From historical data, Harry's Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the
A.) average number of cars in line
B.) average time a car waits before it is washed
C.) average time a car spends in the service system
D.) utilization rate of the car wash
E.) probability that no cars are in the system
Given, Arrival rate = ? = 10 cars per hour
Service rate = ? = 1 car per 5 minutes = cars per hour
Ashley's Department Store in Kansas City maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 12 per hour. The clerk is capable of taking an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $10 per hour, but because of lost goodwill and sales, Ashley's loses $50 per hour of customer time spent waiting for the clerk to take an order.
A.) What is the average time that catalog customers must wait before their calls are transferred to the order clerk?
B.) What is the average number of callers waiting to place an order?
C.) Ashley's is considering adding a second clerk to take calls. The store would pay that person the same $10 per hour. Should it hire another clerk? Explain