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Model Classification and

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Title: Model Classification and


1
Lecture 2
  • Model Classification and
  • Steps in a Simulation Study

2
Definition of Simulation
  • Simulation is the imitation of an operation of a
    real-world process or system over time.
  • Simulation is a method of understanding,
    representing and solving complex interdependent
    system.
  • Simulation is the process of designing a model of
    a real system and conducting experiments with
    this model for the purpose either of
    understanding the behavior of the system or of
    evaluating various strategies (with the limits
    imposed by a criterion or a set of criteria) for
    the operation of the system.

3
Definition of Simulation(cont)
  • Simulation in general is to pretend that one
    deals with a real thing while really working with
    an imitation.
  • A flight simulator on a PC is computer model of
    some aspects of the flight it shows on the
    screen the controls and what the pilot (the
    youngster who operates it) is supposed to see
    from the cockpit (his armchair).

4
When to use Model
  • To fly a simulator is safer and cheaper than the
    real airplane.
  • For precisely this reason, models are used in
    industry, commerce and military it is very
    costly, dangerous and often impossible to make
    experiments with real systems.
  • Provided that models are adequate descriptions of
    reality (they are valid), experimenting with them
    can save money, suffering and even time.

5
When to use Simulations
  • Systems which change with time such as a gas
    station where cars come and go (called dynamic
    systems) and involve randomness (nobody can guess
    at exactly which time and next cars should arrive
    at the station) are good candidates for
    simulation.
  • Modeling complex dynamic systems theoretically
    need too many simplifications and the emerging
    models may not be therefore valid.
  • Simulation does not require that many simplifying
    assumptions, making it the only tool even in
    absence of randomness.

6
How to simulate?
  • Suppose we are interested in a gas station. We
    may describe the behaviour of this system
    graphically by plotting the number of cars in the
    station the state of the system.
  • Every time a car arrives the graph increases by
    one unit while a departing car causes the graph
    to drop one unit.
  • This graph (called sample path), could be
    obtained from observation of a real station, but
    could also be artificially constructed.
  • Such artificial construction and the analysis of
    the resulting sample path consists of the
    simulation.

7
Types of Models
  • Models can be classified as being mathematical or
    physical.
  • A mathematical model uses symbolic notation and
    mathematical equations to represent a system.
  • A simulation model is particular type of
    mathematical model of a system.

8
Type of Simulation
  • Simulation models may be further classified as
    being
  • Static model or Dynamic model
  • Deterministic model or Stochastic model
  • Discrete model or Continuous model

9
Static vs Dynamic
  • Static models and dynamic models are
    classification by the dependency on time
  • A static simulation model, sometimes called a
    Monte Carlo simulation, represents a system at a
    particular point in time.
  • For example, Mark Six, inventory level
  • Dynamic simulation models represent systems in
    which state of the variables change over time.
    The simulation of a bank from 900am to 400pm is
    an example of a dynamic simulation.
  • For example, service time, waiting time.

10
Deterministic vsStochastic
  • Classification by the nature of the variables
  • Simulation models that contain no random
    variables are classified as deterministic.
  • For example, deterministic arrivals would occur
    at a dentists office if all arrived at the
    scheduled appointment time.
  • A stochastic simulation model has one or more
    random variables as input.
  • Random inputs lead to random outputs.
  • For example, random arrival, random product
    demand, random incoming calls.

11
Deterministic vsStochastic (cont)
  • Since the outputs are random, they can be
    considered only as estimates of the true
    characteristics of a model.
  • For example, the simulation of a bank would
    usually involve random interarrival times and
    random service times.

12
Discrete vs Continuous
  • Discrete and continuous models are defined in an
    analogous manner, classification by system
    nature.
  • A discrete model is one in which the state
    variable(s) change only at a discrete set of
    points in time.
  • The bank is an example of a discrete system,
    since the state variable, the number of customers
    in the bank, changes only when a customer arrives
    or when the service provided a customer is
    complete.
  • Other examples, busy/idle counter, occupied/free
    machine.

13
Discrete vs Continuous(cont)
  • A continuous model is one in which the state
    variable(s) change continuously over time.
  • An example is the head of water behind a dam.
    During and for some time after a rain storm,
    water flows into the lake behind the dam.
  • Water is drawn from the dam for flood control and
    to make electricity.
  • Evaporation also decreases the water level.
  • But, continuous system can be approximated by a
    discrete-event system, depending on the expected
    preciseness and the objective of the study.

14
Applications - Service Applications
  • Staffing
  • A bank manager might determine that three tellers
    on duty results in a tolerable wait for service
    during most of the day, but that her customers
    time in queue is too long during the busy lunch
    hour and in the late afternoon.
  • She could then assess the impacts of adding
    additional part-time help during the peak hours.

15
Applications - Service Applications (cont)
  • Procedure Improvement
  • Many organizations have learned that internal
    consumers are customers.
  • In an effort to improve the responsiveness of
    their administrative and support functions many
    of these companies are using simulation to model
    revised procedures designed to streamline
    processing of paperwork, telephone calls and
    other daily transactions.

16
Advantages ofSimulation
  • New policies, operating procedures, decision
    rules, information flows, organizational
    procedures, and so on can be explored without
    disrupting ongoing operations of the real system.
  • New hardware designs, physical layouts,
    transportation systems, and so on, can be tested
    without committing resources for their
    acquisition.
  • Hypotheses about how or why certain phenomena
    occur can be tested for feasibility.
  • Time can be compressed or expanded allowing for a
    speedup or slowdown of the phenomena under
    investigation.

17
Advantages ofSimulation (cont)
  • 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 indicating
    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 individuals
    think the system operates.
  • What-if questions can be answered.

18
Disadvantages ofSimulation
  • Model building requires special training.
  • Simulation results may be difficult to interpret.
  • Simulation modeling and analysis can be time
    consuming and expensive. Skimping on resources
    for modeling and analysis may result in a
    simulation model or analysis that is not
    sufficient for the task.
  • Simulation is used in some cases when an
    analytical solution is possible, or even
    preferable. This might be particularly true in
    the simulation of some waiting lines where
    closed-form queueing models are available.

19
Defense of Simulation
  • Vendors of simulation software have been actively
    developing packages that contain all or part of
    models that need only input data for their
    operation.
  • Many simulation software vendors have developed
    output analysis capabilities within their
    packages for performing very thorough analysis.
  • Simulation can be performed faster today than
    yesterday, and even faster tomorrow. This is
    attributable to the advances in hardware that
    permit rapid running of scenarios.

20
Defense of Simulation (cont)
  • Closed-form models are not able to analyze most
    of the complex systems that are encountered in
    practice.

21
Steps in aSimulation Study
22
Steps in aSimulation Study (cont)
  • Problem formulation
  • If the statement is provided by the policy
    makers, or those that have the problem, the
    analyst must ensure that the problem being
    described is clearly understood. If a problem
    statement is being developed by the analyst, it
    is important that the policy makers understand
    and agree with the formulation.
  • Setting of objectives and overall project plan
  • The objectives indicate the questions to be
    answered by simulation. The overall project plan
    should include a statement of the alternative
    systems to be considered, and a method for
    evaluating the effectiveness of these
    alternatives.

23
Steps in aSimulation Study(cont)
  • Model conceptualization
  • This is another important and difficult subject.
    The basic steps are to consider all the related
    factors first, then evaluate each one (keep or
    ignore) and reach the final model.
  • Data collection
  • The more data you have ? the more complete
    information you have ? the more precise model you
    can build ? the better solution you would get.
  • Model translation
  • Program the model into a computer language.
    Simulation languages are powerful and flexible.
    In most cases, some computer software packages
    are involved. The model development time is
    greatly reduce. Furthermore, software packages
    have added features that enhance their
    flexibility.

24
Steps in aSimulation Study(cont)
  • Verified?
  • Verification pertains to the computer program
    prepared for the simulation model. Is the
    computer program performing properly? If the
    input parameters and logical structure or the
    model are correctly represented in the computer,
    verification has been complete.
  • Validated?
  • Validation is the determination that a model is
    an accurate representation of the real system.
    Validation is usually achieved through the
    calibration of the model, an iterative process of
    comparing the model to actual system behaviour
    and using the discrepancies between the two, and
    the insights gained, to improve the model.

25
Steps in aSimulation Study(cont)
  • Experimental design
  • The alternatives that are to be simulated must be
    determined. For each system design that is
    simulated, decisions need to be made concerning
    the length of the initialization period, the
    length of simulation runs, and the number of
    replications to be made of each run.
  • Production runs and analysis
  • Production runs, and their subsequent analysis,
    are used to estimate measures of performance for
    the system designs that are being simulated.
  • More runs?
  • The analyst determines of additional runs are
    needed and what design those additional
    experiments should follow.

26
Steps in aSimulation Study(cont)
  • Documentation and reporting
  • Program documentation
  • If the program is going to be used again by the
    same or different analysts, it may be necessary
    to understand how the program operates.
  • The model users can change parameters at will in
    an effort to determine the relationships between
    input parameters and output measures of
    performance, or to determine the input parameters
    that optimize some output measure of
    performance.
  • Progress report
  • It provides the important written history of a
    simulation project.

27
Steps in aSimulation Study(cont)
  • Implementation
  • The success of the implementation phase depends
    on how well the previous eleven steps have been
    performed.
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