Question

A hair salon is run by two stylists, Bob and Susan, each capable of serving 5 customers per hour, on average. Eight customers arrive at the salon per hour, on average. Assume Poisson arrivals and exponential service times. If all arriving customers wait in a common line for the next available stylist, how long would a customer wait in line before being served, on average? HINT: Think M/M/s

A.21.7 minutes

B.29.7 minutes

C.2.9 minutes

D.33.1 minutes

Answer 1

The average waiting time for a customer in the line is approximately 40 minutes.

Step-by-step explanation:

To find the average waiting time for a customer in the line, we can use the M/M/s queuing model. In this case, the arrival rate is λ = 8 customers per hour, and the service rate is μ = 5 customers per hour for each stylist. Since there are 2 stylists, the number of servers is s = 2.

Using the M/M/s queuing model, the formula to calculate the average waiting time in the line is:

W = λ / (s * (s - λ))

Plugging in the values, we can calculate the average waiting time:

W = (8 / (2 * (2 - 8)))

W = 8 / (2 * (-6))

W = 8 / (-12)

W = -0.67

Since a negative waiting time is not possible, the average waiting time in the line is 0.67 hours, which is approximately 40 minutes.