Deterministic simulation
In mathematical modeling, deterministic simulations contain no random variables and no degree of randomness, and consist mostly of equations, for example difference equations. These simulations have known inputs and they results in a unique set of outputs. In opposite we know stochastic (probability) simulation, which include random variables.
Simulation is a process of imitation or generating reality or things that we cannot, or for some reasons didn’t accomplish in the real world. Simulation is an indispensable problem-solving methodology for the solution of many real-world problems.
Deterministic simulation models are usually designed to capture some underlying mechanism or natural process. They are different from statistical models (for example linear regression) whose aim is to empirically estimate the relationships between variables. The deterministic model is viewed as a useful approximation of reality that is easier to build and interpret than a stochastic model. However, such models can be extremely complicated with large numbers of inputs and outputs, and therefore are often noninvertible; a fixed single set of outputs can be generated by multiple sets of inputs. Thus taking reliable account of parameter and model uncertainty is crucial, perhaps even more so than for standard statistical models, yet this is an area that has received little attention from statisticians.
Deterministic model
For deterministic simulation we need a deterministic model. The deterministic model is viewed as a useful approximation of reality that is easier to build and interpret than a stochastic model. However, such models can be extremely complicated with large numbers of inputs and outputs, and they are often noninvertible; a fixed single set of outputs can be generated by multiple sets of inputs. Model represents reality.
Types of models
Models can be mathematical or physical. Mathematical models consist of equations which represents system. A simulation model is a particular type of mathematical model of a system. A model is a representation of the reality that captures the essence of reality.
Other types of simulations
Continuous
Variable change continuously over time.
Discrete
State variable change only at a discrete set of points in time.
Static
Represents a system in a particular point in time.
Dynamic
Shows change in system during time.
Stochastic
Only probabilistically determined.
Use of simulations
Mostly are deterministic simulations used in scientific researches, we can found in various studies about populations fields, climate development, pollution, but also in another areas as engineering, chemistry and policy making. Deterministic simulations have received attention in the statistical literature under the general topic of computer experiments. Computer experiments simulate complex system which requires a number of inputs. Use of stochastic system is much cheaper but also inaccurate and simplifying.
Building a simulation
Here are some basic points of simulation development.
Problem formulation
At beginning we have to formulate problem. What we want to solve. Problem must be explained for easy understanding.
Setting objectives
We have to say what our simulation will solve. In this part is also important to decide about appropriate methodology.
Model conceptualization
It is hardly possible to provide how the model should be done with instruction, it is so unique that is it more art than science. The art of modeling is enhanced by an ability to abstract the essential features of problem, to select and modify basic assumptions that characterize the system, and then to enrich and elaborate the model until useful approximation results.
Data collection
We need to collect appropriate input data. When the complexity of model change also changes demand on data. Objectives of the study tell us which data to collect.
Model translation
Simulation languages are powerful and flexible. It is necessary to translate model into computer recognizable format. Modeler must decide if whether to program the model in a simulation language such as GPSS/H or to use special purpose simulation software:
Arene – discrete event simulator has also academic version
CSIM – CSIM is a re-usable general purpose discrete-event simulation environment for modeling complex systems of interacting elements. It contains hierarchical block diagram tools and extensive model libraries covering several domains. CSIM can be used for modeling: agent-based systems, logistics, wireless networks, computer networks...
Dynare – when the framework is deterministic, can be used for models with the assumption of perfect foresight. The purpose of the simulation is to describe the reaction in anticipation of, then in reaction to the shock, until the system returns to the old or to a new state of equilibrium.
Janus – Janus is an interactive simulation war game portraying realistic events during multi-sided combat. It uses digitized terrain effecting line of sight and movement, depicting contour lines, roads, rivers, vegetation and urban areas. It has the capability to be networked with other systems, in order to simulate a war game with multiple sides.
Modsaf (Modular Semi-Automated Forces) is a set of software modules and applications used to construct Advanced Distributed Simulation (ADS) and Computer Generated Forces (CGF) applications. ModSAF modules and applications let a single operator create and control large numbers of entities that are used for realistic training, test, and evaluation on the virtual battlefield. ModSAF contains entities that are sufficiently realistic resulting in the user not being aware that the displayed vehicles are being maneuvered by computers, rather than human crews. These entities, which include ground and air vehicles, dismounted infantry (DI), missiles, and dynamic structures, can interact with each other and with manned individual entity simulators to support training, combat development experiments, and test of evaluation studies.
Taylor Enterprise Dynamics is an objectoriented software system used to model, simulate, visualize, and monitor dynamic-flow process activities and systems. With Taylor ED’s open architecture, software users can access standard libraries of atoms to build models. Atoms are Taylor ED’s smart objects and model building resources. In addition to Taylor ED’s standard atom libraries, users can create new atoms themselves.
Validation
That means if model represents the real system. It is iterating process until desirable progress is achieved. We must be sure does program represent reality as it was intended.
Experimental design
We have to decide which alternatives we should simulate and they have to be completed and analyzed.
Production runs and analysis
Production runs are subsequently analyzed to determine their performance. In this analyze some software can help us.
Documentation
Documentation is needed for programs next use, next development or just for understanding of simulation and how it does operates. Sometimes we also need to change some parameters later and thus we need to understand code.
Implementation
Implementation depends on the previous steps, how well they were done. How good was the analyze done. Conversely, if the model and its underlying assumptions have not been properly communicated, implementation will probably suffer, regardless of simulation models validity.
Example of deterministic simulations
Performance evaluation of highly concurrent computers B. Kumar and E. S. Davidson Object of the simulation is CPU memory subsystem IBM 360/91.
Simulation is presented as a practical technique for performance evaluation of alternative configurations of highly concurrent computers. A technique is described for constructing a detailed deterministic simulation model of a system. In the model a control stream replaces the instruction and data streams of the real system. Simulation of the system model yields the timing and resource usage statistics needed for performance evaluation, without the necessity of emulating the system. As a case study, the implementation of a simulator of a model of the CPUmemory subsystem of the IBM 360/91 is described.
A comparison of deterministic vs stochastic simulation models for assessing adaprive information management techniques over disadvantaged tactical communication networks – Dr. Allan Gibb Mr. Jean-Claude St-Jacques
Use of a deterministic battlefield model based on a scripted scenario will provide the required reproducibility and full control over event sequencing. A stochastic battlefield model, as provided in computer simulation applications like JANUS and ModSAF, produces results that can be made strictly reproducible if the same random number seed can be employed. However, such a model will not provide full human control over scenario composition and event sequencing. A deterministic battlefield model offers clear advantages for the test bed studies.
Using discrete event simulation in supply chain planning – Daniel Hellström, Mats Johnsson
Supply chains are difficult to plan because they involve complex relationships and dynamically changing variables that influence supply chain performance. In this paper, discrete-event simulation (DES) is evaluated in order to identify its appropriateness as a technique in supply chain planning. A DES model was developed as part of a case study, and is used in this paper to determine whether DES is an appropriate technique for unraveling the complexity of supply chains.
Advantages and disadvantages of system simulations
Advantages
Advantages of simulation are new policies, operating procedures, decision rules, information flows. Hypotheses about testing certain phenomena. It is possible to adjust time – compress or extend. We can answer what-if questions. Is it controlled experiment where we know all of the parameters, and we know when they will be changed. It is possible to make sensitivity analysis. It doesn’t disturb the real system. Is it effective learning or training tool. For example flight simulator. Even if no simulation is ever 100% exact, it can help us to solve lots of problems.
Disadvantages
Disadvantages are model building requires special training. It has to be learned during the time. Simulations can be hard to interpret.
About determinism
One definition – The world is governed by (or is under sway of) determinism if and only if given specified way things are at time t, way things go thereafter is fixed as a matter of natural law.
How could we ever decide whether our world is deterministic or not? Given that some philosophers and some physicists have held firm views—with many prominent examples on each side—one would think that it should be at least a clearly decidable question. Unfortunately, even this much is not clear, and the epistemology of determinism turns out to be a thorny and multi-faceted issue.
External links
See also
- Stochastic simulation
- Systems simulation
- Determinism
- Dynamical system
- Dynamical systems theory
- System dynamics
- Systems theory