© Hun Myoung Park (6/14/2015)
Queueing Model: 1
INTERNATIONAL UNIVERSITY OF JAPAN
Public Management and Policy Analysis Program
Graduate School of International Relations
DCC5350 (2 Credits)
Public Policy Modeling
Spring 2015
Homework 5: Queueing Model (70 points)
Instruction: Please write down your student ID and name at the top of your answer.
PLEASE handwrite. Download the Excel queueing template from the course Web page.
Attach the hardcopy of your Excel worksheets. Submit your answer to TA by 18:00 Saturday,
June 13th.
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Organize your answer in the ascending order (1, 2, …) and use single column.
You MUST always show your computation clearly. Otherwise, you may not get the
full credits.
Use at least four digits below the decimal point when calculating probabilities whose
four digits are not zero, in order to avoid rounding errors. Adjust cell formats for
probabilities in Excel so that you have 4 digits below the decimal point,
You may not communicate (including written, verbal, gestural, any other
communication) with others except for the instructor or TA to do this homework.
Collaboration (cheating) is NOT tolerable. However, you may ask TA or other
students only for “technical help” when using Excel.
Do not wait until the last minute to do this homework.
Again, DO NOT ASK your classmates to show their work. DO NOT SHOW your work to other
classmates. You may not share any electronic file with your classmate. Defend yourself by
keeping your work in a safe place to avoid unintended cheating. Failure to comply with this rule
will be considered academic dishonesty and misconduct. The penalties include sanctions up to
and including expulsion from the university. I trust each of you implicitly but you should be
aware IUJ’s policy. If you need clarification regarding this issue, you may contact the instructor
or OAA (ofcgsir@iuj.ac.jp).
Question 1 (35 points) Read 11.9 (pp. 473-476 in the 5th ed. or pp. 468-472 in the 4th ed.)
and Question E11.34 on page 484 (Question E11.33 on p. 479 of the 4th ed.). Assume
M/M/1/FCFS/∞/∞ up to Q1.8. You may use the queueing template but handwrite results.
1.1 (5 points) Report expected interarrival time and service time and then explain them
substantively. Don’t forget to show your calculation clearly.
1.2 (5 points) Report the utilization factor of this Shop and explain it substantively.
1.3 (3 points) Report the average waiting time in the Acme Machine Shop and explain it.
1.4 (3 points) Report the average waiting time in the queue and explain it.
1.5 (4 points) Report L using Little’s formula and explain it substantively.
1.6 (4 points) Report Lq using Little’s formula and explain it substantively.
1.7 (6 points) Report the probability that a customer has to stay in the Shop longer than 30
minutes and then interpret it. Is it acceptable to customers? Why or why not? Assume that
more than 95% of customers in general finish shopping within 30 minutes.
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© Hun Myoung Park (6/14/2015)
Queueing Model: 2
1.8 (5 points) Report the probability that there are more than 3 customers (>3) in the Shop.
Do you think this Shop is busy or slow? Use the .10 significance level to make your
decision as if you are testing H0 that the average number of customers is 3.
Question 2. (35 points) Suppose that the arrival rate becomes 18 (NOT 8) per hour during
the peak time because most customers visit the Acme Machine Shop at this time. Yes, the
arrival rate of the Shop is NOT constant. Therefore, this queueing model M/M/s/FCFS/∞/∞ is
applied just to the peak time. Use Excel to calculate performance indicators and costs.
2.1 (5 points) Calculate ρ, L, Lq, W, and Wq using the Excel queueing template and construct
a summary table for s=2 through 8. Use Excel or Quattro Pro and arrange the number of
servicer (s) in the first column, ρ in the second column, L in the third column, and so
forth. You don’t need to handwrite the result. Submit your Excel worksheet instead.
Don’t forget to add the heading at the top of your Excel worksheet as you did in
homework 3 and 4.
2.2 (6 points) Draw a line chart of ρ and L for s=2 though 8 manually. Locate s at the X-axis.
Interpret the line chart (What did you learn from this chart?). Do not use Excel.
2.3 (5 points) Calculate service provision cost and waiting cost (customers’ opportunity cost)
for question a, b, and c (but Cw is $1,000 NOT 100 in c). Use Excel or Quattro Pro and
construct a summary table; a worksheet will do for Q2.1 and 2.3. Your column titles look
like the number server, service cost, waiting cost, and total cost. Again do not handwrite
the result.
2.4 (7 points) Make your decision about the optimal level of service provision for questions a,
b, and c. Explain your reasoning.
2.5 (7 points) Manually draw a line chart of service cost, waiting cost, and total cost for c
only (ignore question a and b here). Do not use Excel.
2.6 (5 points) What did you learn from 2.4 and 2.5?
█ Checklist.
1. Your answer sheet
2. Excel Worksheet (Template File) for question 1. Add M/M/s (s=2) for question 2.
3. Excel Worksheet for Q 2.1 and Q 2.3
End of homework assignment 5.
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