Homework 3
Question 1
A local garage has only one worker who works a normal eight-hour per day. Local people come to repair their cars with an arrival pattern of people following a Poisson (random) distribution, with a mean of 10 people coming to the garagel each day during the eight-hour interval.
The distribution of time spent by a car to be repaired is exponential, with a mean of 30 minutes.
The garage receives complains from costumers, being reported that indi-viduals often wait over 45 minutes to be served and more than 75 minutes in the queue and being served. The owner knows that the worker works only 5 hours out of 8, on the average and thinks that the customers are wrong.
Are the customers right? If yes, what could the owner do?
[35 marks]
Question 2.
Consider that an office printer can print an average file in one minute.
Every seventy five seconds somebody sends another file to the printer.
a. How long does it take for a user to get the print job?
b. To increase efficiency, the company buys another printer that is exactly the same as the old one. What is the reduction in time for a user to get their file printed when two printers are available?
c. If instead of buying a second printer, the existing printer is replaced with one that can print a file in an average of thirty seconds, how long does it take for a user to get their output with the faster printer?
d. Which of the case b) or c) leads to a shorter time? [35 marks]
Question 3.
A small dental practice with only one dentist can hold only three patients, one being treated and two waiting.
Additional customers are turned away when the system is full. On the average, a patient arrives at the dental practice every half an hour and the dentist usually spends 20 minutes to service one patient.
a. What is the waiting time for each patient before being treated?
b. What is the rate of patients being turned away due to the clinic being full?
[30 marks]