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ECE 466/658: Performance Evaluation and Simulation

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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


1
ECE 466/658 Performance Evaluation and
Simulation
  • Introduction
  • Instructor Christos Panayiotou

2
Syllabus
  • Topics
  • System Modeling and Modeling approaches
  • Discrete Event Simulation
  • Markov Chains
  • Queueing Systems
  • Queueing Networks
  • Applications
  • Additional Information
  • www.eng.ucy.ac.cy/christos/courses/ECE466
  • www.eng.ucy.ac.cy/christos/courses/ECE658
  • Topics have wide applicability
  • Computer systems and networks
  • Manufacturing systems
  • Transportation systems

3
Need for Performance Evaluation
  • Computer system objectives
  • It must perform the functions that was designed
    for.
  • 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
    performance.

4
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.

5
Modeling
  • 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
    science.
  • Depending on the answers we are looking for,
    models can be very detailed and complex or they
    can be very simple.

6
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!

7
Concept of State
OUTPUT
INPUT
MODEL
u(t)
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
    y(t2)?.
  • 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.

8
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

9
Sample Path
  • Evolution of the state over time

Continuous State
Discrete State
10
Example Warehouse
  • System Input
  • System Dynamics

11
Example Warehouse Sample Path
  • System Input
  • System Dynamics

u1(t)
t
u2(t)
t
x(t)
t
12
System Classification
Continuous State Continuous Time
Discrete State Continuous Time
Continuous State Discrete Time
Discrete State Discrete Time
13
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.

14
Closing
  • 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.

15
Closing (2)
  • Simple vs real models
  • Simple models can be used to gain a better
    understanding
  • 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
    model!
  • 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?
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