Question

Fill out the Waiting Lines Analysis Template spreadsheet.
It is set up to show you 17 customers’ interarrival times over a 20-minute period and service times at a checkout line in a store.
Note how many customers arrive. Divide by 20 minutes to get your average arrival rate per minute (λ).
Place your answer in the appropriate spreadsheet cell.
During that same 20-minute period, note how much time (in minutes) the cashier needs to process each customer.
Take the average of these process times.
Then calculate 1/(average process time) to get your average service rate (µ).
Place your answer in the appropriate spreadsheet cell.
Use the spreadsheet to calculate the following information.
Show all formulas:
a. The probability that 2 customers will arrive in 10 minutes.
b. The probability that the resource can process a customer in one-half the average service time (whatever the average service time is in the spreadsheet, take one-half of it).
c. The average utilization of the cashier.
d. The probability that 0 customers are in the system.
e. The probability that 1 customer is in the system.
f. The probability that more than 1 customer is in the system (Hint: all probabilities should sum up to 1 or 100%).
g. The average number of customers in the system (waiting + being served).
h. The average number of customers waiting to be served.
i. The average time customers spend in the system (waiting + being served).
j. The average time customer spend waiting to be served.
k. A short analysis of how you would improve utilization and/or reduce waiting time.
Include 3-5 specific ideas with some rationale for them. Do not simply state generalities like “shorten the waiting line.”

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Waiting Lines Analysis

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