agent-based modelling and simulations

Agent-Based

Modelling and Simulations

Simulation

Agostino Poggi

University of Parma - 2SimulationProf. Agostino Poggi

System, Model & Simulation

♦System

An actual or theoretical system in which distinct entities interact

♦Model

A reproduction of the system at an appropriate level of granularity

♦Simulation

Designing a model of a system, executing the model on a computer, and analyzing the execution output


Simulation Activities


Simulation Goals

♦ Imitate the operation of a real-world process or system over time

♦Prediction

Model should produce quantitatively correct predictions depending on its input values

♦Explanation

Qualitatively significant results are sufficient for understanding the reaction of the system to input values


When Is Appropriate (1/3)

♦Enables the study of an experimentation with the internal interactions of a complex system, or of a subsystem within a complex system

♦ Informational, organizational and environmental changes can be simulated and the effect of those alterations on the model’s behavior can be observer

♦Knowledge gained in designing a simulation model can be of great value toward suggesting improvement in the system under investigation



♦By changing simulation inputs and observing the resulting outputs, valuable insight may be obtained into which variables are most important and how variables interact

♦Can be used as a pedagogical devices to reinforce analytic (exact) solution methodologies

♦Can be used to experiment with new designs or policies prior to implementation, so as to prepare for what may happen

♦Can be used to verify analytic solutions



♦Requirements for a machine can be determined by simulating its different capabilities

♦Simulation models designed for training, allow learning without the cost and disruption of on-the-job learning

♦Animation shows a system in simulated operationso that the plan can be visualized

♦Modern systems (factories, service organizations, computing systems, …) are so complex that the interactions can be treated only through simulation


When Is Not Appropriate (1/2)

♦Simulation should not be used when the problemcan be solved using common sense

♦Simulation should not be used if the problem canbe solved analytically

♦Simulation should not be used, if it is easier to perform direct experiments

♦Simulation should not be used, if the costs exceeds savings

♦Simulation should not be performed, if the resources or time are not available


When Is Not Appropriate (2/2)

♦ If no data are available, not even estimate simulation is not advised

♦ If there is not enough time or persons are not available, simulation is not appropriate

♦ If managers have unreasonable expectation or the power of simulation is over estimated, simulation may not be appropriate

♦ If system behavior is too complex or cannot be defined, simulation is not appropriate


Advantages (1/2)

♦Studies about systems can be done in the design stage

♦Models are run rather than solver

♦New policies, operating procedures, decision rules, information flow can be explored without disrupting the ongoing operations of the real system

♦New hardware designs, physical layouts, transportation systems can be tested without committing resources for their acquisition

♦Hypotheses about how or why certain phenomenaoccur can be tested for feasibility

♦Time can be compressed or expanded allowing for a speedup or slowdown of the studied phenomena


Advantages (2/2)

♦ Insight can be obtained about the interaction of variables

♦ Insight can be obtained about the importance of variables to the performance of the system

♦Bottleneck analysis can be performed findingindication where work-in-process, information materials and so on are being excessively delayed

♦A simulation study can help in understanding how the system operates rather than how individualsthink the system operates

♦What-if questions can be answered (useful in the design of new systems)


Disadvantages

♦Model building requires special training

♦Simulation results may be difficult to interpret

♦Simulation modeling and analysis can be timeconsuming and expensive

♦Simulation is used in some cases when an analytical solution is possible or even preferable


Simulation Model

♦Allows to study the behavior of a system as it evolves over time

♦Takes the form of a set of assumptions concerning the operation of the system

♦Assumptions are expressed in relationships between the entities of the system

Mathematical relationships

Logical relationships

Symbolic relationships


System Components

♦Entity Is an object of interest in a system

♦Attribute Denotes the property of an entity

♦Activity Is a process causing changes in a system

♦State Is a collection of variables necessary to describe a

system at any time

♦Event Is an instantaneous occurrence that may change the

state of the system


Modelling Dilemma

Simplicity

Generality

Lack of error (accuracy of results)

Realism

(design reflects

observations)


System Environment

♦External components which interact with the system and produce necessary changes are said to constitute the system environment

♦ In modeling systems, it is necessary to decide on the boundary between the system and its environment

♦This decision may depend on the purpose of the study


System Adjectives (1/2)

♦Endogenous

Is used to describe activities and events occurring within a system

♦Exogenous

Is used to describe activities and events in the environment that affect the system

♦Closed

Is used for defining a system for which there is no exogenous activity and event


System Adjectives (2/2)

♦Open system

Is used for defining a system for which there are exogenous activities and events

♦Continuous

Is used for defining a system in which the changes are predominantly smooth

♦Discrete

Is used for defining a system in which the changes are predominantly discontinuous


Model Types

♦Mathematical model Represents a system through a symbolic notation and

mathematical equations♦Static model

Represents a system at a particular point of time♦Dynamic model

Represents a system as it changes over time♦Deterministic model

Represents a system for which a specific set of outputsalways corresponds to the same set of inputs (it does not contain random variables)

♦Stochastic model Represents a system having one or more random

variables as inputs that lead to random outputs


Simulation Types Classification

♦Discrete versus continuous time

♦Stochastic versus deterministic

♦Macro versus micro


Discrete Event Simulation

♦Model

Finite state machines, queues, Petri nets, …

♦Execution

Read the “queue” of events and trigger new events as each event is processed

♦Applications

Diagnosing, business decisions, networks analysis, …


Continuous Dynamic Simulation

♦Model

Partial or ordinary differential equations

♦Execution

Periodic numerical resolution of equations

♦Applications

Flight simulators, electrical circuits, …


Monte Carlo Simulation

♦Model

Can be almost anything

♦Execution

Generate inputs randomly from the domain and perform a deterministic computation on them

♦Applications

Physics, engineering, applied statistics, …


Cellular Automata

♦Model

Regular n-dimensional grid of cells whose state is function of the state of their neighborhood

♦ Execution

Periodic application of rules which determine state of a cell as a function of neighboring cells

♦Applications

Theoretical computer science, mathematics, biology, physics, engineering, cryptography, …


Macro Simulation

♦Model

Complete system is modeled as one monolithic entity

• Populations are averaged together

• Model attempts to simulate changes in these averaged characteristics for the whole population

♦Execution

Periodically update the state variables describing the system

♦Applications

Naturally applies to systems that can be modeled centrally and in which the dynamics are dominated by physical laws


Micro Simulation

♦Model

Explicitly attempts to model specific behaviors of specific individuals

♦Execution

Periodic communication between individuals

♦Applications

Most appropriate for domains characterized by a high degree of localization and distribution and dominated by discrete decisions


Simulation Techniques

♦By hand

♦Spreadsheets

♦Computational mathematics systems

♦Programming in general purpose languages

♦Simulation languages

♦Simulation environments


Simulation Paradigms


Lotka-Volterra Prey Predator Model

Size of the prey population at time t

Size of the predator population at time t

Evolution of prey population

Evolution of predator population


Simulation Time

♦Simulation execution consists in stepping through time while updating the variables in the model

♦ In continuous-time models (e.g., differential equations) time steps can be reduced indefinitely

♦ In discrete-time models time is quantized somehow

Leap through time using event scheduling

Employ small time increments using time slicing


Simulation Steps

♦Problem formulation

♦Setting of objectives and overall project plan

♦Model conceptualization

♦Model translation

♦Model validation and verification

♦Documentation and reporting


Problem Formulation

♦Every study begins with a statement of the problem, provided by policy makers

♦Analyst ensures its clearly understood

♦ If it is developed by analyst, policy makers should understand and agree with it


Objectives

♦Objectives indicate the questions to be answered by simulation

♦At this point a determination should be made concerning whether simulation is the appropriate methodology

♦Objectives must be made explicit through the definition of a project plan


Project Plan Definition

♦A statement of the alternative systems

♦A method for evaluating the effectiveness of these alternatives

♦Number of days required to accomplish each phase of the work with the anticipated results

♦Number of people involved

♦Cost


Model Conceptualization

♦Construction of a model of a system is probably as much art as science

♦Art of modeling is enhanced by an ability To abstract the essential features of a problem

To select and modify basic assumptions that characterize the system

To enrich and elaborate the model until a useful approximation of results

♦Thus, it is best to start with a simple model and build toward greater complexity

♦Model conceptualization enhance the quality of the resulting model and increase the confidence of the model user in the application of the model


Model Translation

♦Real-world systems result in models that require a great deal of information storage and computation

♦ It can be programmed by using simulation languages or special purpose simulation environments

♦Simulation languages are powerful and flexible

♦Simulation environments can reduce development time


Validation

♦ It is the determination that a model is an accurate representation of the real system

♦Crucial for guaranteeing that output of simulation will say something meaningful

♦Achieved through calibration of the model, that is an iterative process of comparing the model to actual system behavior and their discrepancies


Verification

♦ Is the process of confirming that the model is correctly implemented

♦Model is tested to find and fix errors in the implementation of the model

♦There are many techniques that can be utilized to verify a model

♦ In particular, many software engineering techniques used for software verification are applicable to simulation


Validation & Verification Process


Validation & Verification Procedures


Instruments for Output Analysis


Program Documentation

♦Can be used again by the same or different analysts to understand how the program operates

♦Further modification of the model will be easier

♦Model users can change the input parameters for better performance


Process Documentation

♦Gives the history of a simulation project

♦Result of all the analysis should be reported clearly and concisely in a final report

♦Enable to review the final formulation and alternatives, results of the experiments and the recommended solution to the problem

♦Final report provides a vehicle of certification


Some Main Simulation Tools

agent-based modelling and simulations

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