Piotr Banasiewicz is a self-employed plumber who offers a 24-hour emergency serv
ID: 3110938 • Letter: P
Question
Piotr Banasiewicz is a self-employed plumber who offers a 24-hour emergency service. For most of the year, calls arrive randomly at a rate of 7 a day. The time he takes to travel to a call and do the repair is randomly distributed with a mean of 80 minutes. Forecasts for February suggest cold weather and last time this happened Piotr received emergency calls at a rate of 18 a day. Because of repeat business, Piotr is anxious not to lose a customer and wants the average waiting time to be no longer in February than during a normal month.
• Assume a Single-Server model.
• In addition to the questions in the stated problem, determine the following:
o Average server utilization
o Average number of customers in the queue (Lq)
o Average number of customers in the system (L)
o Average waiting time in the queue (Wq) – express in days, hoursand minutes.
o Average waiting time in the system (W) ) – express in days, hoursand minutes.
o Probability there is 0 units in the system (P0)
o Probability of "n" units in system with n=0 to up to n=20.
o Probability of more than "n" units in system with n=0 to up to n=20.
Determine what the minimum Service Rate in customers per day should be for February, in order to maintain or improve the average waiting time (Wq) for the rest of the year.
Please give step by step instructions on how to solve in excel.
Explanation / Answer
o Average server utilization = 7*80 / 24*60 = 38.89%
o Average number of customers in the queue (Lq) = 7 - 1 = 6
o Average number of customers in the system (L) = 7
o Average waiting time in the queue (Wq) – express in days, hoursand minutes = 80/person
o Average waiting time in the system (W) ) – express in days, hoursand minutes = 80*6 = 480 minutes
o Probability there is 0 units in the system (P0) = 1/7 (when last person is not in the queue)