This document introduces some key concepts in simulation modeling. It discusses the components of a simulation model including entities, attributes, variables, resources, queues, statistical accumulators, events, the event calendar, and the simulation clock. It provides an example of simulating a simple processing system using these components. The goals of the simulation study are to estimate performance metrics like production, waiting times, queue lengths, and machine utilization. Simulation involves generating sample paths by applying logic and input data to the model components to observe system behavior over time.

1. Fundamental Simulation Concepts
SIE 431/531
Young-Jun Son, PhD
Systems and Industrial Engineering
son@sie.arizona.edu

2. Steps in Simulation Study

3. Example (Simple Processing System)
• General intent
• Estimate expected production
• Waiting time in queue, queue length, proportion of time machine is busy
• Time units
• Can use different units in different places (minutes, seconds, …)
• Be careful to check units when specifying inputs

4. Model Specifics
• Initially (time 0) empty and idle
• Base time units: minutes
• Input data (assume given for now), in minutes:
• Stop when 20 minutes of (simulated) time have passed

5. Sample Path
• Sample path
• Realization of system behavior
• Stochastic realization; trajectory

6. Goals of Study (Performance Metrics)
• Total production of parts over run (P)
• Average waiting time of parts in queue:
• Maximum waiting time of parts in queue:
N
WQ
N
i
i

1
N = no. of parts completing queue wait
WQi = waiting time in queue of ith part
WQ1 = 0 (why?)
i
N
i
WQ
max
,...,
1


7. Goals of Study (Performance Metrics) (2)
• Average number of parts in queue:
• Maximum number of parts in queue:
Q(t) = number of parts in queue at time t
20
)
(
20
0
 dt
t
Q
)
(
max
20
0
t
Q
t


8. Goals of Study (Performance Metrics) (3)
• Average and maximum total time in system of parts (cycle time):
• Utilization of machine (proportion of time busy)
• And, more
TSi = time in system of part i
i
P
i
P
i
i
TS
P
TS
max
,...,
1
1 ,




20
0
( ) 1 if machine is busy at time
, ( ) 0 if machine is idle at time
20
B t dt t
B t t



9. Generation of Sample Path
• Input data + Logic => sample path (realization of a system
behavior)
• What kinds of input data? ( , )
• What kinds of logic?
• Recursive equations for a simple system (spreadsheet based simulation)
• Event mechanism (to be covered)

10. Spreadsheet based Simulation
• Logic: recursive equation

11. Spreadsheet based Simulation (2)

12. Spreadsheet based Simulation (3)
• Popular for static models or very simple dynamic models
• Add-ins – @RISK, Crystal Ball
• Inadequate tool for dynamic simulations if there’s any complexity
• Extremely easy to simulate single-server queue in Arena – Chapter
3
• Can build very complex dynamic models with Arena – most of rest
of book

13. Components (terminologies) of Simulation Model
• Entities
• Dynamic objects in the simulation
• Something moving throughout the system
• Examples: ( )
• It may not be tangible, such as order for the company, requests,
etc

14. Components (terminologies) of Simulation Model (2)
• Attributes
• Local variable (tag) characterizing entities
• Each entity can have same or different values
• Most important thing is that their values are tied to specific entities
• Examples:
• Values can be real number, integer number, texts, or some other object
types: different software supports different data types

15. Components (terminologies) of Simulation Model (3)
• Variables
• Information that reflects some characteristics of the system, regardless
how many or what kinds of entities are around
• Variables are not tied in specific entity, rather pertain to the system at
large
• Examples:
• System (Arena) built-in variables: TNOW (current simulation time)
• User specified variables

16. Components (terminologies) of Simulation Model (4)
• Resources
• Entities compete with each other for service from resources such as
personnel, equipment, or space in storage area of limited size
• Example:
• Seizing and releasing. Capturing and freeing. Changing of system
variables
• Capacity or units of a resource: a resource can represent a group of
several individual and identical servers. If you want to differentiate them,
you need to define another resource
• Definition differs in different simulation packages (for now, we stick to the
Arena’s definition)

17. Components (terminologies) of Simulation Model (5)
• Queues
• A place where entities can wait when no resource is available
• Queue also has a capacity
• Example:
• You must model how to handle an entity arriving at a queue that’s already
full
• Should we allow this happen and do something? Balking!!
• Should we model so that this does not occur?
• This could be a logical queue or physical queue. This differs depending on
different simulation packages

18. Components (terminologies) of Simulation Model (6)
• Statistical Accumulators
• Variables needed for storing statistical information necessary to estimate
the desired performance measures (e.g., mean time in system)
• Several simulation packages take care of statistical accumulation. But, in
our hand simulation, we will do it manually to understand how it works
• Examples:

19. Components (terminologies) of Simulation Model (7)
• Events
• An event is something that happens at an instant of (simulated) time that
might change a system state (such as attributes, variables, or statistical
accumulators)
• There are four kinds of events in our example:
• Initialization to set things up: making all zeroes or initialization values
• Arrival: A new part enters the system
• Departure: A part finishes its service at the machine and leaves the system
• The End: The simulation is stopped at time 15 minutes
• Question: why not the following is not included to the event:
• “parts leave the queue and begin service at the machine, which changes the
system”?

20. Components (terminologies) of Simulation Model (8)
• Event calendar
• Event calendar is the place where future events are stored
• Event calendar has a set of records, where each record is associated with
1) id of an entity, 2) event time, and 3) the kind of event (init, arrive,
depart, or end)
• When it’s time to execute the next event, the top record is removed from
the calendar and the information in this record is used to execute the
appropriate logic, such as changing variables, showing message boxes, or
placing new records to the event calendar
• Arena (or other commercial simulation packages) places newly scheduled
events to the event calendar in increasing order of event times) => the
top one is always the next event to occur
• The variables that describe the system don’t change between successive
events
• Example: machine start processing, machine end processing: no change of
system states

21. Components (terminologies) of Simulation Model (9)
• Simulation clock:
• The current value of simulation clock (TNOW)
• Simulation does not take all values and flow continuously
• Updated when events occur (the event time of the top record from the
event calendar becomes the current simulation time before the associated
logic is performed)
• Stopping rule of simulation:
• Time or number of parts produced, etc
• If stopping rule is not properly given, simulation may run for ever: you
must kill the process (thread)