EGR 549 May 2012

Analysis of Queuing Systems and Report Writing

You may follow the steps below for analysis of queuing system performance.

  1. List all the major performance measures that are important from you point of view.
  2. Decide on what is an acceptable range/value for each performance measure. This step is subjective. You need to have some explanation on why you think that acceptable range/value is suitable for your condition.
  3. Compare each performance measure with your acceptable range and comment on if it is fine.
  4. If it is not fine provide a suggestion on how it can be improved.

Below are some guidelines for selecting acceptable range/value.

Performance Measure / Guideline for Acceptable Rang/Value
Server utilization / It depends on type of industry, culture/county, work regulations, and the likes. In general a value between 75-90% may be considered suitable. A very high or low utilization is not desirable.
Number in queue/line / It depends on type of business and our goals. A high number is not desirable.
Number in system / It depends on type of business and our goals. A high number is not desirable.
Waiting time in line/queue / It depends on type of business and our goals. A high number is not desirable. You may compare it with service time.
Waiting time in system / It depends on type of business and our goals. A high number is not desirable. You may compare it with service time.
Balk rate / A high number is not desirable. You may compare it with arrival rate.
Probability of having (or less than or more than) X number in system / It depends on type of business and our goals.
Probability that a customer has to wait / It depends on type of business and our goals.

Below are some guidelines on improving a system.

·  We usually assume that we cannot control/change the arrival pattern. There are cases that we can make changes but we will not consider it for the level of this class.

·  If server utilization is too low then reduce number of servers or assign some other tasks to the server.

·  If server utilization is too high then increase number of servers or reduce service time.

·  If waiting time in line is too high you will notice that waiting time in system, number in line, number in system, and server utilization will also be high. Then, increase number of servers or reduce service time.

·  If balk rate is high you will notice that waiting time in system and server utilization will also be high. Then, increase number of servers or reduce service time.

In writing a report you should specifically mention the performance measures of your choice, the acceptable ranges/values, your explanations for acceptable ranges/values, comment on how your system is doing (values obtained for performance measures), and suggestion on how the system can be improved in case it needs one.

In general, when writing a report to a manager you need to think about what is important from the manager’s point of view. A report should be written in a simple language understandable by most people/managers. Assume a manager is not in your field and is not familiar with specific terms, specific technique, or tools that you have used to solve the problem. A manager usually cares about:

a)  What is the total cost or profit?

b)  What are the values of performance measures? For example: server utilization, average number in line (system), maximum number in line (system), average waiting time in line (system), maximum waiting time in line (system), and the like.

c)  How acceptable are the performance measures? For example:

·  You may select a suitable range for server utilization and compare the obtained value with this range.

·  You can compare maximum number in line with average number in line and comment if it is too much.

·  You can compare average waiting time with average service time and comment if it is too much.

d)  How can performance measures improve? For example, you can reduce service time and average waiting time will reduce.

e)  What extra information can assist in better decision making (such as sensitivity analysis or any information that you can extract using your CRITICAL THINKING).

Sensitivity Analysis:

What is Sensitivity Analysis in general? Why do we perform Sensitivity Analysis in general? How far do we like to perform sensitivity analysis? How can the result of Sensitivity Analysis be presented for effective communication purposes (graph, table, so on)? What should be in a report?

When writing report on sensitivity analysis the first paragraph should explain motivation for performing sensitivity analysis. Explain why specific input information is selected for this purpose. Explain the logical range used for sensitivity analysis.

The second paragraph should summarize the result of sensitivity analysis. You may use a table or graph. The original software output should be in appendix.

The third paragraph should highlight the findings from sensitivity analysis summary table or graph.

Always prepare a table as below to help you with report writing.

Performance
measure / Calculated
value / Acceptable
Values/range * / Comment
** / Suggestions
***
utilization
Wq
Lq
Prob of …..
……..

* Explain why these values/range is acceptable.

** Compare the calculated value with acceptable range and comment if fine or not.

*** Provide suggestions for improvement, if needed.

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