Similation

Reasons for Simulation

cost in
• time
• money
• people

Types of Simulation

• Physical models
• Prototypes
• Practice exercises
• Mathematical Models

  deterministic

  budgets

  pro forma financial statements

  schedules

  stochastic

  explicitly incorporating probability

Monte Carlo Procedure

Context

• repetition
• variation
• learning

• discrete distributions
• continuous distributions

• average
• maximum
• minimun
• median
• quantiles

The Relational Model

variables of interest
• measurements that change with circumstances or decisions

parameters
• measurements that define the circumstances

relations

calculations

deterministic parameters
• initial values
• persistent values

Random Variables for Parameters

comments on randomness
• randomness is more subtle than equally likely.
• true randomness shows runs of luck.
• naturalness often has a level of randomness, such as in handwriting, or mountain scenery, or waves breaking on the shore.
  discrete probability distributions
  estimating distributions

  Simulated Observations

  Generating Random Decimals
  • tables
  • physical means
  • junior digits
    • computer clocks
    • shares traded
    • old currency
  • pseudo random numbers

  Analysis of Observations

  1. recording
  2. summarizing
  3. distributions of variables
     • means
     • variability
     assessing the reliability of the simulation
     • quantifying experience
     • convergence and the Law of Large Numbers
     • use of the Central Limit Theorem

  Examples

  1. Sales, MONTECA1.WQ1
     • Context: Sales Planning
     • Input RVs: Sales
     • Measure: Sales
  2. Income in a Single Period, MONTECA2.WQ1
     • Context: Profit Planning
     • Input RVs: Sales, Expenses
     • Measure: Profit
  3. Cash Flow over Four Periods, MONTECA3.WQ1
     • Context: Capital Budgeting
     • Input RVs: Units Sold, Sales Price, Unit Cost
     • Measure: Net Present Value, Internal Rate of Return
  4. Scenic View Self Service, MONTECA4.WQ1
     • Context: Highway Planning, Scenic View
     • Input RVs: Arrivals, Viewing Time
     • Measure: Parked Cars, Drive Bys
  5. Queuing M/M/1, MONTECA5.WQ1
     • Context: Waiting Line M/M/1
     • Input RVs: Arrivals, Service
     • Measure: Line Length, Waiting Time
  6. Demography, FAMILY.BAS
     • Context: Demography. Each couple has children until a girl is born
     • Input RVs: Sex of Child Born
     • Measure: Ratio of girls to all children born. Variability of the ratio.
  7. Statistics, NORMALD.BAS
     • Context: Random Walk, Generation of a Normal Distribution
       This simulates the ball bearing cascade at the Seattle Museum of Science.
     • Input RVs: Movement left or right
     • Measure: Frequency of final positions
  8. Traffic Management, TRAFFIC.BAS
     • Context: freeway traffic, one lane specify the problem
     • Input RVs: deviation from target speed
     • Measure: position, speed, acceleration, braking
       Random response leads to compression waves.

  more to come

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  Last updated April 4, 1996.

  send comments to hwarren@calstatela.edu