DECISION MODELING WITH
MICROSOFT EXCEL
Chapter 10
DISCRETE EVENT
SIMULATION
Part 1
Copyright 2001
Prentice Hall
DISCRETE EVENT SIMULATION
INTRODUCTION
Typically, simulation refers to a specific class of
dynamic models involving the detailed
observation of a complex probabilistic system
over time.
Continuous simulation models involve aggregate
variables that change more or less continuously
with time (such as those models in Chapter 9).
Discrete event simulation is applied whenever
individual items are tracked and in which abrupt
or nonsmooth changes in the timing of events is
the norm.
Discrete event simulation models can be used to
delve into the fine details of complex systems
with many interactions.
However, discrete event simulation models can
become extremely complex to build and analyze.
Discrete event simulation models are most
commonly used to create detailed operational
systems representing demands among activities
requiring scarce resources over time.
EXAMPLE 1
A SIMULATION MODEL IN EXCEL
A single server queuing situation will be used to
illustrate a discrete event simulation.
We will illustrate the building of such models
using a non-spreadsheet simulation package
called Extend.
Extend can be used for both continuous
simulation and discrete event simulation.
We will investigate the relative efficiency of an
airport car rental business (Hervis) by modeling
the movement of customers through the rental
office.
Customers arrive in an airport van and queue up,
first come – first serve, for service at the rental
counter.
Eventually, a given customer moves to the head
of the queue and, when the rental clerk is free,
will receive service that consists of
filling out the rental forms
choosing the rental options
receiving some driving instructions
etc.
Finally, customers depart, collect their rental car
and drive away.
Consider the following data giving the relative
frequency distribution of customer arrivals in any
given 5-minute block of time throughout a typical
24-hour day.
Let’s simulate a week of 24-hour operations and
segment time into 5-minute blocks. We assume
that it will always take exactly 5 minutes to serve
a waiting customer.
Because 7*24*60/5 = 2016 time blocks
(exceeding the 256-column limitation in Excel),
the time blocks will be modeled in rows.
To build the Hervis model in Excel, first label the
time blocks by using the Fill Series option from
the Edit menu.
Next, create a probability distribution table:
Cell K8 computes the expected number of
customer arrivals.
The computer will be driven by randomly drawn
probabilities, which in turn will determine the
number of customers arriving in any 5-minute
time block.
The RAND() function will draw a random fraction
greater than or equal to 0 and less than 1, one for
each of the 2016 time blocks.
Set the Tools –
Options – Calculation
option to Manual to
avoid drawing new
random numbers each
time the worksheet is
changed.
Place the =RAND() formula in cell B5 and copy it
down to cell B2020 to create all 2016 random
fractions.
=M5 +=K4
K5
=M6 + K6
=VLOOKUP(B5,$M$4:$N$7,2)
Next, create a modified probability table based on
the =RAND() formulas (the inputs).
The number of customer arrivals, as outputs, are
computed by =VLOOKUP() formulas.
Column D formulas compute the number of
customers in line and being served.
=C5 + F4 =D5 + E5
=MIN(D5,$C$2)
=MAX(D$5:D$2020)
=SUM(D$5:D$2020)
=AVERAGE(D$5:D$2020)
Column F
computes the
number of
customers
remaining
unserved at
the end of the
5-minute
block.
Column E formulas compute the number of
customers receiving rental counter service as
being the minimum of the number in line and the
number of rental counter stations in C2.
The initial results show that on the average, ½
customer arrives in each 5-min. block (or 1
customer every 10 minutes). It always takes only
one 5-min. interval to serve a customer, thus, the
rental counter is busy only ½ the time on
average.
However, during peak times, you could have 9
customers awaiting service, leading to a delay of
45 minutes for the 9th customer.
To alleviate this wait, we could add another
rental station.
We can use this model to evaluate the effect of
adding another rental station, thus allowing up to
two waiting customers to receiver service
simultaneously.
Below is the revised model for 2 rental stations.
The revised statistics indicate that the maximum
number of customers delayed falls from an
average of .499 to an average of .025.
EXAMPLE 2
A SIMULATION MODEL IN EXTEND
The use of Excel for discrete event simulation
suffers from two primary shortcomings:
1. For reasonably sized models, the
resulting Excel spreadsheet quickly fills
up with cells occupied with formulas.
2. Discrete event simulation models in Excel
do not scale well.
Where Excel falls short in handling discrete even
simulation models, Extend has the modeling
capability to:
1. Scale to finer time grids and longer
planning horizons.
2. Compact the model representation to
avoid generating large spreadsheets that
are cumbersome to manipulate and
debug.
3. Easily manipulate and generate results.
4. Develop an environment that embodies
the latest in graphic user interfaces to
facilitate easy model building and selfdocumentation.
Extend’s models for discrete event simulation are
object oriented and are built using predefined
building blocks.
A block is Extend’s object for specifying an action,
process, accumulation, statistical summary, or
other object for creating the simulation.
The blocks are linked together by drawing lines to
form a network of interrelated activities.
Items (e.g., customers) flow through the
connected network of blocks while Extend
gathers statistics on their movements.
Links connect blocks:
two accommodate item input and output,
These links provide the paths that allow
items to flow through the model’s blocks.
These links appear as small connectors on
the edge of each block.
and two accommodate value input and output.
These links pass data and parameters about
items between blocks.
These links appear as connectors on each
parameter values and for reviewing its
results after a simulation run.
Each block in Extend has a dialog window for
specifying parameter values and for reviewing its
results after a simulation run.
Here is an Extend Activity, Delay block typically
used to hold an item for an amount of time and
then release it to the next block.
BUILDING THE HERVIS SIMULATION MODEL
Open the Simulation Setup dialog by selecting
Simulation Setup from the Run menu.
Here, you can specify
how the simulation
will run and for how
long. For most
purposes, start with
the default start time
of 0.
The Number of runs option can be left at 1.
Now, because Hervis models the rental car
operations minute – by – minute for a week, click
on the Global time units button and select the
minutes option.
Hervis will run the simulation for a week of
simulation time (24*7*60 = 10,080 minutes).
Enter 10080 into the End simulation at time field
and click OK.
Choose New Model from Extend’s File menu to
open a new model window. To add a block to the
model window:
1. Open the library containing Extend’s
predefined blocks, if necessary.
2. Add the desired block to the model by
selecting it from the library.
3. Click-drag to move the block to its
desired position in the model window.
4. Connect its input and output connectors
to other blocks.
In order to copy a predefined Extend block into a
model, the library in which that block resides
must be open.
For the Hervis modeling in this chapter, open the
Generic, Discrete Event, Plotter, and Stats
libraries.
To open the Discrete Event library, choose Open
Library … from Extend’s Library menu. Locate
the Libs subdirectory and select Discrete Event
library (DE.lix) and click OK.
Now, open the Generic (GENERIC.lix), Plotter
(PLOTTER.lix) and Stats (STATS.lrx) libraries.
To add a block to a model, click on the Library
menu and select the name of the library that
holds the desired block.
A hierarchical
menu of the
different
types of
blocks in the
library will
appear.
To the right of this menu a list of the names of
the blocks will appear. Selecting the desired
block will put a copy of the block in the Extend
window.
For discrete event simulation modeling, Extend
always requires an Executive block from the
Discrete Event library to be placed as the leftmost
block in the model window.
This block, with an icon of a wall clock,
determines its stopping conditions and handles
the details of event scheduling.
Normally, there is no connection to the Executive
block, and once placed, can be ignored.
The Hervis model begins with the arrival of an
airport van carrying rental-car customers. This is
represented by Extend’s Generator block.
Add a Generator block from the Generators
submenu of the Discrete Event library.
Double-click on the block to open the settings
dialog.
Select a Constant distribution with a parameter
setting of 5 and minutes as the Time Units. Also,
label the block Customers.
Each time a van arrives, it contains a variable
number of customers (a batch).
By default, Extend’s Generator block creates a
batch of size one.
This can be overridden by providing another
number via the V value input connector.
In this case, we want the batch size to be a
random number of customers between 0 and 3.
Specify the random number of customers in the
Input Random Number block.
Go to the Inputs/Outputs menu in the
GENERIC.lix library and add the Input Random
Number block.
Double click to open the dialog. Select Empirical
Table and Discrete and enter the data shown in
the previous table.
Label the block
# of Customers
and click OK.
Add a text box by double-clicking on the white
background. Type Customers Come from Airport
Van in the resulting edit field.
Blocks are hooked together through their
connectors by connection lines.
To connect the blocks, position the mouse cursor
over one of the connectors. When the cursor
changes to a pen, click-drag it to the other tab.
Now, connect the output value connector to the V
input connector.
When you release the
pen/cursor, a thin line
will appear, connecting
the two blocks.
This allows information to flow from the output of
the Input Random Number block to the V input
connector of the Generator block.
This connection will generate an arrival of a batch
of items (customers) varying from 0 to 3 in size
according to the previous probabilities.
Now, in order to have the batch of customers
queue First in, First Out (FIFO) in front of the
rental station, add a Queue, FIFO block from the
Queues menu of the DE.lix library.
Use the cursor-pen as before and connect the
input connector from the Queue, FIFO block to
the output connector of the Generator block.
This allows the customers in
the batch to join the queue.
Double-click on the block to
open it. Enter a label for
the block.
Note that the connecting lines over which items
(customers) flow among blocks are hollow while
the connection lines among blocks providing
information (values) are thin solid lines.
Also note that items (customers) produced by a
Generator block are pushed out immediately and
must have someplace to go in the model.
This usually requires a direct connection from a
Generator block to one of Extend’s Queue or
Resource blocks. Otherwise the Generator block
may lose items, giving incorrect results.
In the original Hervis model, the rental clerk will
delay each customer for 5 minutes to complete
the car rental transaction.
You can introduce this delay in the Activity, Delay
block. However, this block only allows for one
item.
Therefore, use the Activity, Multiple block from
the Activities menu of the DE.lix library.
Items leave the simulation model via Extend’s
Exit block found on the Routing menu of the
DE.lix library.
Another useful block is the Plotter, Discrete Event
block found in the PLOTTER.lix library.
This block captures data and plots up to four
variables during the simulation run.
The Utilization of the Rental Station and the
customer waiting time, W, is captured from the
Queue, FIFO block.
The variables to be collected and plotted are
determined by connecting the Plotter, Discrete
Event block’s connectors to the appropriate value
connectors of other blocks in the model.
RUNNING THE MODEL
Click on the Run - Run Simulation pull-down
menu or on the Run Simulation
button to
begin the simulation.
(Note that results may differ due to the
randomness in the simulation data for customer
batch size.)
When the simulation begins, Extend will:
1. Display a Status bar at the bottom of the
screen based on the designated settings.
2. Open a window for the plotter to
dynamically report its variables,
server utilization and waiting time.
Note how
The avg.
the wait
utilization
time in
was 50%.
line
This
jumps in
implies
discrete
that the
units of 5
station will
minutes.
be busy ½
The max.
the time
wait was
on avg.
35 min.
The avg. utilization is erratic in early time periods
but settles to its long run average value.
To manipulate the graph, click on the Trace
Properties icon
at the top of the graph. This
will bring up the Trace Lines Properties window.
Each of the plotter variables
occupies two rows:
the properties of the
variable’s time stamp and
the properties of the
variable.
Variable
Label
Y1/Y2
Variable
Color
Show
Trace
Line
Weight
Line
Pattern
Style of
Line
Line
Symbol
Format
Note that a variable’s time stamp can have only
its numerical format changed.
Click on the model’s Queue, FIFO block and
Activity, Multiple block to open their respective
dialog windows.
Next, click on the Results tab to reveal the
simulation run statistics for each block.
To see what the effect of adding an additional
sales clerk, double-click on the Activity, Multiple
block and change the Maximum Number in
Activity from 1 to 2.
Now, rerun the simulation to produce the
following results.
The
average
utilization
of 2
servers
tends to
be 25%.
The max. queue length drops to 4 with the max
waiting time of 5 min.
EXAMPLE 3 - HERVIS CAR
RENTAL MODEL EXPANDED
Now, Hervis knows the airport vans experience
traffic delays and don’t always arrive exactly
every 5 minutes.
To model this, modify
the original Extend
model to allow for a
range of interarrival
times for airport vans
from 3 minutes to 7
minutes, with the
most likely
interarrival time
being 5 minutes.
Note that a triangular distribution is used for
simplicity.
So far, we have assumed that it always takes
exactly 5 minutes for the clerks to complete the
car rental contract.
To add some variability to this, add another Input
Random Number block.
Go to the Library pull-down menu and choose
Generic.lix – Inputs/Outputs – Input Random
Number block.
Double-click on the block and specify the
variability via an Exponential distribution with a
mean of 5.
Connect the
block’s output
connector to
the D
connector of
the Activity,
Multiple block.
By keeping the mean of each distribution the
same, the avg. queue length and waiting time will
not be affected.
Rerun the model to produce the following results:
These results show
that adding
variability alone to
the distributions
worsens the average
performance as well
as increasing
performance
variability.
The added variability
increased the max.
wait substantially and
the max. queue length
slightly.
The avg. wait is also
longer and the avg.
queue length increases
dramatically.
Now, run the simulation again to see if adding
another rental clerk to the model will have a
dramatic improvement.
Double-click on the Activity, Multiple block and
change the Maximum Number in Activity from 1
to 2 and click OK.
Click on the Run Simulation
simulation.
icon to start the
Here is the resulting graph:
Remember, results will differ due to the random
effects.
The avg. wait of .7
minutes and max. wait
of 19 minutes look
more reasonable.
End of Part 1
Please continue to Part 2