Systems Engineering Department
SE 405
Lab # 1
INTRODUCTION AND MANUAL SIMULATION
Objective 1: Introduction to Simulation.
A comprehensive introduction to the problem of simulation is given in this lab. The
students are introduced to the area by giving several examples from daily life. The
different nature of simulation-based programming is emphasized. The concepts of
timing and event list are illustrated through the use of relevant examples.
Introduction to the following concepts:
1.
2.
3.
4.
5.
6.
7.
8.
Need of simulation in real world problems.
Objectives attainable by simulation.
Use of simulation as a tool for solving complex problems in real life.
Different ways of simulation of problems.
Use of programming languages in simulation.
Different commercial packages like Awesim and ProModel.
Reliability of the results.
Single server queuing problem and its variations.
Objective 2: Understanding Manual Simulation.
To enable the students to perform manual simulation. This lab will guide the students
in understanding the basic operations behind a simulation problem in a step-by-step
process.
Things to do:
To conduct manual simulation the following is needed.
1.
2.
3.
4.
5.
6.
Define objectives of the single-server queue simulation problem.
Initialization of the problem.
Define Events and Event List.
Understand How to update state variables every time an event happens.
Understand the collection of statistics.
Stopping rule.
Assignment
The students are requested to perform manual simulation as given in the example
from the textbook for the single server queuing model. Tables are provided for
recording the stepwise change in the state variables and different parameters.
Systems Engineering Department
SE 405
Lab # 1
INTRODUCTION AND MANUAL SIMULATION
Assignment
Single Server Queuing System – Manual Simulation.
Consider the Example given in Page 11 in your text book for single server queuing
system. Event wise Table representation on manual simulation is explained. The
explanation in the book is done till the number delayed reaches to 6. Using the
following data, continue working on the same problem till the number delayed
reaches 10.
Arrival Times: A1=0.4, A2=1.2, A3=0.5, A4=1.7, A5=0.2, A6=1.6, A7=0.2, A8=1.4,
A9=1.9, A10=0.8, A11=1.2, A12=0.2, A13=1.0, A14=1.5, A15=0.5.
Service Times: S1=2.0, S2=0.7, S3=0.2, S4=1.1, S5=3.7, S6=0.6, S7=1.0, S8=0.5,
S9=1.5, S10=2.0, S11=1.2, S12=0.5, S13=1.3, S14=1.5, S15=0.5.
Calculate the following performance measures when you stop the simulation at the
number delayed as 10 customers.
a) Average number of customers in the Queue.
b) Average delay per customer.
c) Utilization of the server.
Also Provide the graphs for the number of customers in the queue Q(t) and the
Utilization of the server B(t).
Systems Engineering Department
SE 405
Lab # 2
SIMULATION USING FORTRAN
Objective:
To enable the students to perform simulation using FORTRAN. This lab exercise will
guide the students in understanding the basic simulation program in a high level
programming language. The logic and the flow of the program is implemented in
FORTRAN simply because most of the students are familiar with it. The exercise of
writing subroutines gives hands-on experience for a practical simulation problem.
Things to do:
FORTRAN compilation requires following steps.
9. Understanding the flow of the program
10. Subroutines required are
a)
b)
c)
d)
e)
f)
g)
h)
INIT
TIMING
ARRIVE
DEPART
REPORT
UPTAVG
EXPON(RMEAN)
RAND(I)
11. Main program structure
12. Inputs required to run the program
13. Specification of the desired output statistics
14. Description of the stopping criteria
15. Report generation and interpretation.
Things to do:
Rerun the program with different input values and evaluate the results obtained.
Assignment
1. Rerun the program for different input values.
2. Edit the Fortran Program to change the stopping criteria and run for different
Input values.
Systems Engineering Department
SE 405
Lab # 2
SIMULATION USING FORTRAN
Assignment
The Fortran program provided to you has the stopping criteria by number of
customers. Now change the criteria based on time. Now stop the simulation for the
following data and submit reports for each output.
1) Stopping Time = 2500
Mean Interarrival Time = 2.5
Mean Service Time = 3.2
2) Stopping Time = 2500
Mean Interarrival Time = 2.0
Mean Service Time = 1.5
3) Stopping Time = 2000
Mean Interarrival Time = 1.5
Mean Service Time = 1.6
Systems Engineering Department
SE 405
Lab # 2
SIMULATION USING FORTRAN
Assignment
The Fortran program provided to you has the stopping criteria by number of
customers. Now change the criteria based on time. Now stop the simulation for the
following data and submit reports for each output.
1) Stopping Time = 2500
Mean Interarrival Time = 3.5
Mean Service Time = 3.0
2) Stopping Time = 2500
Mean Interarrival Time = 2.0
Mean Service Time = 2.5
3) Stopping Time = 2000
Mean Interarrival Time = 2.5
Mean Service Time = 2.6
Systems Engineering Department
SE 405
Lab # 3
INTRODUCTION TO AWESIM
Objective:
The students are introduced to the simulation package AWESIM. The concept of
single server queuing model is discussed and a model is developed in AWESIM.
AWESIM description of the following nodes:
1. CREATE
2. ACTIVITY
3. QUEUE
4. TERMINATE
AWESIM description of the following CONTROL statement.
INITIALIZE
The above statement is added in the list of statements in Control file to stop
simulation based on the simulation time.
Assignment:
The students are asked to rework on the single server model developed in AWESIM
by changing the interarrival times (distributions), terminating criteria, service times,
etc.
Systems Engineering Department
SE 405
Lab # 3
INTRODUCTION TO AWESIM
Assignment
Build an Awesim model for the following data. Copy the Network, Control and
Output in MS WORD for the Assignment.
1) Stopping Time = 2500
Interarrival Time = E(2.5)
Service Time =N( 3.2,1.5)
Number of servers = 1, Single Queue.
2) Number of Customers = 500
Interarrival Time = E(2.0)
Service Time =U( 2.5,3.5)
Number of servers = 1, Single Queue.
3) Stopping Time = 2500
Interarrival Time = E(2.5)
Service Time =N( 3.2,1.5)
Number of parallel servers = 2, Single Queue.
4) Number of Customers = 500
Interarrival Time = E(2.0)
Service Time =U( 2.5,3.5)
Number of parallel servers = 2, Single Queue.
Clearly identify the following from each of the reports (4) generated above.
a)
Average number of customers in the queue
b)
Average delay(or waiting time) for the customers
c)
Average utilization of the server.
Systems Engineering Department
SE 405
Lab # 3
INTRODUCTION TO AWESIM
Assignment
Build an Awesim model for the following data. Copy the Network, Control and
Output in MS WORD for the Assignment.
1) Stopping Time = 1000
Interarrival Time = E(5)
Service Time =N( 5,1.5)
Number of servers = 1, Single Queue.
2) Number of Customers = 500
Interarrival Time = E(3.0)
Service Time =U( 3.5,4.5)
Number of servers = 1, Single Queue.
3) Stopping Time = 1000
Interarrival Time = E(5)
Service Time =N( 5,1.5)
Number of parallel servers = 2, Single Queue.
4) Number of Customers = 500
Interarrival Time = E(3.0)
Service Time =U( 3.5,4.5)
Number of parallel servers = 2, Single Queue.
Clearly identify the following from each of the reports (4) generated above.
d)
Average number of customers in the queue
e)
Average delay(or waiting time) for the customers
f)
Average utilization of the server.
Systems Engineering Department
SE 405
Lab # 4
CONDITIONAL AND PROBABLISTIC BRANCHING
Objective:
AWESIM description of the following nodes/Variables:
1.
2.
3.
4.
5.
ASSIGN
GOON
COLCT
TNOW
NNQ
Routing Entities: Probabilistic and deterministic.
Probability Specification
The sum of the probabilities must be equal to 1.
Conditional Specification:
Relational Code
<
<=
==
>
>=
Definition
Less than
Less than or equal
Equal
Greater than
Greater than or equal
Solving Illustrations 4-1, 4-2 and 4-4 from the Hand out.
Assignment:
1. Consider a situation where there are customers coming into a bank with interarrival
times exponentially distributed with a mean of 7 minutes. There are two queues one
for each server in this bank. Each customer would like to join the smallest queue. The
service time for each customer is uniformly distributed with a minimum of 6 and a
max of 9 minutes on any server. Run the simulation for 100 customers and submit the
report with the three performance measures and in the regular assignment format.
2. In the above model change the service time with the current service time and a
small additional service time depending on the queue they are coming from. If the
customer comes from queue 1 then add to the current service time an additional time
of 2 minutes and if the customer comes from queue 2 then add an additional time of 3
minutes. Run the simulation for 100 customers and submit the report with the three
performance measures and in the regular assignment format.
Systems Engineering Department
SE 405
Lab # 4
CONDITIONAL AND PROBABLISTIC BRANCHING
Objective:
AWESIM description of the following nodes/Variables:
1.
2.
3.
4.
5.
ASSIGN
GOON
COLCT
TNOW
NNQ
Routing Entities: Probabilistic and deterministic.
Probability Specification
The sum of the probabilities must be equal to 1.
Conditional Specification:
Relational Code
<
<=
==
>
>=
Definition
Less than
Less than or equal
Equal
Greater than
Greater than or equal
Assignment:
1. Consider a situation where there are customers coming into a bank with interarrival
times exponentially distributed with a mean of 7 minutes. There are two queues one
for each server in this bank. 50% of customers go to queue1 and 50% to queue2. The
service time for each customer is uniformly distributed with a minimum of 6 and a
max of 9 minutes on any server. Run the simulation for 100 customers and submit the
report with the three performance measures and in the regular assignment format.
2. In the above model change the service time with the current service time and a
small additional service time depending on the queue they are coming from. If the
customer comes from queue 1 then add to the current service time an additional time
of 2 minutes and if the customer comes from queue 2 then add an additional time of 3
minutes. Run the simulation for 100 customers and submit the report with the three
performance measures and in the regular assignment format.
Systems Engineering Department
SE 405
Lab # 5
BALKING AND BLOCKING
Objective:
AWESIM description of the following nodes:
COLCT
Concepts of Attributes
ATRIB[I]
XX[I]
LTRIB[I]
LL[I]
STRIB[I]
SZ[I]
Queue Balking
Queue Blocking
Slam Variables
Lastarrive
Solving Example 4-2 (illustrating probabilistic routing) and Example 4-1 (illustrating
balking and blocking of queues.
Assignment:
1) Solve problem # 4-8 from the Hand out.
2) In the design proposed for the television inspection and adjustment situation
(Example 2, page 108) add a checkpoint job where after the adjustment (of
15% jobs) there is a quick check if the job needs to be sent to inspection or
not. It is found that only 30 percent of the jobs are needed to be sent to
inspection and the rest are acceptable. The 30% percent jobs go back for
inspection and the rest are acceptable and go out of the system. Let the time
taken at the check point be uniformly distributed with a minimum of 1 minutes
and a maximum of 2 minutes. Modify the AWESIM model with this change
and compare the results. (Clearly identify if this job made improvement in the
process or not?).
Systems Engineering Department
SE 405
Lab # 6
INTRODUCTION TO OUTPUT ANALYSIS
Objective:
Introduce the students to multiple run concepts and introduce an AWESIM control
statement MONTR for clearing statistics.
Solving the following problems.
Problem 4-4 (multiple runs)
Problem 4-5 (Clearing statistics using MONTR).
WRITE node.
Assignment:
Consider a new bank, which has two tellers. Each teller can handle any kind of
service required by the customers. Each teller has a different queue. After arriving
40% of the customers join first queue and the other 60% join the second queue. The
interarrival times of the customers are found to be exponentially distributed with a
mean of 10 minutes and the service time for the first teller is uniformly distributed
with a minimum of 4 minutes and a maximum of 6 minutes, while the service time for
the second teller is normally distributed with a mean of 5 minutes and standard
deviation of 2 minutes. Simulate the above situation for 480 minutes and run it for 10
runs. Provide the network, control statements and the output of the model developed.
a) Find the average time spend by the customers in the bank.
b) Find the average number of customers served.
c) Find the average utilization for each teller.
d) Find the average waiting time for each customer
e) Find the average number of customers in each queue.
f) For the above model clear the statistic for first 2 hours and repeat the above
questions.
Systems Engineering Department
SE 405
Lab # 7
INTRODUCTION TO RESOURCES
Objective:
AWESIM description of the following nodes:
1. RESOURCE Block
2. AWAIT Node
3. FREE Node
4. PRIORITY Statement
Solving the following illustrations.
Illustration 5-1 (Resource usage for sequential operations)
Illustration 5-2 (Single resource processing different entity types).
Assignment:
Solve problem # 5-2 from the Hand out.
Systems Engineering Department
SE 405
Lab # 8
MORE ABOUT RESOURCES
Objective:
Revising the AWESIM description of the following nodes:
1. RESOURCE Block
2. AWAIT Node
3. FREE Node
Describing the following:
1. ALTER NODE
2. EQUIVALENCE Statement
3. INTLC Statement
4. MONITOR Statement
Solving Example 5-1 (Inventory System with lost sales and backorders)
Assignment:
Redo Example 5-4 (PORT OPERATIONS) from the Hand out.
Systems Engineering Department
SE 405
Lab # 9
COURSE PROJECT DISCUSSIONS
Objective:
This week’s lab is dedicated to help the students with their course projects in using
AWESIM.
Systems Engineering Department
SE 405
Lab # 10
INTRODUCING GATES IN AWESIM
Objective:
AWESIM description of the following nodes:
1. GATE Block
2. OPEN Node
3. CLOSE Node
Solving illustration 5-5 (Gates to model Shifts) and Example 5-5 (Single Lane Traffic
Analysis).
Assignment:
Solve problem # 5-1 from the Hand out.
Systems Engineering Department
SE 405
Lab # 11
BUILDING CONFIDENCE INTERVALS
Objective:
Learning how to collect required data from the AWESIM model and develop
confidence intervals for the performance measure.
Example:
A small factory consists of a machining center and inspection station in series.
Unfinished parts arrive at the factory with exponential interarrival times with a mean
of 1 minute. Processing times at the machine are uniform on the interval [0.65,0.70]
minute, and subsequent inspection times are uniformly distributed as [0.75,0.80]
minute. 90% of the parts are bad and are sent back to the machine for rework.
We would like to obtain 90% confidence interval for the steady state mean hourly
throughput. Run the model for 10 runs and assume a warm up period of 24 hours for
the run length of 160 hours. Find the confidence interval for the throughput and
determine the average production per hour for the small factory being considered.
Systems Engineering Department
SE 405
Lab # 12
HELP SESSION
Objective:
This week’s lab is dedicated to review the students with AWESIM and clear their
doubts.