1. Modeling and simulation of systems Basic simulation concepts Slovak University of Technology Faculty of Material Science and Technology in Trnava

2. Basic simulation concepts Algorithms oriented to:  Events  Activities  processes

3. Simulation methods Simulation methods differentiate from others mainly in transformation of information which are gained from model from changes of its state in the time behaviour. This time is totally separated from the real time and is called simulation time. Work with the simulation time, questions of moments´ planning, where the changes of states happen are important from the point of view of interception of dynamic attributes of model systems.

4. Basic terms for defining of dynamic qualities in discrete simulation Events  their occurrence – change of state activities  represent activities between two events Process  understood as complex of activities time events U0U0 U1U1 U2U2 Activity 1 Activity 2 Process

5. Discrete-event simulation Is defined as simulation in which state variables are changed only in discrete moments in which event occurs (Banks) Represents the basic simulation concept. Includes system, model, entities, attributes, state variables, processes which define discrete- event simulation.

6. Discrete-event simulation – basic procedure define changes of state of model at occurrence of events in discrete time moment. Events are grouped into classes. Each event of given class causes the same change of system state. Each event has assigned time of its occurrence and events are arranged ascending into the list which is called calendar of events. Setting of simulation time and also operation of simulation program is controlled according to calendar of events

7. Discrete-event simulation – basic procedure The states of model in discrete- event simulation are only changed in discrete moments, at the time of certain events appearance. As the state of model between appearance moments of events remains unchanged we can change simulation time step by step whose length is given by intervals between the appearance of events. This approach for interception of dynamic attributes of system is used in majority simulation programs.

8. Beginning Setting of initial conditions TIME=0 Classes events planning TU i i.e. values TU 1, TU 2,,.. TU n TU k = min TU i i = 1,2,..n TIME = TU k Activity realization TU k End? Output of results End nono yes Discrete-event simulation procedure

9. Algorithms oriented to activities basic expressional tool is activity - the conception is used when it is difficult to create calendar of events. For example when event is determined not only by achievement of simulation time but also by fulfilment of condition. - It is needed to define  complex of activities  complex of conditions – certain activities can start at their fulfilment  changes of state caused by impact of activities

10. B Initial conditions Change of state Conditions of activity 1 Conditions of activity k Change of state Change of simulation time Simulation ending? no nono nono yes List of results E Activity 1 Activity k Procedure oriented to activities

11. Algorithms oriented to activities Problems  it is necessary to test the conditions for all activities at each change of simulation time  the speed of algorithm is slower than at events controlled models  the speed depends on number of activities

12. Algorithms oriented to processes Combine advantages of discrete-event models and approach of algorithms oriented on activities (process is a complex of activities) Dynamics of the model is described by its transition of certain process