Nearly every aspect of our lives is impact by waiting on lines (queues), including grocery stores, waiting at red lights, our mail in queues for sorting in the Post Office, waiting on hold for technical support, etc.  The length of the queue, average wait time, etc are byproducts of the number of people entering the queue, the average frequency people enter the queue, the amount of time a server requires to process each person, the number of servers, etc.  

This requires you evaluate the data (on the next sheet) and apply Queueing Theory to determine the characteristics of the queues.  Please refer to the chapter on Queuing Theory for the procedures to do.

The Questions

For each question, show the work to support your answer

Analysis

a) A store has an average of 25 people arriving each minute to checkout and each person on the average require 4 minutes to be processed at the checkout.  What is the minimum number of cashiers required?

b) For the above question, what is the minimum number of cashiers required to get the average wait to be less 1 minute?

c) The number of passengers arriving at an airport terminal average 1200 each hour.  To process passengers (check in, take luggage, etc) take an average of 6 minutes each.  There are 6 airport staffers processing passengers.  How long is the average wait for each passenger?

d) For the above question, on average how many passengers are waiting in line?

e) For the above question, if one airport staffer called in sick, how much longer is the average wait for passengers?

f) In a typical 8 hour work day, 24 customers arrive per hour and the cashier can handle 30 each hour.  How much time will this cashier be idle on the average?

Consulting

g) What recommendations could you make to the store in question a) above in light of the queue

characteristics?  Be specific and make sure the recommendations tie directly to the answers

you gave.

h) What are some of the likely mistakes people make when applying Queuing Theory to a

grocery store?

i) Give an example of an actual queue you have seen in which the waiting line grew at a rate faster than can be processed.

j) In the queue you mentioned in question I above, what concrete recommendations would have alleviated the problem you observed?  Explain why these recommendations would solve the problem?

Please submit your answers in PowerPoint, Word, or Excel