Creating Queuing Simulations with Sparx EA SysML

Creating Queuing Systems Simulations
with Sparx EA SysML Parametric Models
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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.
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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.
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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.
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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.
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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
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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
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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
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Repository
• Queue elements:
– Next Queue: It is a
Queue that follows a
Service element.
input : Real
ItemsInQueue : RealPreviousQueue : Real
output : Real
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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
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Repository
• Queue elements:
– Simple Buffer: It is a
buffer that moves
input items into
output items.
input : Real output : Real
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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.
input : Real
P : Real
output : Real
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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
P : Real
DP : Real
output : Real
defectOutput : Real
input : Real
passOutput : Real
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Repository
• Routing elements:
– Splitter: It randomly
routes an item to
either output 1 or
output 2 based on a
splitting ratio P.
P
input
output1
output2
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Repository
• Routing elements:
– Merger: It combines
two inputs into a
single output.
bdd [Package] QueueSimulationItemRepository [QueueSimulationIte...
input1
input2
output
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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.
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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
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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.
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Configuring and Running the
Parametric Model
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Simulation Results A
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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
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Simulation Results B
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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
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Cohesion Consulting
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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

Creating Queuing Simulations with Sparx EA SysML

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