Question

A small company just opened a new massage station at Philadelphia airport. The company has a stand that offers massages to travelers.Customers can select a length of massage between 5 and 20 minutes and there is a unique rate of $30 independently of the length selected by customers. The average length of massage requested by customers is of 15 minutes with standard deviation of 10 minutes. There are TWO employees delivering massages. The average number of potential customers requesting a massage is of 20 per hour. The inter-arrival times are assumed to be exponentially distributed. If no spot is available when the customer arrives, s/he leaves in order not to risk missing her/his flight. What is the average number of customers serviced per hour? (You should be accurate up to two decimal digits after the decimal point.)

Answer 1

To be calculated:

Average number of customers serviced per hour or flow rate

Given values:

Number of employees delivering massages, m = 4

Average length of massage, p = 15 minutes

Average number of customers requesting a massage = 40 per hour

Arrival time, a = 1.5 minutes (40 per hour)

Solution:

Rate of arrival can be calculated as;

r = p / a

r = 15 / 1.5

r = 10

From the Erlang loss table, probability at m = 4 and r = 10 is equal to;

Pm (r) = 0.6467

Flow rate can be calculated as;

F = 1/a x [1 - Pm(r)]

F = 1/1.5 x [1 - 0.6467]

F = 0.67 x 0.35

F = 0.23 customer per minute or 0.23 x 60 minutes = 13.8 customer per hour

Therefore, the average number of customers serviced per hour is 13.8 customers

Explanation: It implies that with 4 employees, the massage station will be able to serve on an average 13.8 customers per hour. If the massage station wants to increase their revenue, they should either increase the number of employees or reduce the massage time per customer. However, reduction in massage time may lead to the dissatisfaction of the customer.

*Note: Please comment below if you have any doubts.