In order to pay his rent, Tom, a college student, has taken a job in the computer department of a local department store. His only responsibility is to answer telephone calls to the department, most of which are inquiries about store hours and product availability. As Tom is the only person answering calls, the manager of the store is concerned about queuing (or waiting line) problems. Currently, the computer department receives an average of one call every 3 minutes, with standard deviation of 3 minutes in this inter-arrival time.
Tom requires an average of 2 minutes to handle a call. The standard deviation of this activity time is 5 minutes.
Assume that there is no limit on the number of customers that can be on hold, and customers do not hang up even if they are forced to wait a long time. The telephone company charges $5.00 per hour for telephone lines whenever they are in use (either while the customer is in conversation with Tom or on hold because Tom is talking to some other customer).
For one of his courses, Tom has to read a book. He can read 1 page per minute. Tom's boss has agreed that Tom could use his idle time for studying, as long as he drops the book as soon a call comes in. How many pages can Tom read during an 8-hour shift?
How long does a customer have to wait on average, before talking to Tom?
Explain why there is a positive average wait time for customers even though the utilization of Tom is less than 100%.
What is the average total cost of telephone lines over an 8-hour shift? Note that the department store is billed by the phone company whenever the line is in use, including when a line is used to put a customer on hold?
The department store manager is concerned that the average wait time is too high. Provide one suggestion to reduce the average wait time. Justify.