Experiment 6

Subject: Computer Simulation and Modeling

Class: BE IT                                                    Semester: VIII

Experiment No. : 06

Aim: Queuing Simulation (The Buffer Overflow Model) using Rockwell Arena.

A.    The Finite Queue Capacity Model

B.     The Infinite Queue capacity Model

Title: The Buffer Overflow Model

Requirements: Rockwell Arena

Queuing Simulation (The Buffer Overflow Model)

Your task in this lab is to simulate and animate a model of a single machine station with finite buffer (queue) capacity using the simulation modeling environment Arena. In this system, parts arrive at a rate of 6 per hour (one every 10 minutes) and have a mean processing time of 9.9 minutes. You will initially simulate the system with an infinite buffer capacity, then add a capacity restriction.

A. Building the model with Finite Queue Capacity Model

1. Launch ARENA from the Start menu, and then open a new model from the File menu.

2. From the Basic Process panel, place a Create module.

Open the module by double-clicking on it, and then specify the following:

Name : Incoming

Time Between Arrivals

Type : Random

Value : 10

Units : minutes

This module simulates an arrival process, in this case a “Poisson process,” with expected time between arrivals of 10 minutes.

3. From the Basic Process panel, place a Process module.

Open the module, and specify the following:

Name : First Machine

Action : Seize Delay Release

Resources : Add Resource Name: Machine Quantity: 1

Delay Type : Constant

Units : minutes

Value : 9.9

This module represents a potentially multiple server, single waiting line queue. In this example it represents the machine and its buffer, which by default has infinite capacity. The processing time is a deterministic 9.9 minutes.

4. From the Basic Process panel, place a Dispose module. Open it, and specify the following:

Record Entity Statistics: toggle this on

This module represents parts departing from the system.

5. If any of the modules are not connected, then use the connection tool to connect the entity flow from Create to Process to Dispose.

6. In the Run:Setup... menu, specify 1 replication of run length 1000 minutes.

7. From the Animate buttons, select Plot (the button looks like a small plot).

For the Expression Add the expression First Machine.WIP from the drop-down menu.

Set Min to 0, Max to 10. Set the # History Points to 500.

Click and drag the plot to size. This module will plot the number of parts in the buffer as a function of time.

8. Run the model by selecting Go from the Run menu or using the VCR buttons.

Watch the animation until it ends.

9. When asked if you want to view the results, select Yes.

Look at the Queues and Resources reports. Here is how the statistics match up to our queueing notation:

Wait Time	wq
Number Busy	o
Number Waiting	ℓq

10. Select End from the Run menu to stop the simulation.

B. Building the model with Infinite Queue capacity Model

Now we will put a capacity on the machine queue and send the overflow parts to a slower machine.

1. From the Basic Process panel, place another Process module near the First Machine.

Open the module, and specify the following:

Name : Overflow Machine

Action : Seize Delay Release

Resources : Add Resource Name: Overflow Quantity: 1

Delay Type : Constant

Units : minutes

Value : 19

This module will model a secondary machine that takes care of the overflow from the first machine, but is much slower.

2. From the Basic Process panel, place a Dispose module. Open it, and specify the following:

Record Entity Statistics : toggle this on

This module represents parts departing from the Overflow Machine.

3. Place a Decide module between Incoming and First Machine. Specify the following:

Name : Queue Full

Type : 2-way By Condition

If : Variable

Named : First Machine.WIP (from drop-down menu)

Is: <

Value : 5

We will use Queue Full to determine whether an arriving entity goes to the First Machine or Overflow Machine by looking ahead at the number in the First Machine queue.

4. Make sure all appropriate connections have been made.

3. What you should do

Run the model, observe the results and look at the statistics.

Turn in a print out of this model and a summary of the key performance measures.

A screen print is acceptable.

Also, prepare a short (couple of paragraphs) summary of your results.

A clear statement, using proper grammar, of findings and interpretation is key.

Here are some Arena distribution functions that might be useful to you in your projects:

Arena function	distribution
BETA(Alpha1,Alpha2)	sample from beta distribution
ERLA(ExpMean,k)	sample from Erlang distribution with k phases and mean k*ExpMean
EXPO(Mean)	sample from exponential distribution
GAMM(a, b)	sample from gamma distribution
LOGN(Mean,StdDev)	sample from lognormal distribution
NORM(Mean,StdDev)	sample from normal distribution
POIS(Mean)	sample from Poisson distribution
TRIA(Min,Mode,Max)	sample from triangular distribution
UNIF(Min,Max)	sample from continuous uniform distribution
WEIB(a, b)	sample from Weibull distribution

C. Exercise for the Students

An office that dispenses automotive license plates has divided its customers into categories to level the office workload. Customers arrive and enter one of three lines based on their residence location. Model this arrival activity as three independent arrival streams using an exponential interarrival distribution with mean 10 minutes for each stream, and an arrival at time 0 for each stream. Each customer type is assigned a single separate clerk to process the application forms and accept payment with a separate queue for each. The service time is UNIF(8,10) minutes for all customer types. After completion of this step, all customers are sent to a single second clerk who checks the forms and issues the plates (this clerk serves all three customer types, who merge into a single first-come, first-serve queue 4 for this clerk). The service time for this activity is UNIF(2.66,3.33) minutes for all customer types.

A consultant has recommended that the office not differentiate between customers at the first state and use a single line with three clerks who can process any customer type.

What you should do

Develop two models, one for the original system and the one for the consultant’s idea. Run both systems for 5,000 minutes each. Observe the average and maximum time in the system for all customer types combined.

Provide a screen print of each system and a copy of the report page that lists average time and maximum time for all customer types.

Give an written analysis (one or two paragraphs) of the system. Use your results from both of the simulations as the basis for your analysis.

Conclusion:-

Thus, we have studied the simulation and statistics of the Buffer overflow condition using Rockwell Arena.

Exercise:-

1. Simulate a model of an ATM machine. Arrivals are Poisson distributed at 8 per hour. ATM service time is exponentially distributed at 4 minutes. People will balk (choose to not use the ATM) if there are more than 3 people in the queue (and being served). 

2. Model for a walk-in clinic. Arrivals are 2 patients per hour in a Poisson distribution. First, a patient must register with a nurse before seeing the doctor. There is only one nurse on duty with service time being exponentially distributed at 3 minutes. Next, a patient must enter a queue to see the doctor. The doctor takes 18 minutes in an exponential distribution to see each patient. Patients arriving will balk (choose to go home / go to another clinic) if there are more than 5 patients in the entire system (i.e. waiting to register with the nurse, being registered by the nurse, waiting to see the doctor, being seen by the doctor). 

3. An office that dispenses automotive license plates has divided its customers into categories to level the office workload.  Customers arrive and enter one of the three lines based on their residence location.  Model this activity as three independent arrival streams using an exponential interarrival distribution with mean 10 minutes for each stream.  Each customer type is assigned a single, separate clerk to process the application forms and accept payment, with a separate queue for each.  The service time is UNIF (8, 10) minutes for all customer types.  After completion of this step, all customers are sent to a single, second clerk who checks the forms and issues the plates.  This clerk serves all three customer types.  The service time for this activity is UNIF (2.66, 3.33) minutes for all customer types. 

Develop a model of this system and run it for 5000 minutes; observe the average and the maximum time in system for all customers. Find the number in & out, utilization of different stations.

4. Parts arrive in a system serially with Random (Expo) 5 minutes. Drilling center is defined TRIA (1,3,6) minutes. Washing center is defined TRIA (1,3,6) minutes. Inspection center is Constant (5) minutes. It decides 80% parts were clean parts and remaining are dirty parts.

Develop a model of this system and run it for 5000 minutes; observe the number of parts seized by each processes and note down the number of clean and dirty parts.

5. Simulate a model of a single machine station with finite buffer (queue) capacity using the simulation modeling environment Arena. In this system, parts arrive at a rate of 6 per hour (one every 10 minutes (random)) and have a mean processing time of 9.9 minutes (constant). Simulate the system with an infinite buffer capacity, and then add a capacity restriction. Plot any function.