Question

Fantastic Styling Salon is run by three stylists, Jenny Perez, Jill Sloan, and Jerry Tiller, each capable of serving four customers per hour, on average. Use POM for Windows or OM Explorer to answer the following questions: During busy periods of the day, when nine customers on average arrive per hour, all three stylists are on staff.

a. If all customers wait in a common line for the next available stylist, how long would a customer wait in line, on average, before being served?

b. Suppose that each customer wants to be served by a specific stylist, 1/3 want Perez, 1/3 want Sloan, 1/3 want Tiller. How long would a customer wait in line, on average, before being served? During less busy periods of the day, when six customers on average arrive per hour, only Perez and Sloan are on staff.

c. If all customers wait in a common line for the next available stylist, how long would a customer wait in line, on average, before being served?

d. Suppose that each customer wants to be served by a specific stylist, 60 percent want Perez and 40 percent want Sloan. How long would a customer wait in line, on average, before being served by Perez? By Sloan? Overall?

Answer 1

a.Number of stylists (service provider) = 3

Service rate of each = 4 per hour

Service rate per system = per hour

During busy periods of the day, when arrival rate is 9

Average waiting of customer before being served

Wq = PW

P =

W =

Wq =

Average waiting time in live = minutes.

b.When each customer wants to be served by a specific stylist.1/3 want perez, 1/3 want Sloan, and 1/3 want Tiller.

Since, the arrival rate is 9 per hour there is probability selecting each stylist by customer is equal. Hence, there will be no change in customer waiting line.

During less busily period of the day

When customer arrival rate is = 6 per hour

Number of stylists serving is 2

Service rate per each 4 customers

Service rate per system = customers

c. Average waiting of customers before being served

Wq = PL

P = =

L =

Wq = PL

=

Average waiting time in live

= minutes

d. When 60% want Perez and 40% want Sloan

Customer arrival rate for Perez =

Customer arrival rate for Sloan =

Service rate for each = 4 customer per hour

Average waiting time of customer at Perez before being served

Wq = PL

P =

L =

Wq =

Average waiting time in line = munities

Average waiting time of customers at Sloan before being served

Wq = PL

P =

L =

Wq =

Average waiting time of customers at Sloan = munities

Over all waiting before being served = munities.