Simple Throughput Analysis Example: Difference between revisions

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[[Image:system behavior.png|center]]
[[Image:system behavior.png|center]]


'''Event 1:  <math>B</math> Fails at 50'''
'''Event 1:  B  Fails at 50'''


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:• At 50,  <math>B</math> fails.   
:• At 50,  B  fails.   
:• From 0 to 50,  <math>A</math> processes  <math>50\cdot 60=3000</math>  items.
:• From 0 to 50,  A  processes  <math>50\cdot 60=3000</math>  items.
:• 500 are sent to  <math>B</math> , 1000 to  <math>C</math>  and 1500 to  <math>D</math> .  There is no excess capacity at  <math>B</math> ,  <math>C</math>  or  <math>D</math> .
:• 500 are sent to  B , 1000 to  <math>C</math>  and 1500 to  <math>D</math> .  There is no excess capacity at  B ,  <math>C</math>  or  <math>D</math> .
:• <math>B</math> ,  <math>C</math>  and  <math>D</math>  process and send 3000 items to  <math>E</math> .  Because the capacity of  <math>E</math>  is 3500,  <math>E</math>  now has an excess capacity of 500.
:• B ,  <math>C</math>  and  <math>D</math>  process and send 3000 items to  <math>E</math> .  Because the capacity of  <math>E</math>  is 3500,  <math>E</math>  now has an excess capacity of 500.
:• The next table summarizes these results:
:• The next table summarizes these results:
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====Event 2:  <math>B</math> is Down 50 to 54====
'''Event 2:  B  is Down 50 to 54'''
Event overview:
Event overview:
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:• From 50 to 54,  <math>B</math> is down.
:• From 50 to 54,  B  is down.
:• <math>A</math> processes 240 items and sends 96 to  <math>C</math>  and 144 to  <math>D</math> .
:• A  processes 240 items and sends 96 to  <math>C</math>  and 144 to  <math>D</math> .
:• <math>D</math>  and  <math>C</math>  can only process 80 and 120 respectively during this time.  Thus, they get backlogs of 16 and 24 respectively.
:• <math>D</math>  and  <math>C</math>  can only process 80 and 120 respectively during this time.  Thus, they get backlogs of 16 and 24 respectively.
:• The 200 processed are sent to  <math>E</math> .  <math>E</math>  has an excess capacity of 80 during this time period.
:• The 200 processed are sent to  <math>E</math> .  <math>E</math>  has an excess capacity of 80 during this time period.
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====Event 3: All Up 54 to 55====
'''Event 3: All Up 54 to 55'''
The next table summarizes the results:
The next table summarizes the results:
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====Event 4:  <math>C</math>  is Down 55 to 59====
'''Event 4:  <math>C</math>  is Down 55 to 59'''
The next table summarizes the results:
The next table summarizes the results:
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====Event 5: All Up 59 to 60====
'''Event 5: All Up 59 to 60'''
The next table summarizes the results:
The next table summarizes the results:
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====Event 6:  <math>D</math>  is Down 60 to 64====
'''Event 6:  <math>D</math>  is Down 60 to 64'''
The next table summarizes the results:
The next table summarizes the results:
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====Event 7: All Up 64 to 65====
'''Event 7: All Up 64 to 65'''
The next table summarizes the results:
The next table summarizes the results:
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====Event 8:  <math>A</math> is Down 65 to 69====
'''Event 8:  A  is Down 65 to 69'''
Between 65 and 69,  <math>A</math> fails.  This stops the flow of items in the system and provides an opportunity for the other blocks to process their backlogs.  As an example,  <math>B</math> processes 40 items from the 60 items in its backlog.  Specifically:
Between 65 and 69,  A  fails.  This stops the flow of items in the system and provides an opportunity for the other blocks to process their backlogs.  As an example,  B  processes 40 items from the 60 items in its backlog.  Specifically:
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[[Image:event 8.png|center|500px|]]
[[Image:event 8.png|center|500px|]]
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====Event 9: All Up 69 to 70====
'''Event 9: All Up 69 to 70'''
The next table summarizes the results:
The next table summarizes the results:
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====Event 10:  <math>E</math>  is Down 60 to 64====
'''Event 10:  <math>E</math>  is Down 60 to 64'''
From 70 to 74,  <math>E</math>  is down.  Because we specified that we will not send items to failed units,  <math>B</math> ,  <math>C</math>  and  <math>D</math>  receive items from  <math>A</math> but they do not process them, since processing would require that items be sent to  <math>E</math> .  The items received by  <math>B</math> ,  <math>C</math>  and  <math>D</math>  are added to their respective backlogs.  Furthermore, since they could have processed them if  <math>E</math>  had been up, all three blocks have an excess capacity for this period.  Specifically:
From 70 to 74,  <math>E</math>  is down.  Because we specified that we will not send items to failed units,  B ,  <math>C</math>  and  <math>D</math>  receive items from  A  but they do not process them, since processing would require that items be sent to  <math>E</math> .  The items received by  B ,  <math>C</math>  and  <math>D</math>  are added to their respective backlogs.  Furthermore, since they could have processed them if  <math>E</math>  had been up, all three blocks have an excess capacity for this period.  Specifically:
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[[Image:event 10.png|center|500px|]]
[[Image:event 10.png|center|500px|]]
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It should be noted that if we had allowed items to be sent to failed blocks,  <math>B</math> ,  <math>C</math>  and  <math>D</math>  would have processed the items received and the backlog would have been at  <math>E</math> .  The rest of the time, all units are up.
It should be noted that if we had allowed items to be sent to failed blocks,  B ,  <math>C</math>  and  <math>D</math>  would have processed the items received and the backlog would have been at  <math>E</math> .  The rest of the time, all units are up.
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====Event 11: All Up 74 to 100====
'''Event 11: All Up 74 to 100'''
The next table summarizes the results:
The next table summarizes the results:
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====Exploring the Results====
'''Exploring the Results'''
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BlockSim provides all of these results via the Simulation Results Explorer.  The figure below shows the system throughput summary.
BlockSim provides all of these results via the Simulation Results Explorer.  The figure below shows the system throughput summary.

Revision as of 10:31, 26 July 2012

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Consider the simple system shown in figure below, but with [math]\displaystyle{ E }[/math] operating.

The system diagram


In addition, consider the following deterministic failure and repair characteristics:

Also:

• Set all units to operate through system failure.
• Do not add spare part pools or crews (use defaults).
• Do not send items to failed units.
• Use a weighted allocation scheme.


Then the system behavior from 0 to 100 time units is given in table below. The system event history is as follows:


Event history.png


Once the system history has been established, we can examine the throughput behavior of this system from 0 to 100 by observing the sequence of events and their subsequent effect on system throughput.

System behavior.png

Event 1: B Fails at 50


• At 50, B fails.
• From 0 to 50, A processes [math]\displaystyle{ 50\cdot 60=3000 }[/math] items.
• 500 are sent to B , 1000 to [math]\displaystyle{ C }[/math] and 1500 to [math]\displaystyle{ D }[/math] . There is no excess capacity at B , [math]\displaystyle{ C }[/math] or [math]\displaystyle{ D }[/math] .
• B , [math]\displaystyle{ C }[/math] and [math]\displaystyle{ D }[/math] process and send 3000 items to [math]\displaystyle{ E }[/math] . Because the capacity of [math]\displaystyle{ E }[/math] is 3500, [math]\displaystyle{ E }[/math] now has an excess capacity of 500.
• The next table summarizes these results:


Event 1.png


Event 2: B is Down 50 to 54 Event overview:

• From 50 to 54, B is down.
• A processes 240 items and sends 96 to [math]\displaystyle{ C }[/math] and 144 to [math]\displaystyle{ D }[/math] .
[math]\displaystyle{ D }[/math] and [math]\displaystyle{ C }[/math] can only process 80 and 120 respectively during this time. Thus, they get backlogs of 16 and 24 respectively.
• The 200 processed are sent to [math]\displaystyle{ E }[/math] . [math]\displaystyle{ E }[/math] has an excess capacity of 80 during this time period.
• The next table summarizes these results:


Table 2.png


Event 3: All Up 54 to 55 The next table summarizes the results:

Event 3.png


Event 4: [math]\displaystyle{ C }[/math] is Down 55 to 59 The next table summarizes the results:

Event 4.png


Event 5: All Up 59 to 60 The next table summarizes the results:

Event 5.png


Event 6: [math]\displaystyle{ D }[/math] is Down 60 to 64 The next table summarizes the results:

Event 6.png


Event 7: All Up 64 to 65 The next table summarizes the results:

Event 7.png


Event 8: A is Down 65 to 69 Between 65 and 69, A fails. This stops the flow of items in the system and provides an opportunity for the other blocks to process their backlogs. As an example, B processes 40 items from the 60 items in its backlog. Specifically:

Event 8.png


Event 9: All Up 69 to 70 The next table summarizes the results:

Event 9.png


Event 10: [math]\displaystyle{ E }[/math] is Down 60 to 64 From 70 to 74, [math]\displaystyle{ E }[/math] is down. Because we specified that we will not send items to failed units, B , [math]\displaystyle{ C }[/math] and [math]\displaystyle{ D }[/math] receive items from A but they do not process them, since processing would require that items be sent to [math]\displaystyle{ E }[/math] . The items received by B , [math]\displaystyle{ C }[/math] and [math]\displaystyle{ D }[/math] are added to their respective backlogs. Furthermore, since they could have processed them if [math]\displaystyle{ E }[/math] had been up, all three blocks have an excess capacity for this period. Specifically:

Event 10.png


It should be noted that if we had allowed items to be sent to failed blocks, B , [math]\displaystyle{ C }[/math] and [math]\displaystyle{ D }[/math] would have processed the items received and the backlog would have been at [math]\displaystyle{ E }[/math] . The rest of the time, all units are up.

Event 11: All Up 74 to 100 The next table summarizes the results:

Event 11.png


Exploring the Results
BlockSim provides all of these results via the Simulation Results Explorer. The figure below shows the system throughput summary.

9.10.gif


System level results present the total system throughput, which is 5484 items in this example. Additionally, the results include the uptime utilization of each component. The block level result summary, shown next, provides additional results for each item.

9.11.gif

Finally, specific throughput results and metrics for each block are provided, as shown next.


9.12.gif