simulation lecture 6 - faculteit wiskunde en informaticamarko/2wb05/lecture6.pdf · 2wb05...

2WB05 SimulationLecture 6: Process-interactionapproach

Marko Boonhttp://www.win.tue.nl/courses/2WB05

December 6, 2012

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Department of Mathematics and Computer Science

This approach focusses on describing processes;In the event-scheduling approach one regards a simulation as executing a sequence of events ordered in time;but no time elapses within an event.The process-interaction approach provides a process for each entity in the system; and time elapses during aprocess.

In production systems we have processes for:

• Arrivals

• Buffers

• Machines

• Exit

Process-Interaction approach

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Example: Single-stage production system

Machine

BufferArrivals Exit

A single machine processes jobs in order of arrival. The interarrival times and processing times are exponentialwith parameters λ and µ (with λ < µ).

• What is the mean waiting time?

• What is the mean queue length?

• What is the mean length of a busy period?

• How does the performance change if we speed up the machine?


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Arrival process

Generate arrival after random (exponential) time units

arrival


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Buffer process

Add job to buffer and remove job from buffer (if there is any)

0 1 n n+1


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Machine process

Process job (if there is any)

idle

busy


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Exit process

Accept completed job and do accounting

departure accounting


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The specification language χ :

Modelling and simulation tool for the design of manufacturing systems

The language χ has been developed by the Systems Engineering group

For documentation, see http://se.wtb.tue.nl/sewiki/chi


http://se.wtb.tue.nl

http://se.wtb.tue.nl/sewiki/chi

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Implementation in χ

G EMBa b c

Processes: G, B, M, E.

Channels: a, b, c.

Jobs are generated in G, then they are sent over channel a to B. When M is idle, the first job is sent over channelb to M. After a delay, the job is sent over channel c to exit process E.


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0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80 90 100

Mean sojourn time as a function of the number of jobs processed for λ = 1 and µ = 2


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Example: Single-stage production system with three parallel machines

G EMBa b c

M

M


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Example: Two-stage production system

JobsMachine 1 Machine 2

Jobs are processed by two machines in series. Each machine has its own local buffer and processes jobs inorder of arrival. The interarrival and processing times of jobs are exponential with parameters λ, µ1 and µ2.

What is the mean (overall) sojourn time?


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In the χ program we only have to change the model:

G EMBa b c

MBd e


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The simulation system Arena

In Arena you can construct simulation models without programming, but simply with click, drag and drop...

At the department of Mathematics and Computer science we have a limited license. See the TU/e softwareinstallation page for more details how to get access.

Book with CD-ROM:

W. David Kelton, Randall P. Sadowski, Deborah A. Sadowski:Simulation with Arena. 3rd ed., London: McGraw-Hill, 2004


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M|M|1 in Arena


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M|M|3 in Arena

Just change the capacity of the Service resource from 1 to 3.


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Two M|M|1 queues in series

Duplicate the server and change the name of the resource of the second server!


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Simulation of a queueing network:

network = QueueingNetworkProcess[gamma, P, EB, c];Table[QueueProperties[{network, i}], {i, 1, Length[EB]}]data = RandomFunction[network, {0, 1000}];ListLinePlot[data]Table[QueueProperties[{data, i}], {i, 1, Length[EB]}]

Mathematica 9

simulation lecture 6 - faculteit wiskunde en informaticamarko/2wb05/lecture6.pdf · 2wb05...

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