# Question

Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs for customers who are waiting to begin a haircut, so the number of customers in the shop varies between 0 and 4. For n = 0, 1, 2, 3, 4, the probability Pn that exactly n customers are in the shop is P0 = 1/16, P1 = 4/16, P2 = 6/16, P3 = 4/16, P4 = 1/16.

(a) Calculate L. How would you describe the meaning of L to Newell and Jeff?

(b) For each of the possible values of the number of customers in the queueing system, specify how many customers are in the queue. Then calculate Lq. How would you describe the meaning of Lq to Newell and Jeff?

(c) Determine the expected number of customers being served.

(d) Given that an average of 4 customers per hour arrive and stay to receive a haircut, determine W and Wq. Describe these two quantities in terms meaningful to Newell and Jeff.

(e) Given that Newell and Jeff are equally fast in giving haircuts, what is the average duration of a haircut?

(a) Calculate L. How would you describe the meaning of L to Newell and Jeff?

(b) For each of the possible values of the number of customers in the queueing system, specify how many customers are in the queue. Then calculate Lq. How would you describe the meaning of Lq to Newell and Jeff?

(c) Determine the expected number of customers being served.

(d) Given that an average of 4 customers per hour arrive and stay to receive a haircut, determine W and Wq. Describe these two quantities in terms meaningful to Newell and Jeff.

(e) Given that Newell and Jeff are equally fast in giving haircuts, what is the average duration of a haircut?

## Answer to relevant Questions

Consider a birth-and-death process with just three attainable states (0, 1, and 2), for which the steady-state probabilities are P0, P1, and P2, respectively. The birth-and-death rates are summarized in the following ...Consider a single-server queueing system where interarrival times have an exponential distribution with parameter λ and service times have an exponential distribution with parameter μ. In addition, customers renege (leave ...Consider a queueing system that has two classes of customers, two clerks providing service, and no queue. Potential customers from each class arrive according to a Poisson process, with a mean arrival rate of 10 customers ...You have been hired as an operations research consultant by a company to reevaluate the inventory policy for one of its products. The company currently uses the basic EOQ model. Under this model, the optimal order quantity ...A company owns both a factory to produce its products and a retail outlet to sell them. A certain new product will be sold exclusively through this retail outlet. Its inventory of this product will be replenished when needed ...Post your question

0