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ECE 466/658: Performance Evaluation and Simulation


System Modeling and Modeling approaches. Discrete Event Simulation. Markov Chains ... Alternatively, one can build a model of the system, analyze it, and predict the ... – PowerPoint PPT presentation

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Title: ECE 466/658: Performance Evaluation and Simulation

ECE 466/658 Performance Evaluation and
  • Introduction
  • Instructor Christos Panayiotou

  • Topics
  • System Modeling and Modeling approaches
  • Discrete Event Simulation
  • Markov Chains
  • Queueing Systems
  • Queueing Networks
  • Applications
  • Additional Information
  • Topics have wide applicability
  • Computer systems and networks
  • Manufacturing systems
  • Transportation systems

Need for Performance Evaluation
  • Computer system objectives
  • It must perform the functions that was designed
  • It must have adequate performance
  • Should perform its tasks under most circumstances
  • Should do them in reasonable time and cost
  • When typing a text file, reasonable time is a few
    milliseconds whereas when running complicated
    simulations, reasonable may be a few days
  • When designing a systems people usually pay a lot
    of attention to the functionality but not enough
    attention to the performance evaluation!
  • People address the issue of performance once the
    system is built when it is generally more
    difficult and more costly to achieve better

Modeling and Performance Evaluation
  • Once a system is built, we may be able to use it
    to measure its performance
  • Opportunities to redesign and reengineer the
    system are lost or become a lot more costly!
  • When the systems performance depends on some
    parameters, how can we figure out the best
    parameter settings?
  • Alternatively, one can build a model of the
    system, analyze it, and predict the performance
    of the actual system based on the model.
  • This approach is more flexible allowing for
    redesign and reengineering before investing in
    the final system.

  • Model
  • It is a set of equations or a piece of software
    (simulator) that imitates the behavior of the
    real system.
  • There may be several models that can capture the
    behavior of a system.
  • Modeling is mostly an art and not an exact
  • Depending on the answers we are looking for,
    models can be very detailed and complex or they
    can be very simple.

Modeling Process
  • A model predicts what the systems output would
    be given an input u(t).
  • A model is as good as its input garbage in,
    garbage out!

Concept of State
y(t) g(u(t), t)
  • Suppose that at a time instant t1, u(t1)a and
    y(t1)Y. Then, at time t2, u(t2)a then what is
  • Example
  • Let x(t)x(t-1)u(t)
  • y(u(t))u(t)x(t)5
  • The state of a system at time t0 is the
    information required at t0 such that the output
    y(t), for all tt0, is uniquely determined from
    this information and from the input u(t), tt0.

State Space Modeling
  • State equations The set of equations required to
    specify the state x(t) for all tt0 given x(t0)
    and the function u(t).
  • State Space X The set of all possible values
    that the state can take.
  • Examples

Sample Path
  • Evolution of the state over time

Continuous State
Discrete State
Example Warehouse
  • System Input
  • System Dynamics

Example Warehouse Sample Path
  • System Input
  • System Dynamics

System Classification
Continuous State Continuous Time
Discrete State Continuous Time
Continuous State Discrete Time
Discrete State Discrete Time
Deterministic and Stochastic Systems
  • In many occasions the input functions u(t) are
    not known exactly but we can only characterize
    them through some probability distribution.
  • Signal noise at a mobile receiver
  • Arrival time of customers at a bank
  • If the input function is not known exactly, then
    the state cannot be determined exactly, but it
    constitutes a random variable
  • A system is stochastic if at least one of its
    output variables is a random variable. Otherwise
    the system is deterministic.
  • In general, the state of a stochastic system
    defines a random process.

  • Depending on the type of system and/or the
    objectives of the analysis, one may be interested
    in various measures
  • Average number of customers in the system
  • Number of packets dropped in an interval 0,T.
  • Average delay in a system
  • The most general tool for answering the above
    questions is computer simulation, however,
    simulation does not provide good understanding of
    the problem.
  • There are no general analytical tools that can
    address problems of some complexity with adequate
    accuracy, however, analytical tools can be used
    to gain a better understanding of the nature of
    the problem.

Closing (2)
  • Simple vs real models
  • Simple models can be used to gain a better
  • More complex models may be used to imitate real
    real scenarios
  • Accuracy vs Complexity
  • When modeling a system, it is important to always
    have in mind what questions the specific model
    will help you answer.
  • Changing the questions, may require changing the
  • Some questions may require accuracy.
  • Does the network meet the requirement of only
    0.1 packet loss?
  • Some questions may not require much accuracy
  • Comparing two designs (ordinal optimization)
  • What does measure mean?
  • What does it mean packet loss probability does
    not exceed 0.1?
  • What does it mean packet loss probability does
    not exceed 10-3?
  • What does it mean packet loss probability does
    not exceed 10-6?