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This tutorial will talk you through a very basic workbench queueing simulation. - PowerPoint PPT Presentation


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This tutorial will talk you through a very basic workbench queueing simulation. The queueing system modelled is of customers entering an infinite capacity queue at non-random intervals . That is their arrival times are precisely known.

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Presentation Transcript
slide1

This tutorial will talk you through a very basic

workbench queueing simulation.

The queueing system modelled is of customers

entering an infinite capacity queue at non-random

intervals. That is their arrival times are precisely known.

This will enable us to understand precisely what happens

when we run the model. The random case isn’t any more

difficult and will be dealt with later.

Similarly the length of time taken to serve them

is non-random.

We set up the model and generate and check

some results

Just follow the screenshots.

slide5

Let’s give the model some modules.

Right click on the icon in the workspace and choose ‘specification’

slide8

Okay, our model will contain the module ‘tutorial’.

Double click on the module icon and a blank workspace appears.

slide9

Workbench allows us to put many sub-modules inside a module. This is useful

for simulating complicated systems. We will create one sub-module into which we

will place our queueing system. Click on the icon labelled submodel node

slide10

Now click in the white workspace area to place the sub-module..

We have to give it a name so ……..

slide11

Right click on it and choose ‘specification’. When the dialog box

opens give it a name.. When you are finished double click on the sub-module.

Another blank workspace opens. We can now start to build a queuing system.

slide12

Specify the inter-arrival time

One or more customers will be

created every time unit according to the new transactions rule below.

You can choose seconds, hours, or arbitrary ‘module units’.

Give it a name…

Specify the number of new customers created each time-unit.

Here I have chosen a constant, 1, but I could have

decided on a random process, e.g. poisson(0.5), a Poisson

process with mean equal to 0.5… more about them in a later

presentation

From the menu choose the ‘source node’ icon and place one in

the workspace. Right click on it and choose specifications..

slide13

Give it a name… that’s all that’s of interest for these

guys.

Now place a sink-node. Right click to specify it…

slide14

Give it a name…

How long does it take to serve

a customer?

Here I have set it as a constant, 2. A later demo will explain how

to make the service time an exponential random variable.

And now place a service node, where the queueing occurs. Again right click

to specify ….

slide16

Having clicked on the topology arc we click near the source node until we find a

blue spot. Click on this and drag an arc over to the blue spot near the service node.

slide18

Our model has been physically built. Now we need to tell Workbench what data we would like

to collect. Open the specifications for the service node and open the ‘type’ tab.

slide19

Choose the statistics tab and right click in the space below to specify a statistic.

Choose the insert a row option.

slide20

Click on ‘class’ to specify what statistic you would like to collect. You can choose from a

Variety of statistics. We will choose population and qpopulation.

These are stats on the number of customers in the system and the number of customers in the

queue throughout the simulation.

slide21

Give them a name so that they are easily recognised in the final report..

This is more important in more complicated models where you are collecting data from many

nodes and don’t want to get confused between them.

slide22

Almost ready to run the model, but we have to tell Workbench how long to run it for.

Choose ‘Edit Main’ from the ‘Model’ menu at the top of the screen.

slide23

Do we want a warm-up period ( to allow the model to reach steady state) ?

In general you should choose yes for this if you are trying to replicate analytical results

which are predicated on the system having reached steady state.

You can specify how many time-units count as the warm-up period. We won’t need one

for our simple model.

Workbench lets you know how quickly

things are progressing by issuing reports as

time-units elapse.

You can specify how often these reports

should be made.

How long do you want to run your model for?

You can specify a fixed number of time-units.

Or you can run it until some sort of convergence

(in the form of an ever more tightly bounded

confidence interval) is observed.

We fill in data about the length of time we want to run the simulation for.

slide25

The first time we do this we are told that the module has not been explicitly included in

Our model yet and we are asked whether we would like to continue… press yes

slide28

Hopefully it compiles without errors… if there are any errors they will be reported here

and you have to go and debug your model..

slide30

The model runs… Note that it reports every 2 time units as previously specified, so we know

that it is running correctly and hasn’t crashed..

slide32

Here is the report that is generated.. Note that we have statistical information about the two

quantities that we stipulated, population and queue population. It suggests here that the mean

population in the system was 2.9, while the mean queue size was 2. We can verify this easily..

slide33

Queue Service Finished

Time = 0

Time = 1

Time = 2

Time = 3

Time = 4

Time = 5

Time = 6

Time = 7

Time = 8

Time = 9

Time = 10

It is a simple matter to keep track of the system in this case. People join at the rate of 1 per second

while people leave every 2 seconds. So the system is empty for the first second, and then a person

enters and immediately begins to get served. At t = 2 another person enters and joins the queue

while the first person is still getting served etc… What is the average number of people in the system?

slide34

Well the first row of the last slide represents the first

time unit of action. In this period there were an average

of zero people in the system (and zero in the queue).

So at t=1: The average population during the first time unit

was zero… while the average queueing

population was also zero.

A single customer arrives just at the end of the first

time unit and is present for the whole of the second one.

So at t = 2: The average population during the first 2 time

units was a half… while the average queueing

population was zero.

We can continue on in this fashion until we get to t = 10.

slide35

Now the first 10 seconds are shown in the rows marked 0 to 9

So at t= 10 we see that there were

0 customers present for the first time-unit.

1 customers present for the second time-unit.

2 customers present for the third time-unit.

2 customers present for the fourth time-unit.

3 customers present for the fifth time-unit.

3 customers present for the sixth time-unit.

4customers present for the seventh time-unit.

4 customers present for the eighth time-unit.

5 customers present for the ninth time-unit.

5 customers present for the tenth time-unit.

The average number of customers present over the first 10

Seconds is thus 29/10 = 2.9 as reported in our Workbench

Results. Verify for yourself the qpop statistic as shown.