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.

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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).

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Defense of Simulation (cont)

• Closed-form models are not able to analyze most
  of the complex systems that are encountered in
  practice.

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Steps in aSimulation Study
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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.

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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.

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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.

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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.

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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.

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Steps in aSimulation Study(cont)

• Implementation
• The success of the implementation phase depends
  on how well the previous eleven steps have been
  performed.