to Welcome ISyE 320/321!!
Introduction to Simulation
Systems
System facility or process, actual or planned Examples abound ...
Fast-food restaurant Supermarket Bank operation Airport operations (passengers, security, planes, crews, baggage) Transportation/logistics/distribution operation Hospital facilities (emergency room, operating room, admissions) Computer network; Freeway system; Business process (insurance office); Criminal justice system; Chemical plant; Theme park; Manufacturing facility; Emergency-response system
Work With the System?
Study the system measure, improve, design, control
Maybe just play with the actual system
Advantage -- unquestionably looking at the right thing
But it's often impossible to do so in reality with the actual system
System doesn't exist Would be disruptive, expensive, or dangerous
Models
Model set of assumptions/approximations about how the system works
Study the model instead of the real system ... usually much easier, faster, cheaper, safer Can try wide-ranging ideas with the model
Make your mistakes on the computer where they don't count, rather than for real where they do count
Often, just building the model is instructive regardless of results All models are wrong, some models are useful
Types of Models
Physical (iconic) models
Tabletop material-handling models Mock-ups of fast-food restaurants Flight simulators
Logical (mathematical) models
Approximations and assumptions about a system's operation Often represented via computer program in appropriate software Exercise the program to try things, get results, learn about model behavior
Studying Logical Models
If model is simple enough, use traditional mathematical analysis ... get exact results, lots of insight into model
Queueing theory Differential equations Linear programming
But complex systems can seldom be validly represented by a simple analytic model
Danger of over-simplifying assumptions ... model validity? Type III error working on the wrong problem
Often, a complex system requires a complex model, and analytical methods don't apply ... what to do?
Simulation Is ...
Simulation very broad term methods and applications to imitate or mimic real systems, usually via computer Applies in many fields and industries Very popular and powerful method Games, Rehearsal, Practice, Experiments, etc.
Applications Example
How the # of operators working at a phone bank affects the # of people getting a busy signal:
Build a computer model replicating the arrival and handling of calls
Random numbers to replicate:
Time between calls Time talking to operator
Run the model:
Accumulate data Determine number of bank operators
Other Applications
Grocery stores (waiting time) Jobs (workers' utilization) Inventory models:
Demands (variation) Incoming volume
Traffic patterns Air traffic control (time to land, delays in landing) Bank teller schedule (customer waiting lines) Location of fire stations (response times)
Advantages of Simulation
Flexibility to model things as they are Allows uncertainty, nonstationarity in modeling
The only thing that's for sure: nothing is for sure Danger of ignoring system variability Model validity Even if messy and complicated
Advantages of Simulation (cont'd.)
Advances in computing/cost ratios
Estimated that 75% of computing power is used for various kinds of simulations Dedicated machines (e.g., real-time shop-floor control)
Advances in simulation software
Far easier to use No longer as restrictive in modeling constructs (hierarchical, down to C) Statistical design & analysis capabilities
Pitfalls of Simulation
Model building is an art!
Quality of the results depends on quality of the model: Only simulate a well defined system!
Not well defined system?
Unfocused simulation runs Little or no information
How to avoid:
Undertake a simulation project only if there is a clearly defined question to be answered or decision to be made
Pitfalls of Simulation (cont.)
Initial project (initial plant capacity):
Low level of detail Rough answers OK
are Advanced project (optimize plant efficiency):
Need more detail
Don't use simulation when a simple analytical model is enough!
Misinterpretation of simulation output:
This is the most common problem!
Disadvantage of Simulation
Don't get exact answers, only approximations, estimates
Also true of many other modern methods Can bound errors by machine roundoff
Get random output (RIRO) from stochastic simulations
Statistical design, analysis of simulation experiments Exploit: noise control, replicability, sequential sampling, variance-reduction techniques Catch: "standard" statistical methods seldom work
Different Kinds of Simulation
Computer-based Simulation Vs. Simulation by Hands Static vs. Dynamic
Does time have a role in the model?
Continuous-change vs. Discrete-change
Can the "state" change continuously or only at discrete points in time?
Deterministic vs. Stochastic
Is everything for sure or is there uncertainty?
Most operational models:
Computer-based, Dynamic, Discrete-change, Stochastic
Continuous Simulation
How a system changes in response to continuous controls
Smoothly over time
You often hear of simulations such as:
Driver training Weather prediction
Discrete Event Simulation
This is our topic in ISyE 320! How a system changes (instantaneously) in response to sudden or discrete events:
A situation that takes place at a specific period of time
Elements of Simulation
Elements of simulation modeling:
Use of random variables Representation of dynamic behavior (model)
Random Variables
Used to mimic real life phenomena in the computer:
Know you need a random variable Select appropriate probability distribution Generate random value from distribution
Example (phone bank):
Need to generate intervals between calls
Random Variables (cont.)
Selection of probability distribution is critical to model building Choice of probability distribution:
Collect data Fit data to various possible distributions
How to tell if a distribution is appropriate?
Generate a data set from the proposed distribution It should be statistically indistinguishable from empirical observations of the phenomenon
Dynamic Behavior
Representation of dynamic behavior:
Second building block of simulation
Track events over time, and Consider how the events change the state of the system
Dynamic Behavior
Use a simulation language or software package Excel provides a model ...