1. Chapter 9: Waiting Line Management
1. Quick Lube Inc. operates a fast lube and oil change garage. On a typical day, customers
arrive at the rate of three per hour, and lube jobs are performed at an average rate of one
every 15 minutes. The mechanics operate as a team on one car at a time.
Assuming Poisson arrivals and exponential service, find a) Utilization of the lube team,
b) The average number of cars in line, c) The average time a car waits before it is lubed,
and d) The total time it takes to go through the system.
2. A photographer at the Driving License office takes pictures at an average rate of 20
persons per hour. Customers arrive at an average rate of 19 customers per hour.
Assuming relevant distributions for arrival and service,
(i)
What is the utilization of the photographer?
(ii)
How much time will an average customer spend at the Driving License office for
the photograph step?
3. A study was conducted by HDFC Bank located at Hiranandani Gardens Powai. One teller
facility was considered for servicing the customers. The following data were observed:
Customer arrival at the rate = 15 per hour
Service rate at the teller
= 20 per hour
Determine the following:
(i)
Utilization of teller facility
(ii)
Probability of at most three customers in the system
(iii)
Average number of customers in the waiting line
(iv)
Average number of customers in the system
(v)
Average time a customer spends waiting in line
(vi)
Average time a customer spends in the system