Simulation algorithms for coupled DEVS explained

Given a coupled DEVS model, simulation algorithms are methods to generate the model's legal behaviors, which are a set of trajectories not to reach illegal states. (see behavior of a Coupled DEVS model.) [Zeigler84] originally introduced the algorithms that handle time variables related to lifespan

t _{s} \in [ 0 , inf ty] and elapsed time t _{e\in} [ 0 , inf ty) by introducing two other time variables, last event time, t _{l\in} [ 0 , inf ty) , and next event time t _{n\in} [ 0 , inf ty] with the following relations: t _{e} = t - t _{l}

and

t _{s} = t _{n} - t _{l}

where

t\in [ 0 , inf ty) denotes the current time. And the remaining time,t _{r=t} _{s-t} _{e}

is equivalently computed as

t _{r} = t _{n} - t,

apparently

t _{r} \in [ 0 , inf ty] .Based on these relationships, the algorithms to simulate the behavior of a given Coupled DEVS are written as follows.

Algorithm

algorithm DEVS-coordinator Variables: parent // parent coordinator

t _{l} : // time of last event t _{n} : // time of next event N = (X, Y, D, \{M _{i\},} C _{xx} , C _{yx} , C _{yy} ,Select) // the associated Coupled DEVS model when receive init-message(Time t) for each i \in D do send init-message(t) to child i t _{l} \leftarrow max \{t _{li} : i \in D\} ; t _{n} \leftarrow min \{t _{ni} : i \in D\} ; when receive star-message(Time t) if t \ne t _{n} then error: bad synchronization; i ^{*} \leftarrow Select(\{i \in D: t _{ni} = t _{n\});} send star-message(t)to i ^{*} t _{l} \leftarrow max \{t _{li} : i \in D\} ; t _{n} \leftarrow min \{t _{ni} : i \in D\} ; when receive x-message(x \in X , Time t) if ( t _{l} \le t and t \le t _{n} )

false then error: bad synchronization; for each

(x,x _{i)} \in C _{xx} do send x-message(x _{i} ,t) to child i t _{l} \leftarrow max \{t _{li} : i \in D\} ; t _{n} \leftarrow min \{t _{ni} : i \in D\} ; when receive y-message(y _{i} \in Y _{i} , Time t) for each (y _{i,x} _{i)} \in C _{yx} do send x-message(x _{i} ,t) to child i if C _{yy} (y _{i)\ne} \phi then send y-message(C _{yy} (y _{i)} , t) to parent; t _{l} \leftarrow max \{t _{li} : i \in D\} ; t _{n} \leftarrow min \{t _{ni} : i \in D\} ;

See also

• Coupled DEVS
• Behavior of Coupled DEVS
• Simulation Algorithms for Atomic DEVS

References

• [Zeigler84] Book: Bernard Zeigler . 1984. Multifacetted Modeling and Discrete Event Simulation . Academic Press, London; Orlando . 978-0-12-778450-2 .
• [ZKP00] Book: Bernard Zeigler . Tag Gon Kim . Herbert Praehofer . 2000. Theory of Modeling and Simulation. Academic Press, New York . 978-0-12-778455-7 . second.