Creating Queuing Systems Simulations
with Sparx EA SysML Parametric Models
1
Copyrights (c) 2011-2013 Pragmatic Cohesion C...
Queuing Systems Simulation
• This presentation illustrates how to use Sparx
Enterprise Architect Parametric Model features...
Queuing Systems
• Queuing Systems are generally made of waiting lines (also called
queues) and processing centers that per...
Queuing System Simulation Item
Repository
• We use the Enterprise
Architect SysML Block
Definition Constraint
Blocks to de...
Queuing System Simulation Elements
Repository
• We have defined four main groups of modeling elements:
– Source elements: ...
Queuing System Simulation Elements
Repository
• Source elements:
– Custom Arrival: It
generates a number of
items at speci...
Queuing System Simulation Elements
Repository
• Source elements:
– Simple Source: It
generates an item if
the value of a r...
Queuing System Simulation Elements
Repository
• Queue elements:
– Simple Queue: It is the
first queue an item
enters from ...
Queuing System Simulation Elements
Repository
• Queue elements:
– Next Queue: It is a
Queue that follows a
Service element...
Queuing System Simulation Elements
Repository
• Queue elements:
– Sink: It is a Queue
from which no items
are taken from o...
Queuing System Simulation Elements
Repository
• Queue elements:
– Simple Buffer: It is a
buffer that moves
input items int...
Queuing System Simulation Elements
Repository
• Service elements:
– Simple Service: It is a
service center that
does not c...
Queuing System Simulation Elements
Repository
• Service elements:
– Service with Defects:
It is a service center
that can ...
Queuing System Simulation Elements
Repository
• Routing elements:
– Splitter: It randomly
routes an item to
either output ...
Queuing System Simulation Elements
Repository
• Routing elements:
– Merger: It combines
two inputs into a
single output.
b...
Queuing System Simulation Models
• We use the Enterprise
Architect SysML
Parametrics Property
and Constraint Property
obje...
Work Items Queuing System Parametric Model
par [Package] QueueingParametricModelExample [QueueingParametricModelExample]
t...
Work Items Queuing System
Parametric Model
• In this model, Work items are submitted over time according to a custom
sched...
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 ...
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
...
Copyrights (c) 2011-2013 Pragmatic
Cohesion Consulting
24
Contact didier@pragmaticohesion.com to find out how to
create Sy...
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Creating queuing system simulations with enterprise architect sysml parametric models

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This presentation illustrates how to use Sparx Enterprise Architect Parametric Model features found in the Systems Engineering and Ultimate editions to simulate queuing systems.

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Creating queuing system simulations with enterprise architect sysml parametric models

  1. 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 http://www.mypragmaticohesion.com/Queueing/index.htm
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 19. Configuring and Running the Parametric Model 19 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  20. 20. Simulation Results A 20 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  21. 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. 22. Simulation Results B 22 Copyrights (c) 2011-2013 Pragmatic Cohesion Consulting
  23. 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. 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 http://www.mypragmaticohesion.com/Queueing/index.htm Check the interactive Model at:

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