, called
37:, and continuous state systems which might be described by
3612:) which were designated to support verification analysis.
3502:
3475:
3212:
changes its components' states (1) when an external event
4502:
Bernard Zeigler; Tag Gon Kim; Herbert Praehofer (2000).
3449:
4299:
IEEE Transactions on Automation Science and Engineering
3809:
We can also define the external transition function as
74:, in 1976, while Zeigler was an associate professor at
632:{\displaystyle ta:S\rightarrow \mathbb {T} ^{\infty }}
4149:
4079:
4059:
4017:
3991:
3933:
3884:
3815:
3661:
3634:
3593:, Parallel DEVS, Dynamic Structuring DEVS, Cell-DEVS
3406:
3357:
3317:
3291:
3264:
3244:
3218:
3198:
3078:
2916:
2877:
2835:
2797:
2768:
2739:
2610:
2542:
2464:
2370:
2299:
2258:
2221:
2195:
2169:
2143:
2008:
1955:
1929:
1909:
1877:
1857:
1830:
1810:
1784:
1758:
1738:
1161:
1054:
1010:
965:
922:
871:
832:
706:
651:
601:
562:
532:
506:
480:
367:
306:
271:
4456:
Multifacetted Modeling and Discrete Event Simulation
4396:
Gabriel A. Wainer and Pieter Mosterman Eds. (2010).
689:{\displaystyle \delta _{ext}:Q\times X\rightarrow S}
262:
The following formal definition is for Classic DEVS
4233:
1724:Both Player A and Player B are atomic DEVS models.
643:
which is used to determine the lifespan of a state;
4162:
4131:
4065:
4045:
4003:
3977:
3919:
3870:
3667:
3640:
3422:
3392:
3343:
3303:
3277:
3250:
3230:
3204:
3176:
3064:
2902:
2863:
2821:
2783:
2754:
2725:
2582:
2522:
2444:
2350:
2283:
2240:
2201:
2175:
2149:
2123:
1970:
1941:
1915:
1895:
1863:
1843:
1816:
1796:
1770:
1744:
1713:
1144:
1022:
996:
947:
902:
845:
814:
688:
631:
581:
538:
512:
486:
460:
339:
297:
4376:
4213:of which this engineer is the conceptor and main
4522:
4439:(first ed.). Wiley Interscience, New York.
4430:(Ph.D. Thesis ed.). University of Michigan.
4472:
4453:
4434:
4425:
4046:{\displaystyle t_{s}\in \mathbb {T} ^{\infty }}
948:{\displaystyle \lambda :S\rightarrow Y^{\phi }}
3754:: a formal method for state transition systems
265:. In this article, we will use the time base,
4506:(second ed.). Academic Press, New York.
4312:Saurabh Mittal; Jose L. Risco Martin (2013).
3599:
3547:
3527:, and Finite & Real-time DEVS (FRT-DEVS)
4330:
4301:, Volume 6, Issue 3, 2009, pp. 454–467,
4253:Francois E. Cellier; Ernesto Kofman (2006).
4132:{\displaystyle t_{e}\in (\mathbb {T} \cap )}
3865:
3853:
3059:
2933:
2897:
2894:
2816:
2804:
2778:
2775:
2749:
2746:
2648:
2635:
2235:
2222:
2046:
2033:
1309:
1285:
1265:
1236:
1219:
1206:
1189:
1176:
991:
985:
903:{\displaystyle \delta _{int}:S\rightarrow S}
809:
713:
16:Concept within modeling and systems analysis
3187:
1044:The atomic DEVS Model for Ping-Pong Players
1727:
78:. DEVS can be seen as an extension of the
4097:
4033:
3913:
3899:
2600:The coupled DEVS model for Ping-Pong Game
2583:{\displaystyle Select:2^{D}\rightarrow D}
1299:
997:{\displaystyle Y^{\phi }=Y\cup \{\phi \}}
772:
619:
309:
273:
4221:programs checking and operator training.
3698:
2864:{\displaystyle M_{A}{\text{ and }}M_{B}}
298:{\displaystyle \mathbb {T} =[0,\infty )}
168:
3503:Verification for discrete event systems
3476:Simulation for continuous state systems
355:An atomic DEVS model is defined as a 7-
340:{\displaystyle \mathbb {T} ^{\infty }=}
173:Fig. 1. A DEVS Model for Ping-Pong Game
86:associating a lifespan with each state
4523:
4428:On the Feedback Complexity of Automata
4294:, pp. 57–65, Huntsville, Alabama, USA,
3780:Specification and Description Language
3740:Simulation algorithms for coupled DEVS
3490:, and Prof. Kofman wrote a text book,
3470:Simulation Algorithms for Coupled DEVS
3439:Simulation Algorithms for Coupled DEVS
3735:Simulation algorithms for atomic DEVS
3608:) and Finite and Deterministic DEVS (
3542:
3466:Simulation Algorithms for Atomic DEVS
3450:Simulation for discrete event systems
2532:the external output coupling function
1987:Simulation Algorithms for Atomic DEVS
1683:
1666:
1640:
1614:
1588:
1549:
1523:
1484:
1464:
1426:
1338:
1280:
1270:
1214:
1184:
3978:{\displaystyle (s,t_{s},t_{e})\in Q}
3551:
3520:), Finite & Deterministic DEVS (
255:captures the system behavior, while
4458:. Academic Press, London; Orlando.
3745:
3444:
2360:the set of external input couplings
259:describes the structure of system.
57:, who is emeritus professor at the
31:Discrete Event System Specification
13:
4292:Proceedings of 2006 DEVS Symposium
4277:Proceedings of 2005 DEVS Symposium
4038:
3904:
1557:
1304:
624:
331:
314:
289:
14:
4547:
4504:Theory of Modeling and Simulation
4437:Theory of Modeling and Simulation
64:Theory of Modeling and Simulation
3714:Verifiable sub-classes of DEVS:
3686:) denotes the expressiveness of
3555:
3482:differential algebraic equations
912:the internal transition function
698:the external transition function
3799:
3594:
3591:
3537:
3534:
3531:
3528:
3525:
3497:
3494:
3488:
1992:
1023:{\displaystyle \phi \not \in Y}
263:
251:In the classic DEVS formalism,
126:
96:
87:
4536:Formal specification languages
4177:
4126:
4123:
4104:
4093:
3966:
3934:
3844:
3803:
3792:
3393:{\displaystyle C_{xx},C_{yx},}
3344:{\displaystyle y_{i}\in Y_{i}}
3165:
3141:
3116:
3092:
3056:
2999:
2993:
2936:
2574:
2507:
2211:the name set of sub-components
1965:
1959:
1890:
1884:
1694:
1678:
1651:
1635:
1625:
1609:
1599:
1583:
1560:
1544:
1534:
1518:
1495:
1479:
1469:
1453:
1437:
1421:
1418:
1415:
1368:
1362:
1349:
1333:
1255:
1251:
1239:
932:
894:
806:
803:
800:
794:
779:
768:
739:
735:
716:
680:
614:
350:
334:
322:
292:
280:
153:systems) and science (such as
19:For other uses of "devs", see
1:
4400:(first ed.). CRC Press.
4381:(first ed.). CRC Press.
4316:(first ed.). CRC Press.
4279:, San Diego, Apr. 2-8, 2005,
4227:
3258:; (2) when one of components
2454:the set of internal couplings
1778:: (1) when an external input
4257:(first ed.). Springer.
4255:Continuous System Simulation
4238:(first ed.). Springer.
4234:Francois E. Cellier (1991).
3927:such that for a total state
3786:
3492:Continuous System Simulation
2284:{\displaystyle i\in D,M_{i}}
1903:. (At the same time of (2),
1824:; (2) when the elapsed time
548:the set of sequential states
164:
7:
4139:is the elapsed time since
3693:
2903:{\displaystyle C_{xx}=\{\}}
1971:{\displaystyle \lambda (s)}
10:
4552:
4487:10.1177/003754978704900506
4377:Gabriel A. Wainer (2009).
4236:Continuous System Modeling
4196:University of Valenciennes
3600:Restrictions (subclassing)
3548:Extensions (superclassing)
3486:Continuous System Modeling
582:{\displaystyle s_{0}\in S}
187:, and the output event is
48:
18:
4335:(first ed.). Wiley.
3620:whose expressiveness are
2822:{\displaystyle D=\{A,B\}}
2592:the tie-breaking function
2250:the set of sub-components
2241:{\displaystyle \{M_{i}\}}
641:the time advance function
552:the set of partial states
237:is transmitted to Player
4454:Bernard Zeigler (1984).
4435:Bernard Zeigler (1976).
4426:Bernard Zeigler (1968).
4420:10.1177/0037549708092833
3730:Behavior of coupled DEVS
3668:{\displaystyle \subset }
3641:{\displaystyle \subset }
3435:Behavior of Coupled DEVS
3188:Behavior of coupled DEVS
2185:the set of output events
1851:reaches the lifespan of
522:the set of output events
3725:Behavior of atomic DEVS
2871:is described as above;
2159:the set of input events
1728:Behavior of atomic DEVS
496:the set of input events
128:which was published in
35:state transition tables
4531:Automata (computation)
4364:Cite journal requires
4198:, and now part of the
4164:
4133:
4067:
4047:
4005:
4004:{\displaystyle s\in S}
3979:
3921:
3872:
3669:
3642:
3424:
3423:{\displaystyle C_{yy}}
3394:
3345:
3305:
3304:{\displaystyle i\in D}
3279:
3252:
3232:
3231:{\displaystyle x\in X}
3206:
3178:
3066:
2904:
2865:
2823:
2785:
2784:{\displaystyle Y=\{\}}
2756:
2755:{\displaystyle X=\{\}}
2727:
2597:
2584:
2524:
2446:
2352:
2285:
2242:
2203:
2177:
2151:
2125:
1972:
1943:
1942:{\displaystyle y\in Y}
1917:
1897:
1865:
1845:
1818:
1804:comes into the system
1798:
1797:{\displaystyle x\in X}
1772:
1771:{\displaystyle s\in S}
1746:
1722:
1715:
1146:
1041:
1024:
998:
949:
904:
847:
816:
690:
633:
583:
540:
514:
488:
462:
341:
299:
174:
147:communications systems
76:University of Michigan
39:differential equations
4331:James Nutaro (2010).
4165:
4163:{\displaystyle t_{s}}
4134:
4068:
4048:
4006:
3980:
3922:
3873:
3699:DEVS-related articles
3670:
3643:
3425:
3395:
3346:
3306:
3280:
3278:{\displaystyle M_{i}}
3253:
3233:
3207:
3179:
3067:
2905:
2866:
2824:
2786:
2757:
2728:
2585:
2525:
2447:
2353:
2286:
2243:
2204:
2178:
2152:
2135:
2126:
1973:
1944:
1918:
1898:
1896:{\displaystyle ta(s)}
1866:
1846:
1844:{\displaystyle t_{e}}
1819:
1799:
1773:
1752:can change its state
1747:
1716:
1154:
1147:
1025:
999:
950:
905:
848:
846:{\displaystyle t_{e}}
817:
691:
634:
584:
541:
515:
489:
472:
463:
342:
300:
172:
59:University of Arizona
4147:
4077:
4057:
4015:
4011:is a partial state,
3989:
3931:
3882:
3813:
3758:Finite-state machine
3659:
3632:
3456:Time synchronization
3404:
3355:
3315:
3289:
3262:
3242:
3216:
3196:
3076:
2914:
2875:
2833:
2795:
2766:
2737:
2608:
2540:
2462:
2368:
2297:
2256:
2219:
2193:
2167:
2141:
2006:
1953:
1949:which is defined by
1927:
1923:generates an output
1907:
1875:
1871:which is defined by
1855:
1828:
1808:
1782:
1756:
1736:
1159:
1052:
1008:
963:
920:
869:
830:
704:
649:
599:
560:
530:
504:
478:
365:
304:
269:
21:Dev (disambiguation)
4217:, that is used for
4053:is the lifespan of
3461:Message propagation
1383: for all
957:the output function
824:set of total states
4206:is a feature of a
4200:Schneider Electric
4160:
4129:
4063:
4043:
4001:
3975:
3917:
3868:
3710:Timed event system
3665:
3638:
3567:. You can help by
3543:Variations of DEVS
3514:reachability graph
3420:
3390:
3341:
3301:
3275:
3248:
3228:
3202:
3174:
3062:
2900:
2861:
2819:
2781:
2752:
2723:
2580:
2520:
2496:
2442:
2431:
2402:
2348:
2337:
2281:
2238:
2199:
2173:
2147:
2121:
1968:
1939:
1913:
1893:
1861:
1841:
1814:
1794:
1768:
1742:
1711:
1709:
1142:
1020:
994:
945:
900:
843:
812:
686:
629:
579:
536:
510:
484:
458:
337:
295:
248:, and vice versa.
199:, has its states:
175:
70:2012-06-21 at the
55:Bernard P. Zeigler
43:timed event system
4513:978-0-12-778455-7
4465:978-0-12-778450-2
4407:978-1-4200-7233-4
4388:978-1-4200-5336-4
4342:978-0-470-41469-9
4308:, Article No. 43,
4264:978-0-387-26102-7
4245:978-0-387-97502-3
4066:{\displaystyle s}
3585:
3584:
3251:{\displaystyle N}
3205:{\displaystyle N}
2849:
2481:
2416:
2387:
2322:
2202:{\displaystyle D}
2176:{\displaystyle Y}
2150:{\displaystyle X}
1916:{\displaystyle M}
1864:{\displaystyle s}
1817:{\displaystyle M}
1745:{\displaystyle M}
1685:
1668:
1642:
1616:
1590:
1551:
1525:
1486:
1466:
1428:
1384:
1340:
1282:
1272:
1216:
1186:
591:the initial state
539:{\displaystyle S}
513:{\displaystyle Y}
487:{\displaystyle X}
178:Intuitive Example
4543:
4517:
4498:
4469:
4450:
4431:
4411:
4392:
4373:
4367:
4362:
4360:
4352:
4346:
4327:
4268:
4249:
4222:
4181:
4175:
4172:Behavior of DEVS
4169:
4167:
4166:
4161:
4159:
4158:
4138:
4136:
4135:
4130:
4122:
4121:
4100:
4089:
4088:
4072:
4070:
4069:
4064:
4052:
4050:
4049:
4044:
4042:
4041:
4036:
4027:
4026:
4010:
4008:
4007:
4002:
3984:
3982:
3981:
3976:
3965:
3964:
3952:
3951:
3926:
3924:
3923:
3918:
3916:
3908:
3907:
3902:
3877:
3875:
3874:
3869:
3831:
3830:
3807:
3801:
3796:
3746:Other formalisms
3674:
3672:
3671:
3666:
3647:
3645:
3644:
3639:
3580:
3577:
3559:
3552:
3445:Analysis methods
3429:
3427:
3426:
3421:
3419:
3418:
3399:
3397:
3396:
3391:
3386:
3385:
3370:
3369:
3350:
3348:
3347:
3342:
3340:
3339:
3327:
3326:
3310:
3308:
3307:
3302:
3284:
3282:
3281:
3276:
3274:
3273:
3257:
3255:
3254:
3249:
3237:
3235:
3234:
3229:
3211:
3209:
3208:
3203:
3183:
3181:
3180:
3175:
3140:
3139:
3091:
3090:
3071:
3069:
3068:
3063:
2929:
2928:
2909:
2907:
2906:
2901:
2890:
2889:
2870:
2868:
2867:
2862:
2860:
2859:
2850:
2847:
2845:
2844:
2828:
2826:
2825:
2820:
2790:
2788:
2787:
2782:
2761:
2759:
2758:
2753:
2732:
2730:
2729:
2724:
2698:
2697:
2682:
2681:
2666:
2665:
2647:
2646:
2589:
2587:
2586:
2581:
2573:
2572:
2529:
2527:
2526:
2521:
2519:
2518:
2506:
2505:
2495:
2477:
2476:
2451:
2449:
2448:
2443:
2441:
2440:
2430:
2412:
2411:
2401:
2383:
2382:
2357:
2355:
2354:
2349:
2347:
2346:
2336:
2312:
2311:
2290:
2288:
2287:
2282:
2280:
2279:
2247:
2245:
2244:
2239:
2234:
2233:
2208:
2206:
2205:
2200:
2182:
2180:
2179:
2174:
2156:
2154:
2153:
2148:
2130:
2128:
2127:
2122:
2096:
2095:
2080:
2079:
2064:
2063:
2045:
2044:
1983:Behavior of DEVS
1977:
1975:
1974:
1969:
1948:
1946:
1945:
1940:
1922:
1920:
1919:
1914:
1902:
1900:
1899:
1894:
1870:
1868:
1867:
1862:
1850:
1848:
1847:
1842:
1840:
1839:
1823:
1821:
1820:
1815:
1803:
1801:
1800:
1795:
1777:
1775:
1774:
1769:
1751:
1749:
1748:
1743:
1720:
1718:
1717:
1712:
1710:
1687:
1686:
1670:
1669:
1644:
1643:
1618:
1617:
1592:
1591:
1582:
1581:
1553:
1552:
1527:
1526:
1517:
1516:
1488:
1487:
1468:
1467:
1452:
1451:
1430:
1429:
1414:
1413:
1385:
1382:
1342:
1341:
1325:
1324:
1308:
1307:
1302:
1284:
1283:
1274:
1273:
1258:
1218:
1217:
1188:
1187:
1151:
1149:
1148:
1143:
1132:
1131:
1113:
1112:
1085:
1084:
1029:
1027:
1026:
1021:
1003:
1001:
1000:
995:
975:
974:
954:
952:
951:
946:
944:
943:
909:
907:
906:
901:
887:
886:
852:
850:
849:
844:
842:
841:
821:
819:
818:
813:
775:
764:
763:
742:
734:
733:
695:
693:
692:
687:
667:
666:
638:
636:
635:
630:
628:
627:
622:
588:
586:
585:
580:
572:
571:
550:(or also called
545:
543:
542:
537:
519:
517:
516:
511:
493:
491:
490:
485:
467:
465:
464:
459:
448:
447:
429:
428:
401:
400:
346:
344:
343:
338:
318:
317:
312:
302:
301:
296:
276:
243:
232:
4551:
4550:
4546:
4545:
4544:
4542:
4541:
4540:
4521:
4520:
4514:
4466:
4447:
4408:
4389:
4365:
4363:
4354:
4353:
4343:
4324:
4265:
4246:
4230:
4225:
4182:
4178:
4154:
4150:
4148:
4145:
4144:
4117:
4113:
4096:
4084:
4080:
4078:
4075:
4074:
4058:
4055:
4054:
4037:
4032:
4031:
4022:
4018:
4016:
4013:
4012:
3990:
3987:
3986:
3960:
3956:
3947:
3943:
3932:
3929:
3928:
3912:
3903:
3898:
3897:
3883:
3880:
3879:
3820:
3816:
3814:
3811:
3810:
3808:
3804:
3797:
3793:
3789:
3752:Automata theory
3748:
3701:
3696:
3660:
3657:
3656:
3633:
3630:
3629:
3602:
3581:
3575:
3572:
3565:needs expansion
3550:
3545:
3536:, and FRT-DEVS
3505:
3478:
3452:
3447:
3411:
3407:
3405:
3402:
3401:
3378:
3374:
3362:
3358:
3356:
3353:
3352:
3335:
3331:
3322:
3318:
3316:
3313:
3312:
3290:
3287:
3286:
3269:
3265:
3263:
3260:
3259:
3243:
3240:
3239:
3217:
3214:
3213:
3197:
3194:
3193:
3190:
3132:
3128:
3083:
3079:
3077:
3074:
3073:
2921:
2917:
2915:
2912:
2911:
2882:
2878:
2876:
2873:
2872:
2855:
2851:
2848: and
2846:
2840:
2836:
2834:
2831:
2830:
2796:
2793:
2792:
2767:
2764:
2763:
2738:
2735:
2734:
2690:
2686:
2674:
2670:
2658:
2654:
2642:
2638:
2609:
2606:
2605:
2568:
2564:
2541:
2538:
2537:
2514:
2510:
2501:
2497:
2485:
2469:
2465:
2463:
2460:
2459:
2436:
2432:
2420:
2407:
2403:
2391:
2375:
2371:
2369:
2366:
2365:
2342:
2338:
2326:
2304:
2300:
2298:
2295:
2294:
2275:
2271:
2257:
2254:
2253:
2252:where for each
2229:
2225:
2220:
2217:
2216:
2194:
2191:
2190:
2168:
2165:
2164:
2142:
2139:
2138:
2131:
2088:
2084:
2072:
2068:
2056:
2052:
2040:
2036:
2007:
2004:
2003:
1995:
1954:
1951:
1950:
1928:
1925:
1924:
1908:
1905:
1904:
1876:
1873:
1872:
1856:
1853:
1852:
1835:
1831:
1829:
1826:
1825:
1809:
1806:
1805:
1783:
1780:
1779:
1757:
1754:
1753:
1737:
1734:
1733:
1730:
1708:
1707:
1697:
1682:
1681:
1672:
1671:
1665:
1664:
1654:
1639:
1638:
1629:
1628:
1613:
1612:
1602:
1587:
1586:
1571:
1567:
1564:
1563:
1548:
1547:
1537:
1522:
1521:
1506:
1502:
1499:
1498:
1483:
1482:
1472:
1463:
1462:
1447:
1443:
1425:
1424:
1403:
1399:
1396:
1395:
1381:
1371:
1353:
1352:
1337:
1336:
1326:
1320:
1316:
1313:
1312:
1303:
1298:
1297:
1279:
1278:
1269:
1268:
1254:
1229:
1223:
1222:
1213:
1212:
1199:
1193:
1192:
1183:
1182:
1169:
1162:
1160:
1157:
1156:
1121:
1117:
1102:
1098:
1080:
1076:
1053:
1050:
1049:
1009:
1006:
1005:
970:
966:
964:
961:
960:
939:
935:
921:
918:
917:
876:
872:
870:
867:
866:
837:
833:
831:
828:
827:
771:
759:
755:
738:
729:
725:
705:
702:
701:
656:
652:
650:
647:
646:
623:
618:
617:
600:
597:
596:
567:
563:
561:
558:
557:
531:
528:
527:
505:
502:
501:
479:
476:
475:
468:
437:
433:
418:
414:
396:
392:
366:
363:
362:
359:
353:
313:
308:
307:
305:
272:
270:
267:
266:
241:
230:
191:. Each player,
167:
108:random variable
72:Wayback Machine
51:
29:, abbreviating
24:
17:
12:
11:
5:
4549:
4539:
4538:
4533:
4519:
4518:
4512:
4499:
4481:(5): 219–230.
4470:
4464:
4451:
4445:
4432:
4423:
4412:
4406:
4393:
4387:
4374:
4366:|journal=
4347:
4341:
4328:
4323:978-1439827062
4322:
4309:
4302:
4295:
4288:
4273:
4269:
4263:
4250:
4244:
4229:
4226:
4224:
4223:
4185:discrete event
4176:
4157:
4153:
4128:
4125:
4120:
4116:
4112:
4109:
4106:
4103:
4099:
4095:
4092:
4087:
4083:
4062:
4040:
4035:
4030:
4025:
4021:
4000:
3997:
3994:
3974:
3971:
3968:
3963:
3959:
3955:
3950:
3946:
3942:
3939:
3936:
3915:
3911:
3906:
3901:
3896:
3893:
3890:
3887:
3867:
3864:
3861:
3858:
3855:
3852:
3849:
3846:
3843:
3840:
3837:
3834:
3829:
3826:
3823:
3819:
3802:
3790:
3788:
3785:
3784:
3783:
3777:
3767:
3761:
3755:
3747:
3744:
3743:
3742:
3737:
3732:
3727:
3722:
3712:
3707:
3700:
3697:
3695:
3692:
3664:
3637:
3601:
3598:
3583:
3582:
3562:
3560:
3549:
3546:
3544:
3541:
3504:
3501:
3477:
3474:
3451:
3448:
3446:
3443:
3417:
3414:
3410:
3389:
3384:
3381:
3377:
3373:
3368:
3365:
3361:
3338:
3334:
3330:
3325:
3321:
3300:
3297:
3294:
3272:
3268:
3247:
3227:
3224:
3221:
3201:
3189:
3186:
3173:
3170:
3167:
3164:
3161:
3158:
3155:
3152:
3149:
3146:
3143:
3138:
3135:
3131:
3127:
3124:
3121:
3118:
3115:
3112:
3109:
3106:
3103:
3100:
3097:
3094:
3089:
3086:
3082:
3061:
3058:
3055:
3052:
3049:
3046:
3043:
3040:
3037:
3034:
3031:
3028:
3025:
3022:
3019:
3016:
3013:
3010:
3007:
3004:
3001:
2998:
2995:
2992:
2989:
2986:
2983:
2980:
2977:
2974:
2971:
2968:
2965:
2962:
2959:
2956:
2953:
2950:
2947:
2944:
2941:
2938:
2935:
2932:
2927:
2924:
2920:
2899:
2896:
2893:
2888:
2885:
2881:
2858:
2854:
2843:
2839:
2818:
2815:
2812:
2809:
2806:
2803:
2800:
2780:
2777:
2774:
2771:
2751:
2748:
2745:
2742:
2722:
2719:
2716:
2713:
2710:
2707:
2704:
2701:
2696:
2693:
2689:
2685:
2680:
2677:
2673:
2669:
2664:
2661:
2657:
2653:
2650:
2645:
2641:
2637:
2634:
2631:
2628:
2625:
2622:
2619:
2616:
2613:
2602:
2601:
2596:
2595:
2579:
2576:
2571:
2567:
2563:
2560:
2557:
2554:
2551:
2548:
2545:
2535:
2517:
2513:
2509:
2504:
2500:
2494:
2491:
2488:
2484:
2480:
2475:
2472:
2468:
2457:
2439:
2435:
2429:
2426:
2423:
2419:
2415:
2410:
2406:
2400:
2397:
2394:
2390:
2386:
2381:
2378:
2374:
2363:
2345:
2341:
2335:
2332:
2329:
2325:
2321:
2318:
2315:
2310:
2307:
2303:
2292:
2278:
2274:
2270:
2267:
2264:
2261:
2237:
2232:
2228:
2224:
2214:
2198:
2188:
2172:
2162:
2146:
2120:
2117:
2114:
2111:
2108:
2105:
2102:
2099:
2094:
2091:
2087:
2083:
2078:
2075:
2071:
2067:
2062:
2059:
2055:
2051:
2048:
2043:
2039:
2035:
2032:
2029:
2026:
2023:
2020:
2017:
2014:
2011:
2002:
1994:
1991:
1967:
1964:
1961:
1958:
1938:
1935:
1932:
1912:
1892:
1889:
1886:
1883:
1880:
1860:
1838:
1834:
1813:
1793:
1790:
1787:
1767:
1764:
1761:
1741:
1729:
1726:
1706:
1703:
1700:
1698:
1696:
1693:
1690:
1680:
1677:
1674:
1673:
1663:
1660:
1657:
1655:
1653:
1650:
1647:
1637:
1634:
1631:
1630:
1627:
1624:
1621:
1611:
1608:
1605:
1603:
1601:
1598:
1595:
1585:
1580:
1577:
1574:
1570:
1566:
1565:
1562:
1559:
1556:
1546:
1543:
1540:
1538:
1536:
1533:
1530:
1520:
1515:
1512:
1509:
1505:
1501:
1500:
1497:
1494:
1491:
1481:
1478:
1475:
1473:
1471:
1461:
1458:
1455:
1450:
1446:
1442:
1439:
1436:
1433:
1423:
1420:
1417:
1412:
1409:
1406:
1402:
1398:
1397:
1394:
1391:
1388:
1380:
1377:
1374:
1372:
1370:
1367:
1364:
1361:
1358:
1355:
1354:
1351:
1348:
1345:
1335:
1332:
1329:
1327:
1323:
1319:
1315:
1314:
1311:
1306:
1301:
1296:
1293:
1290:
1287:
1277:
1267:
1264:
1261:
1257:
1253:
1250:
1247:
1244:
1241:
1238:
1235:
1232:
1230:
1228:
1225:
1224:
1221:
1211:
1208:
1205:
1202:
1200:
1198:
1195:
1194:
1191:
1181:
1178:
1175:
1172:
1170:
1168:
1165:
1164:
1141:
1138:
1135:
1130:
1127:
1124:
1120:
1116:
1111:
1108:
1105:
1101:
1097:
1094:
1091:
1088:
1083:
1079:
1075:
1072:
1069:
1066:
1063:
1060:
1057:
1046:
1045:
1040:
1039:
1019:
1016:
1013:
993:
990:
987:
984:
981:
978:
973:
969:
942:
938:
934:
931:
928:
925:
915:
899:
896:
893:
890:
885:
882:
879:
875:
863:
862:
859:the last event
840:
836:
811:
808:
805:
802:
799:
796:
793:
790:
787:
784:
781:
778:
774:
770:
767:
762:
758:
754:
751:
748:
745:
741:
737:
732:
728:
724:
721:
718:
715:
712:
709:
685:
682:
679:
676:
673:
670:
665:
662:
659:
655:
644:
626:
621:
616:
613:
610:
607:
604:
594:
578:
575:
570:
566:
555:
535:
525:
509:
499:
483:
457:
454:
451:
446:
443:
440:
436:
432:
427:
424:
421:
417:
413:
410:
407:
404:
399:
395:
391:
388:
385:
382:
379:
376:
373:
370:
361:
352:
349:
336:
333:
330:
327:
324:
321:
316:
311:
294:
291:
288:
285:
282:
279:
275:
180:
179:
166:
163:
104:Moore machines
100:
99:
90:
50:
47:
15:
9:
6:
4:
3:
2:
4548:
4537:
4534:
4532:
4529:
4528:
4526:
4515:
4509:
4505:
4500:
4496:
4492:
4488:
4484:
4480:
4476:
4471:
4467:
4461:
4457:
4452:
4448:
4446:0-12-778455-1
4442:
4438:
4433:
4429:
4424:
4421:
4417:
4413:
4409:
4403:
4399:
4394:
4390:
4384:
4380:
4375:
4371:
4358:
4348:
4344:
4338:
4334:
4329:
4325:
4319:
4315:
4310:
4307:
4303:
4300:
4296:
4293:
4289:
4286:
4285:1-56555-293-8
4282:
4278:
4274:
4270:
4266:
4260:
4256:
4251:
4247:
4241:
4237:
4232:
4231:
4220:
4216:
4212:
4209:
4205:
4201:
4197:
4193:
4190:
4186:
4180:
4173:
4155:
4151:
4142:
4118:
4114:
4110:
4107:
4101:
4090:
4085:
4081:
4060:
4028:
4023:
4019:
3998:
3995:
3992:
3972:
3969:
3961:
3957:
3953:
3948:
3944:
3940:
3937:
3909:
3894:
3891:
3888:
3885:
3862:
3859:
3856:
3850:
3847:
3841:
3838:
3835:
3832:
3827:
3824:
3821:
3817:
3806:
3800:
3795:
3791:
3781:
3778:
3775:
3771:
3768:
3765:
3762:
3759:
3756:
3753:
3750:
3749:
3741:
3738:
3736:
3733:
3731:
3728:
3726:
3723:
3721:
3717:
3713:
3711:
3708:
3706:
3705:Event segment
3703:
3702:
3691:
3689:
3685:
3681:
3678:(DEVS) where
3677:
3662:
3654:
3650:
3635:
3627:
3623:
3619:
3615:
3611:
3607:
3597:
3595:
3592:
3588:
3579:
3576:November 2007
3570:
3566:
3563:This section
3561:
3558:
3554:
3553:
3540:
3538:
3535:
3532:
3529:
3526:
3523:
3519:
3515:
3510:
3500:
3498:
3495:
3493:
3489:
3487:
3483:
3473:
3471:
3467:
3462:
3457:
3442:
3440:
3436:
3431:
3415:
3412:
3408:
3387:
3382:
3379:
3375:
3371:
3366:
3363:
3359:
3336:
3332:
3328:
3323:
3319:
3298:
3295:
3292:
3270:
3266:
3245:
3225:
3222:
3219:
3199:
3185:
3171:
3168:
3162:
3159:
3156:
3153:
3150:
3147:
3144:
3136:
3133:
3129:
3125:
3122:
3119:
3113:
3110:
3107:
3104:
3101:
3098:
3095:
3087:
3084:
3080:
3053:
3050:
3047:
3044:
3041:
3038:
3035:
3032:
3029:
3026:
3023:
3020:
3017:
3014:
3011:
3008:
3005:
3002:
2996:
2990:
2987:
2984:
2981:
2978:
2975:
2972:
2969:
2966:
2963:
2960:
2957:
2954:
2951:
2948:
2945:
2942:
2939:
2930:
2925:
2922:
2918:
2891:
2886:
2883:
2879:
2856:
2852:
2841:
2837:
2813:
2810:
2807:
2801:
2798:
2772:
2769:
2743:
2740:
2720:
2717:
2714:
2711:
2708:
2705:
2702:
2699:
2694:
2691:
2687:
2683:
2678:
2675:
2671:
2667:
2662:
2659:
2655:
2651:
2643:
2639:
2632:
2629:
2626:
2623:
2620:
2617:
2614:
2611:
2599:
2598:
2593:
2577:
2569:
2565:
2561:
2558:
2555:
2552:
2549:
2546:
2543:
2536:
2533:
2515:
2511:
2502:
2498:
2492:
2489:
2486:
2482:
2478:
2473:
2470:
2466:
2458:
2455:
2437:
2433:
2427:
2424:
2421:
2417:
2413:
2408:
2404:
2398:
2395:
2392:
2388:
2384:
2379:
2376:
2372:
2364:
2361:
2343:
2339:
2333:
2330:
2327:
2323:
2319:
2316:
2313:
2308:
2305:
2301:
2293:
2276:
2272:
2268:
2265:
2262:
2259:
2251:
2230:
2226:
2215:
2212:
2196:
2189:
2186:
2170:
2163:
2160:
2144:
2137:
2136:
2134:
2118:
2115:
2112:
2109:
2106:
2103:
2100:
2097:
2092:
2089:
2085:
2081:
2076:
2073:
2069:
2065:
2060:
2057:
2053:
2049:
2041:
2037:
2030:
2027:
2024:
2021:
2018:
2015:
2012:
2009:
2001:
2000:
1990:
1988:
1984:
1979:
1962:
1956:
1936:
1933:
1930:
1910:
1887:
1881:
1878:
1858:
1836:
1832:
1811:
1791:
1788:
1785:
1765:
1762:
1759:
1739:
1725:
1721:
1704:
1701:
1699:
1691:
1688:
1675:
1661:
1658:
1656:
1648:
1645:
1632:
1622:
1619:
1606:
1604:
1596:
1593:
1578:
1575:
1572:
1568:
1554:
1541:
1539:
1531:
1528:
1513:
1510:
1507:
1503:
1492:
1489:
1476:
1474:
1459:
1456:
1448:
1444:
1440:
1434:
1431:
1410:
1407:
1404:
1400:
1392:
1389:
1386:
1378:
1375:
1373:
1365:
1359:
1356:
1346:
1343:
1330:
1328:
1321:
1317:
1294:
1291:
1288:
1275:
1262:
1259:
1248:
1245:
1242:
1233:
1231:
1226:
1209:
1203:
1201:
1196:
1179:
1173:
1171:
1166:
1153:
1139:
1136:
1133:
1128:
1125:
1122:
1118:
1114:
1109:
1106:
1103:
1099:
1095:
1092:
1089:
1086:
1081:
1077:
1073:
1070:
1067:
1064:
1061:
1058:
1055:
1043:
1042:
1037:
1033:
1017:
1014:
1011:
988:
982:
979:
976:
971:
967:
958:
940:
936:
929:
926:
923:
916:
913:
897:
891:
888:
883:
880:
877:
873:
865:
864:
860:
856:
838:
834:
825:
797:
791:
788:
785:
782:
776:
765:
760:
756:
752:
749:
746:
743:
730:
726:
722:
719:
710:
707:
699:
683:
677:
674:
671:
668:
663:
660:
657:
653:
645:
642:
611:
608:
605:
602:
595:
592:
576:
573:
568:
564:
556:
553:
549:
533:
526:
523:
507:
500:
497:
481:
474:
473:
471:
455:
452:
449:
444:
441:
438:
434:
430:
425:
422:
419:
415:
411:
408:
405:
402:
397:
393:
389:
386:
383:
380:
377:
374:
371:
368:
360:
358:
348:
328:
325:
319:
286:
283:
277:
264:
260:
258:
254:
249:
247:
240:
236:
233:output event
229:
224:
222:
218:
214:
210:
206:
202:
198:
194:
190:
186:
177:
176:
171:
162:
160:
156:
152:
151:manufacturing
148:
142:
140:
136:
131:
127:
123:
121:
117:
113:
112:exponentially
109:
105:
97:
95:
91:
88:
85:
84:
83:
81:
80:Moore machine
77:
73:
69:
66:
65:
60:
56:
46:
44:
40:
36:
32:
28:
22:
4503:
4478:
4474:
4455:
4436:
4427:
4397:
4378:
4357:cite journal
4332:
4313:
4305:
4298:
4291:
4276:
4254:
4235:
4204:quantization
4203:
4179:
4140:
3805:
3794:
3770:Markov chain
3687:
3683:
3679:
3675:
3648:
3621:
3603:
3589:
3586:
3573:
3569:adding to it
3564:
3513:
3509:verification
3508:
3506:
3491:
3485:
3479:
3460:
3455:
3453:
3432:
3191:
2603:
2591:
2531:
2453:
2359:
2249:
2210:
2184:
2158:
2132:
1996:
1993:Coupled DEVS
1980:
1731:
1723:
1155:
1047:
1035:
1034:event or an
1031:
956:
911:
858:
855:elapsed time
854:
823:
697:
640:
590:
551:
547:
521:
495:
469:
354:
261:
257:Coupled DEVS
256:
252:
250:
245:
244:input event
238:
234:
227:
225:
220:
216:
215:, while the
212:
208:
204:
200:
196:
192:
188:
184:
181:
143:
129:
124:
101:
93:
63:
52:
30:
26:
25:
4351:Techniques.
4141:last update
3238:comes into
1152:such that
351:Atomic DEVS
253:Atomic DEVS
4525:Categories
4475:Simulation
4228:References
4208:simulation
3774:stochastic
3764:Petri nets
3533:, FD-DEVS
1036:unobserved
130:Simulation
120:stochastic
4215:developer
4102:∩
4091:∈
4039:∞
4029:∈
3996:∈
3970:∈
3910:×
3905:∞
3895:×
3851:×
3845:→
3839:×
3818:δ
3787:Footnotes
3688:formalism
3684:formalism
3663:⊂
3636:⊂
3329:∈
3296:∈
3223:∈
3172:ϕ
3123:ϕ
2575:→
2516:ϕ
2508:→
2490:∈
2483:⋃
2425:∈
2418:⋃
2414:×
2396:∈
2389:⋃
2385:⊆
2331:∈
2324:⋃
2320:×
2314:⊆
2263:∈
1957:λ
1934:∈
1789:∈
1763:∈
1705:ϕ
1692:σ
1676:λ
1649:σ
1633:λ
1597:σ
1569:δ
1558:∞
1532:σ
1504:δ
1435:σ
1401:δ
1390:∈
1379:σ
1305:∞
1295:∈
1292:σ
1263:∈
1249:σ
1137:λ
1119:δ
1100:δ
1012:ϕ
989:ϕ
983:∪
972:ϕ
941:ϕ
933:→
924:λ
895:→
874:δ
777:∩
766:∈
747:∈
681:→
675:×
654:δ
625:∞
615:→
574:∈
453:λ
435:δ
416:δ
332:∞
315:∞
290:∞
165:Formalism
159:sociology
116:uniformly
4495:62648626
4211:software
4192:engineer
3694:See also
1015:∉
246:?receive
221:?receive
185:?receive
94:coupling
68:Archived
4202:. This
3720:FD-DEVS
3716:SP-DEVS
3653:FD-DEVS
3626:SP-DEVS
3618:FD-DEVS
3614:SP-DEVS
3610:FD-DEVS
3606:SP-DEVS
3590:G-DEVS
3522:FD-DEVS
3518:SP-DEVS
1465:receive
1185:receive
853:is the
822:is the
470:where
155:biology
139:FD-DEVS
135:SP-DEVS
49:History
4510:
4493:
4462:
4443:
4404:
4385:
4339:
4320:
4283:
4261:
4242:
4189:French
4073:, and
3878:where
3285:where
3072:; and
2733:where
2133:where
1032:silent
959:where
857:since
826:, and
242:'s
231:'s
157:, and
4491:S2CID
2615:=<
2013:=<
1999:tuple
1978:.) .
1030:is a
372:=<
357:tuple
235:!send
213:!send
189:!send
4508:ISBN
4460:ISBN
4441:ISBN
4402:ISBN
4383:ISBN
4370:help
4337:ISBN
4318:ISBN
4281:ISBN
4272:2001
4259:ISBN
4240:ISBN
3772:: a
3616:and
3468:and
3400:and
2721:>
2119:>
1684:Wait
1667:send
1641:Send
1615:Send
1589:Wait
1550:Wait
1524:Send
1485:Send
1427:Wait
1339:Send
1281:Send
1271:Wait
1215:send
1140:>
1056:<
1004:and
456:>
217:Wait
209:Send
205:Wait
203:and
201:Send
137:and
27:DEVS
4483:doi
4416:doi
4219:PLC
4143:of
3571:.
2590:is
2530:is
2452:is
2358:is
2248:is
2209:is
2183:is
2157:is
1623:0.1
1493:0.1
1347:0.1
955:is
910:is
696:is
639:is
589:is
546:is
520:is
494:is
114:or
4527::
4489:.
4479:49
4477:.
4361::
4359:}}
4355:{{
3985:,
3718:,
3690:.
3628:)
3524:)
3472:.
3441:.
3430:.
3184:.
2910:;
2829:;
1989:.
861:;
554:);
223:.
207:.
195:,
161:)
149:,
122:.
45:.
4516:.
4497:.
4485::
4468:.
4449:.
4422:.
4418::
4410:.
4391:.
4372:)
4368:(
4345:.
4326:.
4287:,
4267:.
4248:.
4174:.
4156:s
4152:t
4127:)
4124:]
4119:s
4115:t
4111:,
4108:0
4105:[
4098:T
4094:(
4086:e
4082:t
4061:s
4034:T
4024:s
4020:t
3999:S
3993:s
3973:Q
3967:)
3962:e
3958:t
3954:,
3949:s
3945:t
3941:,
3938:s
3935:(
3914:T
3900:T
3892:S
3889:=
3886:Q
3866:}
3863:1
3860:,
3857:0
3854:{
3848:S
3842:X
3836:Q
3833::
3828:t
3825:x
3822:e
3682:(
3680:E
3676:E
3655:)
3651:(
3649:E
3624:(
3622:E
3578:)
3574:(
3416:y
3413:y
3409:C
3388:,
3383:x
3380:y
3376:C
3372:,
3367:x
3364:x
3360:C
3337:i
3333:Y
3324:i
3320:y
3299:D
3293:i
3271:i
3267:M
3246:N
3226:X
3220:x
3200:N
3169:=
3166:)
3163:d
3160:n
3157:e
3154:s
3151:!
3148:.
3145:B
3142:(
3137:y
3134:y
3130:C
3126:,
3120:=
3117:)
3114:d
3111:n
3108:e
3105:s
3102:!
3099:.
3096:A
3093:(
3088:y
3085:y
3081:C
3060:}
3057:)
3054:e
3051:v
3048:i
3045:e
3042:c
3039:e
3036:r
3033:?
3030:.
3027:A
3024:,
3021:d
3018:n
3015:e
3012:s
3009:!
3006:.
3003:B
3000:(
2997:,
2994:)
2991:e
2988:v
2985:i
2982:e
2979:c
2976:e
2973:r
2970:?
2967:.
2964:B
2961:,
2958:d
2955:n
2952:e
2949:s
2946:!
2943:.
2940:A
2937:(
2934:{
2931:=
2926:x
2923:y
2919:C
2898:}
2895:{
2892:=
2887:x
2884:x
2880:C
2857:B
2853:M
2842:A
2838:M
2817:}
2814:B
2811:,
2808:A
2805:{
2802:=
2799:D
2791:;
2779:}
2776:{
2773:=
2770:Y
2762:;
2750:}
2747:{
2744:=
2741:X
2718:t
2715:c
2712:e
2709:l
2706:e
2703:S
2700:,
2695:y
2692:y
2688:C
2684:,
2679:x
2676:y
2672:C
2668:,
2663:x
2660:x
2656:C
2652:,
2649:}
2644:i
2640:M
2636:{
2633:,
2630:D
2627:,
2624:Y
2621:,
2618:X
2612:N
2578:D
2570:D
2566:2
2562::
2559:t
2556:c
2553:e
2550:l
2547:e
2544:S
2534:;
2512:Y
2503:i
2499:Y
2493:D
2487:i
2479::
2474:y
2471:y
2467:C
2456:;
2438:i
2434:X
2428:D
2422:i
2409:i
2405:Y
2399:D
2393:i
2380:x
2377:y
2373:C
2362:;
2344:i
2340:X
2334:D
2328:i
2317:X
2309:x
2306:x
2302:C
2277:i
2273:M
2269:,
2266:D
2260:i
2236:}
2231:i
2227:M
2223:{
2213:;
2197:D
2187:;
2171:Y
2161:;
2145:X
2116:t
2113:c
2110:e
2107:l
2104:e
2101:S
2098:,
2093:y
2090:y
2086:C
2082:,
2077:x
2074:y
2070:C
2066:,
2061:x
2058:x
2054:C
2050:,
2047:}
2042:i
2038:M
2034:{
2031:,
2028:D
2025:,
2022:Y
2019:,
2016:X
2010:N
1966:)
1963:s
1960:(
1937:Y
1931:y
1911:M
1891:)
1888:s
1885:(
1882:a
1879:t
1859:s
1837:e
1833:t
1812:M
1792:X
1786:x
1766:S
1760:s
1740:M
1702:=
1695:)
1689:,
1679:(
1662:!
1659:=
1652:)
1646:,
1636:(
1626:)
1620:,
1610:(
1607:=
1600:)
1594:,
1584:(
1579:t
1576:n
1573:i
1561:)
1555:,
1545:(
1542:=
1535:)
1529:,
1519:(
1514:t
1511:n
1508:i
1496:)
1490:,
1480:(
1477:=
1470:)
1460:?
1457:,
1454:)
1449:e
1445:t
1441:,
1438:)
1432:,
1422:(
1419:(
1416:(
1411:t
1408:x
1405:e
1393:S
1387:s
1376:=
1369:)
1366:s
1363:(
1360:a
1357:t
1350:)
1344:,
1334:(
1331:=
1322:0
1318:s
1310:}
1300:T
1289:,
1286:}
1276:,
1266:{
1260:d
1256:|
1252:)
1246:,
1243:d
1240:(
1237:{
1234:=
1227:S
1220:}
1210:!
1207:{
1204:=
1197:Y
1190:}
1180:?
1177:{
1174:=
1167:X
1134:,
1129:t
1126:n
1123:i
1115:,
1110:t
1107:x
1104:e
1096:,
1093:a
1090:t
1087:,
1082:0
1078:s
1074:,
1071:S
1068:,
1065:Y
1062:,
1059:X
1018:Y
992:}
986:{
980:Y
977:=
968:Y
937:Y
930:S
927::
898:S
892:S
889::
884:t
881:n
878:i
839:e
835:t
810:}
807:)
804:]
801:)
798:s
795:(
792:a
789:t
786:,
783:0
780:[
773:T
769:(
761:e
757:t
753:,
750:S
744:s
740:|
736:)
731:e
727:t
723:,
720:s
717:(
714:{
711:=
708:Q
684:S
678:X
672:Q
669::
664:t
661:x
658:e
620:T
612:S
609::
606:a
603:t
593:;
577:S
569:0
565:s
534:S
524:;
508:Y
498:;
482:X
450:,
445:t
442:n
439:i
431:,
426:t
423:x
420:e
412:,
409:a
406:t
403:,
398:0
394:s
390:,
387:S
384:,
381:Y
378:,
375:X
369:M
335:]
329:,
326:0
323:[
320:=
310:T
293:)
287:,
284:0
281:[
278:=
274:T
239:B
228:A
197:B
193:A
98:.
89:,
23:.
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