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Creating Queuing Systems Simulations
with Sparx EA SysML Parametric Models
1
Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
Add Performance Analysis to your EA Processes and System Models
with Queuing Systems Simulations
Queuing Systems Simulation
• This presentation illustrates how to use Sparx
Enterprise Architect Parametric Model features
found in the Systems Engineering and Ultimate
editions to simulate queuing systems.
• The presentation assumes that user is already
familiar with the use of Parametric Models. We
recommend reading the following reference for an
introduction to Parametric Models: Embedded
Systems Development using SysML Chapter 5.
2
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing Systems
• Queuing Systems are generally made of waiting lines (also called
queues) and processing centers that perform some operation or
provide a service on people/items taken from queues.
• A typical example would be customers waiting in line at a bank to
be serviced by tellers or automated teller machines.
3
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Item
Repository
• We use the Enterprise
Architect SysML Block
Definition Constraint
Blocks to define several
generic modeling
elements that will be
combined to create
Queuing System
Simulation parametric
models.
4
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• We have defined four main groups of modeling elements:
– Source elements: they model the arrival of the queuing system
items such as customers arrival or work items submission.
– Queue elements: they model the waiting lines or queues of
source items. No queue rules such as First In first Out (FIFO) or
Last In First Out (LIFO) are enforced.
– Service elements: they model actions performed on a source
item when it is time to process or service it.
– Routing elements: they model routing items between services
and queues.
• Each element behavior is scripted
• The states of the Queuing System Simulation elements are
evaluated at time intervals controlled by the progression of
a global variable t representing the passage of time.
5
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Source elements:
– Custom Arrival: It
generates a number of
items at specific values
of t. User defines the
number of items
created for any value
of t.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemReposit...
t output
6
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Source elements:
– Simple Source: It
generates an item if
the value of a random
variable is between
the parameters P1 and
P2
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepositor...
P1 : Real
output : RealP2 : Real
7
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Queue elements:
– Simple Queue: It is the
first queue an item
enters from a Source
element.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository]
input : Real ItemsInQueue : Real
output : Real
8
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Queue elements:
– Next Queue: It is a
Queue that follows a
Service element.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository]
input : Real
ItemsInQueue : RealPreviousQueue : Real
output : Real
9
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Queue elements:
– Sink: It is a Queue
from which no items
are taken from once
they enter it.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepositor...
input : Real
ItemsInSink : RealPreviousQueue : Real
10
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Queue elements:
– Simple Buffer: It is a
buffer that moves
input items into
output items.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository]
input : Real output : Real
11
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Service elements:
– Simple Service: It is a
service center that
does not create any
defects. It processes
one item at the time at
a rate set by P.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository]
input : Real
P : Real
output : Real
12
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Service elements:
– Service with Defects:
It is a service center
that can create
defects. It processes
one item at the time at
a rate set by P. It
generates defective
items at a rate set by
DP
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository]
P : Real
DP : Real
output : Real
defectOutput : Real
input : Real
passOutput : Real
13
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Routing elements:
– Splitter: It randomly
routes an item to
either output 1 or
output 2 based on a
splitting ratio P.
bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository]
P
input
output1
output2
14
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Elements
Repository
• Routing elements:
– Merger: It combines
two inputs into a
single output.
bdd [Package] QueueSimulationItemRepository [QueueSimulationIte...
input1
input2
output
15
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Queuing System Simulation Models
• We use the Enterprise
Architect SysML
Parametrics Property
and Constraint Property
objects to create
Queuing System
Simulation models.
• An example of a model is
presented next.
16
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Work Items Queuing System Parametric Model
par [Package] QueueingParametricModelExample [QueueingParametricModelExample]
t
WorkCreationOutput: SimpleBufferinput output
m_UnassignedWorkQueue : SimpleQueue
input
ItemsInQueue UnassignedWorkQueue: SimpleBufferinput output
output
m_WorkAssignment: SimpleService
P
WorkAssignmentRate
input
output : SimpleBufferinput output
m_WorkAssignedQueue : NextQueue
input
output ItemsInQueue
PreviousQueue
WorkCompletionRate
: SimpleBufferinput output WorkAssignedQueue
: SimpleBufferinput output
WorkDefectRate
m_WorkCompletionAndVerification : ServiceWithDefects
P
DP
passOutput
defectOutput
: SimpleBufferinput output
DefectiveWorkDetectedCount
m_DefectiveWorkQueue : NextQueue
input
output
PreviousQueue
ItemsInQueueZeroRate
m_WorkCompleted : Sink
input
ItemsInSink CompletedWorkCount
PreviousQueue
CompletionOutput
input output
WorkAssignmentOutput
CustomSource : CustomArrival
t output
m_TotalWorkQueue : NextQueue
input PreviousQueue
output ItemsInQueue : SimpleBufferinput output TotalWorkSubmittedCount
17
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Work Items Queuing System
Parametric Model
• In this model, Work items are submitted over time according to a custom
schedule.
• Work items once created enter an Unassigned Work Queue
• The Work Assignment Service then assigns work items one at a time to a
Work Assigned Queue
• The Work completion and Verification Service then takes one job at the
time from the Work Assigned Queue and completes it. Upon completion
the Work item is tested for defects
• If a Work item is not defective, it is added to the Work Completed Sink
otherwise it remains in the Work Assigned Queue for re-processing
• If a Work item is found defective, it is recorded in the Detected Defects
Queue
• The Detected Defects Queue only serves as a counter of the number of
defective Work Items found. We could have used a Sink Queue Element
instead but the behavior is the same as long as the Queue Output Rate
parameter is set to zero.
18
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Configuring and Running the
Parametric Model
19
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Simulation Results A
20
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Simulation Results A
Input
Parameters
Values
t 0 to 200 step 0.05
Work
Assignment
Rate
0.5
Work
Completion
Rate
0.25
Work Defect
Rate
0.15
ZeroRate 0
Outputs Min Max Mean
Completed Work count 0 657 404
Defective Work
detected
0 114 71.75
Work Assigned Queue 0 178 65.5
Unassigned Work
Queue
0 115 12.67
Work is fully completed at t = 152.35
21
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Simulation Results B
22
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Simulation Results B (Higher Work
Defect Rate)
Input
Parameters
Values
t 0 to 200 step 0.05
Work
Assignment
Rate
0.5
Work
Completion
Rate
0.25
Work Defect
Rate
0.30
ZeroRate 0
Outputs Min Max Mean
Completed Work count 0 657 352
Defective Work
detected
0 301 153.6
Work Assigned Queue 0 232 117.8
Unassigned Work
Queue
0 115 12.67
Work is fully completed at t = 187.65
23
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
24
Contact didier@pragmaticohesion.com to find out how to
create Systems and Processes Performance Analysis
Models with your Sparx EA SysML Edition
http://pragmaticohesion.com/
Compute the following Performance Measures:
• Workloads
• Processing Times
• Utilizations

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Creating queuing system simulations with enterprise architect sysml parametric models

  • 1. Creating Queuing Systems Simulations with Sparx EA SysML Parametric Models 1 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting Add Performance Analysis to your EA Processes and System Models with Queuing Systems Simulations
  • 2. Queuing Systems Simulation • This presentation illustrates how to use Sparx Enterprise Architect Parametric Model features found in the Systems Engineering and Ultimate editions to simulate queuing systems. • The presentation assumes that user is already familiar with the use of Parametric Models. We recommend reading the following reference for an introduction to Parametric Models: Embedded Systems Development using SysML Chapter 5. 2 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 3. Queuing Systems • Queuing Systems are generally made of waiting lines (also called queues) and processing centers that perform some operation or provide a service on people/items taken from queues. • A typical example would be customers waiting in line at a bank to be serviced by tellers or automated teller machines. 3 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 4. Queuing System Simulation Item Repository • We use the Enterprise Architect SysML Block Definition Constraint Blocks to define several generic modeling elements that will be combined to create Queuing System Simulation parametric models. 4 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 5. Queuing System Simulation Elements Repository • We have defined four main groups of modeling elements: – Source elements: they model the arrival of the queuing system items such as customers arrival or work items submission. – Queue elements: they model the waiting lines or queues of source items. No queue rules such as First In first Out (FIFO) or Last In First Out (LIFO) are enforced. – Service elements: they model actions performed on a source item when it is time to process or service it. – Routing elements: they model routing items between services and queues. • Each element behavior is scripted • The states of the Queuing System Simulation elements are evaluated at time intervals controlled by the progression of a global variable t representing the passage of time. 5 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 6. Queuing System Simulation Elements Repository • Source elements: – Custom Arrival: It generates a number of items at specific values of t. User defines the number of items created for any value of t. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemReposit... t output 6 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 7. Queuing System Simulation Elements Repository • Source elements: – Simple Source: It generates an item if the value of a random variable is between the parameters P1 and P2 bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepositor... P1 : Real output : RealP2 : Real 7 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 8. Queuing System Simulation Elements Repository • Queue elements: – Simple Queue: It is the first queue an item enters from a Source element. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository] input : Real ItemsInQueue : Real output : Real 8 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 9. Queuing System Simulation Elements Repository • Queue elements: – Next Queue: It is a Queue that follows a Service element. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository] input : Real ItemsInQueue : RealPreviousQueue : Real output : Real 9 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 10. Queuing System Simulation Elements Repository • Queue elements: – Sink: It is a Queue from which no items are taken from once they enter it. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepositor... input : Real ItemsInSink : RealPreviousQueue : Real 10 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 11. Queuing System Simulation Elements Repository • Queue elements: – Simple Buffer: It is a buffer that moves input items into output items. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository] input : Real output : Real 11 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 12. Queuing System Simulation Elements Repository • Service elements: – Simple Service: It is a service center that does not create any defects. It processes one item at the time at a rate set by P. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository] input : Real P : Real output : Real 12 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 13. Queuing System Simulation Elements Repository • Service elements: – Service with Defects: It is a service center that can create defects. It processes one item at the time at a rate set by P. It generates defective items at a rate set by DP bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository] P : Real DP : Real output : Real defectOutput : Real input : Real passOutput : Real 13 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 14. Queuing System Simulation Elements Repository • Routing elements: – Splitter: It randomly routes an item to either output 1 or output 2 based on a splitting ratio P. bdd [Package] QueueSimulationItemRepository [QueueSimulationItemRepository] P input output1 output2 14 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 15. Queuing System Simulation Elements Repository • Routing elements: – Merger: It combines two inputs into a single output. bdd [Package] QueueSimulationItemRepository [QueueSimulationIte... input1 input2 output 15 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 16. Queuing System Simulation Models • We use the Enterprise Architect SysML Parametrics Property and Constraint Property objects to create Queuing System Simulation models. • An example of a model is presented next. 16 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 17. Work Items Queuing System Parametric Model par [Package] QueueingParametricModelExample [QueueingParametricModelExample] t WorkCreationOutput: SimpleBufferinput output m_UnassignedWorkQueue : SimpleQueue input ItemsInQueue UnassignedWorkQueue: SimpleBufferinput output output m_WorkAssignment: SimpleService P WorkAssignmentRate input output : SimpleBufferinput output m_WorkAssignedQueue : NextQueue input output ItemsInQueue PreviousQueue WorkCompletionRate : SimpleBufferinput output WorkAssignedQueue : SimpleBufferinput output WorkDefectRate m_WorkCompletionAndVerification : ServiceWithDefects P DP passOutput defectOutput : SimpleBufferinput output DefectiveWorkDetectedCount m_DefectiveWorkQueue : NextQueue input output PreviousQueue ItemsInQueueZeroRate m_WorkCompleted : Sink input ItemsInSink CompletedWorkCount PreviousQueue CompletionOutput input output WorkAssignmentOutput CustomSource : CustomArrival t output m_TotalWorkQueue : NextQueue input PreviousQueue output ItemsInQueue : SimpleBufferinput output TotalWorkSubmittedCount 17 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 18. Work Items Queuing System Parametric Model • In this model, Work items are submitted over time according to a custom schedule. • Work items once created enter an Unassigned Work Queue • The Work Assignment Service then assigns work items one at a time to a Work Assigned Queue • The Work completion and Verification Service then takes one job at the time from the Work Assigned Queue and completes it. Upon completion the Work item is tested for defects • If a Work item is not defective, it is added to the Work Completed Sink otherwise it remains in the Work Assigned Queue for re-processing • If a Work item is found defective, it is recorded in the Detected Defects Queue • The Detected Defects Queue only serves as a counter of the number of defective Work Items found. We could have used a Sink Queue Element instead but the behavior is the same as long as the Queue Output Rate parameter is set to zero. 18 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 19. Configuring and Running the Parametric Model 19 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 20. Simulation Results A 20 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 21. Simulation Results A Input Parameters Values t 0 to 200 step 0.05 Work Assignment Rate 0.5 Work Completion Rate 0.25 Work Defect Rate 0.15 ZeroRate 0 Outputs Min Max Mean Completed Work count 0 657 404 Defective Work detected 0 114 71.75 Work Assigned Queue 0 178 65.5 Unassigned Work Queue 0 115 12.67 Work is fully completed at t = 152.35 21 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 22. Simulation Results B 22 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 23. Simulation Results B (Higher Work Defect Rate) Input Parameters Values t 0 to 200 step 0.05 Work Assignment Rate 0.5 Work Completion Rate 0.25 Work Defect Rate 0.30 ZeroRate 0 Outputs Min Max Mean Completed Work count 0 657 352 Defective Work detected 0 301 153.6 Work Assigned Queue 0 232 117.8 Unassigned Work Queue 0 115 12.67 Work is fully completed at t = 187.65 23 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  • 24. Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting 24 Contact didier@pragmaticohesion.com to find out how to create Systems and Processes Performance Analysis Models with your Sparx EA SysML Edition http://pragmaticohesion.com/ Compute the following Performance Measures: • Workloads • Processing Times • Utilizations