Discrete-Event Simulation Overview
Basic Discrete-Event System Models 1
Doug Bodner
ISyE 3044 – Simulation Analysis and Design
Spring 2022
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Topics
• Concepts
• Worldviews
▪ Event-scheduling
▪ Process-interaction
▪ Activity scanning
• Mechanics
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DES Concepts
•
System
▪ Collection of interacting components that operate together to achieve a goal
•
System model
▪ Abstract representation of a system (mathematical or computational) used for
design or analysis
•
System state
▪ Collection of variables containing all the information needed to describe the
system at any time
•
Entity
▪ An active object or component in the system that requires representation
•
Resource
▪ A passive object or component in the system that requires representation
•
Attribute
▪ Property of a given entity or resource
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DES Concepts
•
List
▪
•
Event
▪
•
Duration of time of specified length (end time is a scheduled event)
Delay
▪
•
List of event notices for future events ordered by scheduled time of occurrence
Activity
▪
•
Record of an event to occur now or in the future, including data needed for event execution
(type and scheduled time)
Event list (event calendar)
▪
•
Instantaneous occurrence causing system state to change
Event notice
▪
•
Collection of temporarily or permanently associated entities or resources in some logical order
Duration of time of unspecified length
Clock
▪
▪
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Keeps time in simulation
Can start with 𝑡 = 0 or some pre-specified time (2/9/2022 11:00am)
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Call Center Example
• A call center has two operators. Able has a
faster service time and takes a call if both are
idle. Baker takes a call if idle and Able busy.
• Single queue with two servers
• System state
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Call Center Example (cont’d)
• Events
▪ Customer arrives
▪ Able completes service
▪ Baker completes service
• Other events?
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Call Center Example (cont’d)
• Activities
• Delays
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Call Center Example (cont’d)
• Entities
• Resources
• Attributes
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DES Worldviews
• How we conceptualize a dynamic system
• Event-scheduling
▪ Focus on events and state changes (explicit event calendar)
▪ Events occur and schedule future events
▪ Move onto next event
• Process-interaction
▪ Focus on active entities moving through resource network
▪ Aligned with network of queues
▪ Predominant worldview
• Activity scanning
▪ Focus on activities
▪ Scan system at each time-step to see if any activities are enabled and
if so start them
▪ Computationally expensive
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Event-Scheduling
1.
Define system state and code different event types
▪ State changes for each event
▪ Events caused by each event
2.
3.
4.
Set initial state and schedule first event to initialize simulation
Move clock time to next event time on event calendar
Execute next event
▪ Remove event from event calendar
▪ Make state changes
▪ Schedule future events (update event calendar)
5.
6.
Go to 3 unless 6 is enabled
End simulation with
▪ No more events left
▪ Defined end time
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Event-Scheduling Example
• Call center with 2 operators Able and Baker
• Initialize with arrival
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Event-Scheduling Example (cont’d)
• Call center with 2 operators Able and Baker
• Assume 2nd arrival occurs before end of 1st
service
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Event-Scheduling Example (cont’d)
• Call center with 2 operators Able and Baker
• Assume Able completes service next
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Single Queue Example
• Events
• State variables
• Event logic is state dependent
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Process-Interaction
1.
Code the lifecycle of an entity
(job or customer)
▪ Set of resources through which it
moves
2.
3.
4.
5.
6.
Initialize simulation with initial
state and first arrival
Use inter-arrival times for
subsequent arrivals
Entities move through “blocks”
seizing and releasing resources
Entities exit system
End simulation with
▪ No more events left
▪ Defined end time
•
Under the hood, the simulation is
executing events and advancing
clock time to the next event
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Process-Interaction Example
• Single server queue with two customers
contending for server
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Activity Scanning
1. Define system state and
code different activities
that can occur
▪
▪
Primary activities/events
Conditional activities/events
2. Handle primary
activities/events using
event-scheduling
3. At each event, scan all
conditional
activities/events and start
any that are enabled
4. End simulation with
▪ No more activities/events left
▪ Defined end time
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Dump Truck Example
• Look at lists in more detail
• Six dump trucks are used to transport coal
from a mine to the railroad.
• The dump trucks are loaded at one of two
stations and then are weighed at one station.
• They travel to the railroad and back for
additional coal.
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Dump Truck Example (cont’d)
• System state
• Entities
• Resources
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Dump Truck Example (cont’d)
• Lists
• Activities
• Events
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Dump Truck Example (cont’d)
• Attributes of entities
• Attributes of resources
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Dump Truck Example (cont’d)
• Load times (minutes)
▪ 5 with probability 0.30
▪ 10 with probability 0.50
▪ 15 with probability 0.20
• Weight times (minutes)
▪ 12 with probability 0.70
▪ 16 with probability 0.30
• Travel times (minutes)
▪
▪
▪
▪
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40 with probability 0.40
60 with probability 0.30
80 with probability 0.20
100 with probability 0.10
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Dump Truck Example (cont’d)
• Assume FIFO queues
• Initialization of system
▪ 𝑇2 and 𝑇3 are being loaded
▪ 𝑇1 is being weighed
▪ 𝑇4 , 𝑇5 and 𝑇6 are in loader queue
• Event calendar
▪ EL at 𝑡 = 5, 𝑇3
▪ EL at 𝑡 = 10, 𝑇2
▪ EW at 𝑡 = 12, 𝑇1
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Dump Truck Example Execution
0
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𝐿
𝐿𝑞
Time
3
2
𝑊
𝑊𝑞
0
1
LQ
𝑇4
𝑇5
𝑇6
WQ
EC
BL
BW
-
EL, 5, 𝑇3
EL, 10, 𝑇2
EW, 12, 𝑇1
0
0
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Dump Truck Example Execution (cont’d)
Time
Spring 2022
𝐿𝑞
𝐿
𝑊𝑞
𝑊
LQ
WQ
EC
BL
BW
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Dump Truck Example Execution (cont’d)
Time
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𝐿𝑞
𝐿
𝑊𝑞
𝑊
LQ
WQ
EC
BL
BW
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Dump Truck Example Statistics
• Resource utilization
• Truck 1 statistics
•
Note: Simulation must be run for a long time (e.g., one week of simulated time) to get
reasonably accurate statistics, and we should do multiple replications
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Dump Trucks Using Process-Interaction
• Dump truck life cycle
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Dump Trucks Using Activity Scanning
Activity
Pre-conditions
Loading time
Truck is at front of loader queue and
At least one loader is idle
Weighing time
Truck is at front of weighing queue and
Weigh station is idle
Travel time
Truck has just completed weighing
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Different Size Dump Trucks
• Trucks 1-3 have twice the capacity as trucks 45
• How does this change the model?
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Different Queue Discipline for Trucks
• The larger trucks have priority in the queue
• Ties in size revert to FIFO
• How does this change the model?
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Other Statistics of Interest
• Number of trucks spending more than 20
minutes in a queue
• Proportion of trucks spending more than 20
minutes in a queue
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List Processing
• Using singly linked lists for event calendar and
queues
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Wrap-Up
• Concepts
• Worldviews
▪ Event-scheduling
▪ Process-interaction
▪ Activity scanning
• Mechanics
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