EASTERN MEDITERRANEAN UNIVERSITY
FACULTY OF ENGINEERING
Department of Industrial Engineering
IENG362 System Modeling and Simulation
Fall 2009-2010
Laboratory Session 2
Modeling a Single Queue Single Server System with ARENA
Patients are arriving to the single queue of a doctor’s clinic. Interarrival times of arriving
patients are exponentially distributed with a mean of 13 time unit/arrival. The examination
times are normally distributed with mean 8 and standard deviation 3.
You are required to develop and run a simple simulation model of this system (a SINGLE
replication for 20000 time units) and obtain values for the following performance measures:





Average patient flow time
Average time that patients spend in the queue
Average number of patients in the queue
Utilization of the clinic
Number of patients served by the clinic (doctor) within the mentioned time period.
Develop your Arena Model by following these instructions:
First, open a new ARENA window (i.e File  New)
STEP1: Your system should consist of Arrive, Server and Depart modules. These modules are
available in the COMMON TEMPLATE. Therefore, you should attach this template to the
ARENA environment (i.e Attach  Common.tpo)
STEP2: Place these modules from the Common template into your model. Save your Arena
model in your desktop with your name
STEP3: Double click on Arrive module. You will see the default style of it. Change some
information as follows;
Enter Data
 Station:
ArrivingPatients
Arrival Data
 Time Between : EXPO(13)
 Mark Time Attribute: Time of Arrival
Leave Data
 Connect
STEP4: Double click on Server module. Again default style appears. Do following changes;
Server Data
 Process Time: NORM(8, 3)
Leave Data
 Connect
Enter Data
 Station: Clinic
STEP5: Double click on Depart module. Default of it is shown again. Do following changes;
Enter Data
 Station: Departure
Count
 Individual Counter
Tally



Individual Tally
Tally: Flow Time
Attribute: Time
of Arrival
STEP6: Double click on Simulate module. Do following changes;
Project
 Title: My Model
 Analyst: (write your name here )
Replicate
 Length of replication: 20000
STEP7: Connect the individual modules in your model with the CONNECT connector.
STEP8: Now, this is the time for checking your model with clicking that button
STEP9: Run your model by clicking that button
STEP10: Compare your solution with following:
ARENA Simulation Results
IE_XP - License #9400000
Summary for Replication 1 of 1
Project: IE 362 Lab 02
Analyst: ElifVahid
Run execution date : 10/ 2/2007
Model revision date: 10/ 2/2007
Replication ended at time
: 20000.0
TALLY VARIABLES
Identifier
Average Half Width Minimum Maximum Observations
_______________________________________________________________________________
Flow time
13.867
1.2503
.00000
59.323
1531
Clinic_R_Q Queue Time 6.0486
1.1968
.00000
52.589
1532
DISCRETE-CHANGE VARIABLES
Identifier
Average Half Width Minimum Maximum Final Value
_______________________________________________________________________________
Clinic_R Available
# in Clinic_R_Q
Clinic_R Busy
1.0000
.46348
.59850
(Insuf)
.11539
.03116
1.0000
.00000
.00000
1.0000
7.0000
1.0000
1.0000
1.0000
1.0000
COUNTERS
Identifier
Count Limit
_________________________________________
Departure_C
Simulation run time: 0.07 minutes
Simulation run complete
1531 Infinite
Results:
 Average patient flow time is 13.867
 Average time that patients spend in the queue is 6.0486
 Average number of patients in the queue is .46348
 Utilization of the clinic is .59850 or 59.850%
 Number of patients served by the doctor within the mentioned time period 1531.
Note: The above results are based on a single replication of the simulation run. For them to
be more accurate we need to have more than 1 replication of the model and take the
averages of the respective performance measures.
Problem
People are arriving to an ATM machine and they are served with triangular distribution,
TRIA(1,4,8). Their interarrival times are exponentially distributed with mean 6.5 time of
units/arrival.
Develop your Single Queue Single Server Arena model with 5 replications (length of
replication: 5000) and find their averages to measure the performances.
SYSTEM PERFORMANCE MEASURES
Average Queue Time for the ATM server
Rep 1
Rep 2
Rep 3
Rep 4
Rep 5
AVERAGE
Average Time Customers Spent in the System
Average Number of Customers in the Queue
Utilization of the ATM server
Total Number of Customers Served by the ATM server
Inspect Module
“The Inspect module is similar to the Server module except that the Inspect module indicates the
fraction of entities that pass or fail inspection and allows for different destinations for passed and
failed entities. A user-specified “failure” probability is used to make an independent decision for
each entity as to whether it “passes” or “fails” inspection. The Inspect module has two Leave
Data sections, one for entities that pass inspection and one for entities that fail inspection.”
Example 1: In a company that produces measurement tools, engineers have decided to add a
new product to their product family. A new production line is established for the product.
Interarrival times are determined EXPO (15) and the processing time of the product is TRIA (2, 5,
9) on Machine A. After production, products are inspected for quality control. Inspection time is
EXPO (8) and the failure probability is found to be 0.09. If the product doesn’t have any defect, it
is sent to shipping department; otherwise it is sent to the scrap area.
1. Create a simulation model of this new production line in ARENA (with 2000 length of
replication, 5 replications)
2. Keeping in mind that inspection is critical for these measurement tools, so decide if the
company needs another inspector. Why?
(HINT 1) - The model will look like the following picture:
(HINT 2) - Details of the Inspect Module will be as follows:
Process and PickQueue Modules:
To select between several queues according to a rule, the PickQueue module may be used in
conjunction with a Process, Batch, Match, Seize, Request, Allocate, or Access module. However,
to pick from a queue at one of these modules, the queue must be specified in the module as an
Individual Queue (i.e., not an internal queue). The Process module is used to define a processing
step. When an entity enters a Process module, it waits until the specified server is available. The
server may be a resource or a transporter. Also, the server may be specified as “none” if no
constraining element is needed to process arriving entities.
Example 2: Suppose distribution of interarrival times for cars arriving to a car wash facility in
Lefkosa is TRIA (6, 9, 12). There are three servers with the following process time distributions: TRIA
(11, 14, 28), TRIA (12, 15, 27), EXPO(24).
1. Create a simulation model of the car wash facility in ARENA (with 20,000 length of replication,
5 replications)
2. Tabulate the following performance measures:
Average Queue Times of each car wash server
Average Time that a car spends in the system
Utilizations of each server
Total number of cars served by car wash servers
(HINT 1) PickQueue module will be used in order to select queues (according to “cyclical
selection” rule. (PLEASE CHECK THE OTHER SELECTION RULES FROM PICKQUEUE MODULE)
Details of the PickQueue module:
(HINT 2) Server module cannot be used in conjunction with PickQueue module, therefore
instead of SERVER modules, PROCESS modules will be used.
Details of the Process module for car wash #1:
In this way, the model will look like the following picture: