Why building models? n Cannot experience on the real system of interest n Cost n Danger n The real system does not exist Why using simulation? n Reduced cost of computers n Improved facilities of modern computers n Ease to use n Flexibility

Real World Simulator modeling relation simulation relation Each entity can be formalized as a Mathematical Dynamic System (mathematical manipulations to prove system properties) Structure generating behavior claimed to represent real world Device for executing model Model Conditions under which the system is experimented with/observed Experimental Frame Data: Input/output relation pairs M&S Entities and Relations

Modelling System Dynamics

Interested in modeling systems’ dynamic behavior  how it organizes itself over time in response to imposed conditions and stimuli. n Predict how a system will react to external inputs and proposed structural changes. Modelling system dynamics

Modelling techniques classification n Example: waiting in a line for service. n Conceptual Modelling: informal model. –Communicates the basic nature of the process –Provides a vocabulary for the system (ambiguous) –General description of the system to be modeled

n Advantage of Formal Methods –Correctness and completeness  Testing –Communication means  Teamwork n Formalism –Communication convention –Formal specification in unambiguous manner –Abstraction (representation) + Manipulation of abstraction –Formal model - Formal specification Formal Modelling

Declarative models n System states (representing system entities) n Transitions between states n State-based declarative models –Example: States = number of persons waiting in line –Transitions: arrival of new customers/departure of serviced ones

Declarative models (cont.) n Event-based declarative models n Arcs: represent scheduling. n Event relation: from arrival of token i to departure of token i.

Functional models n “Black box”. n Input: signal defined over time n Output: depending on the internal function. n Timing delays: discrete or continuous –Example: inputs = customers arriving –Outputs = delayed output of the input customers

Spatial models n Space notions included n Relationship between time and space positions –Example: customers moving through the server.

A Systems Dynamics classification Classifying modelling techniques according to the system dynamics

Classification Vars./TimeContinuousDiscrete Continuous[1] DESS Partial Differential Equations Ordinary Differential Equations Bond Graphs Modelica Electrical circuits [2] DTSS Difference Equations Finite Element Method Finite Differences Numerical methods (in general, any computing method for the continuous counterparts], like Runge-Kutta, Euler, DASSL and others. Discrete[3] DEVS DEVS Formalism Timed Petri Nets Timed Finite State Machines Event Graphs [4] Automata Finite State Machines Finite State Automata Petri Nets Boolean Logic Markov Chains

Discrete time/Discrete variable n Finite State Machines n Finite State Automata n Petri Nets n CSP n CCS n Markov chains

Automata a c b s

Markov Chains 01 P 0,1 P 1,1 P 1,0

Finite State Machines S  X Y (a)Moore machine; (b) Mealy machine S  X Y

n Characteristic of DES (DTS is a special case of DES) –Man-made system –Naturally concurrent system –Not well-grounded mathematical formalism form modeling –Difficulties in computer experimentation –Non-linear –No accurate analytic solution –No transformation method DES modelling

n Examples of Discrete Event System : Man-made system –Multi-computer system –communication network –Distributed control –Manufacturing system –Game –Traffic system Examples of Discrete Event Systems

Discrete variable/Continuous time n Min-max algebra n Timed Finite State Machines n Timed Petri Nets n Generalized Semi-Markov Process (GSMP) n Timed automata n Timed graphs n Event graphs n Event scheduling n DEVS

Event Graphs

Timed Automata

Statecharts

Classification

n Different Abstraction Level of Dynamic System time state time state time state time state Higher Abstraction Level S/W Real-time program Concurrent program Sequential program H/W Timed DES Untimed DES Finite State Automata Diff. Eqn FMS event 1 event 2 event 3 event 4 event 5 Multiformalism utility

Operator Planning/scheduling Discrete Event Controller PID controller analog/digital Plant Command Discrete state actuationSensor Event-based control Time-based control Supervisory control Example: hierarchical control

Basic definitions n System: “natural” or artificial entity. Ordered set of related objects that interact. Source of observational data or more specifically, behavior. Data viewed or acquired through an experimental frame of interest to the modeller. n Model: abstract representation of a system. Constructed to generate behavior, indistinguishable from system behavior within one or more experimental frames. Behavior generated using specific rules, equations or a modelling formalism.

More Definitions n Behavior: specific form of data observable in a system over time within an experimental frame. n Experimental Frame: conditions under which a system or model are observed or experimented with. We do not reason but on MODELS. Problems cannot be solved on the real systems. Every problem is studied on abstract representations of the systems. Problem solving is related to an experimental frame in which the model is analyzed.

A definition Simulation is the reproduction of the dynamic behavior of a real system with the goal of obtaining conclusions that can be applied to the real system. n Dynamic behavior n Real system n Obtaining conclusions

More definitions n Event: a change in the state of the model, which occurs at a given instant (called the event time), causing the model to activate. n model's activation produce state change (i.e., at least one attribute in the model will change). n model's state is the set of values of all the attributes of the model at a given instant. n State variables: those that can be used to uniquely define the model’s behavior in the future

More definitions n Abstraction: basic process we use when modeling to extract a set of entities and relations from a complex reality. n Higher level of abstraction: information is lost, but allows to better define the model's behavior, prove properties of the system by manipulating the abstract model definition. n Verification and Validation (V&V) –Validation: relationship between model, system and experimental frame (it is possible to distinguish behavior of model/system within EF?) –Verification: process of checking that a simulator of a model correctly generates the desired behavior.

Types of Simulation Models n According to the objectives and decisions to be taken we distinguish: n Exploration: to better understand the operation of the system; n Prediction: to predict the future behavior of the system. n Improvement: to optimize performance through analysis of alternatives; n Conception: system does not exist yet; model is used to test different options prior construction. n Engineering design: design devices in engineering applications (ranging from bridges to electron devices). n Rapid prototyping: quickly obtain a working model to test ideas and get early feedback from stakeholders. n Planning: risk-free mechanism for thinking about the future (manufacturing to governance). n Acquisition: very large pieces of equipment (i.e., helicopters, airplanes, submarines) are extremely expensive. M&S can help to decide in the purchasing process, enabling the customer to exploring different alternatives without the need of constructing the equipment prior to take the decision. n Proof of concept: test ideas and put them to work before creating the actual application. n Training: controlled experiments to enhance decision making skills in defense (called constructive simulation). business gaming and virtual simulators (human-in-the-loop simulators to learn and enhance motor skills when operating complex vehicles). n Education: used in sciences to provide insight into the nature of dynamic phenomena as well as the underlying mechanisms. n Entertainment: games and animations are the two most popular applications of simulation.

Phases in a M&S study n Problem definition n Input/output data collection and analysis n Modelling n Implementation n Verification and validation n Experimentation n Experiment optimization n Output data analysis