Tracy and Diane, working as twohairstylists at coiffeur, dress hair of women at a rate of 3 women per hour. The hairdressing time for Tracy and Dianeis exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 5 per hour. a) What is the probability that Tracy is busy? b) What is the probability that Diane is idle? c)On average, how many women are waiting for hairdressing?

Tracy and Diane, working as twohairstylists at coiffeur, dress hair of women at a rate of 3 women per hour. The hairdressing time for Tracy and Dianeis exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 5 per hour. a) What is the probability that Tracy is busy? b) What is the probability that Diane is idle? c)On average, how many women are waiting for hairdressing?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

See similar textbooks

Similar questions

Tracy, working as a single hairstylist at coiffeur, dresses hair of women at a rate of 5 women per hour. The hairdressing time is exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 4 per hour. a) What is the probability that Tracy is busy? b) What is the probability that there are 3 or more women in the coiffeur? c) On average, how many women are waiting for hairdressing? d) On average, how long must a woman wait before hairdressing begins? e) What is the average time a woman spends in the coiffeur? f) Find the probability that a woman’s waiting time in the coiffeur is more than 90 minutes? g) Find the probability that total time spent by a woman in the coiffeur is more than 120 minutes?
An automated car wash will wash a car in 10 minutes.Arrivals occur an average of 15 minutes apart (exponentiallydistributed).a On the average, how many cars are waiting in linefor a wash?b If the car wash could be speeded up, what wash timewould reduce the average waiting time to 5 minutes?
At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average hair cut taking 19 minutes. It is assumed that because of excellent reputation, customers were always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a haircut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chair
A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find The probability of there being no customer in the system The average number of customers in the system iii. Average number of customers waiting to be served iv. Average time a customer spends in the system v. Average waiting time for a customer
When customers arrive at Gilley’s Ice Cream Shop, theytake a number and wait to be called to purchase ice creamfrom one of the counter servers. From experience in pastsummers, the store’s staff knows that customers arrive atthe rate of 35 per hour (Poisson distributed) on summerdays between 3:00 P.M. and 10:00 P.M. and a server canserve 15 customers per hour on average (Poisson distributed). Gilley’s wants to make sure that customers wait nolonger than 5 minutes for service. Gilley’s is contemplatingkeeping three servers behind the ice cream counter duringthe peak summer hours. Will this number be adequate tomeet the waiting time policy?
Customer arrive at one-window drive in bank according to Poisson distribution with mean 10 per hour. Service time per customer is exponential with mean 5 minutes. There are three spaces in front of the window, including the car being served. Other arriving cars can wait outside these three spaces. A. What is the probability that an arriving customer can enter one of these three spaces? B. What is the probability that an arriving customer is expected to wait outside the three spaces. C.How long is an arriving customer expected to wait before starting service.
At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 11 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? b. What is the average time that a vehicle must wait to get through the system? c. What is the utilization of the inspector? d. What is the probability that when you arrive there will be three or more vehicles ahead of you?
Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…