Suppose that arrivals to a hairdresser follow a Poisson process with mean 12 customers per hour. Calculate the probabilities of (a) no customers in 20 minutes; (b) exactlyone customer in 5 minutes; (c) exactly 12 customers in a hour; and (d) fewer than threecustomers in 10 minutes.

Suppose that arrivals to a hairdresser follow a Poisson process with mean 12 customers per hour. Calculate the probabilities of (a) no customers in 20 minutes; (b) exactlyone customer in 5 minutes; (c) exactly 12 customers in a hour; and (d) fewer than threecustomers in 10 minutes.

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

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Suppose that arrivals to a hairdresser follow a Poisson process with mean 12 customers per hour. Calculate the probabilities of: a) no customers in 20 minutes; b) exactly one customer in 5 minutes; c) exactly 12 customers in a hour; d) fewer than three customers in 10 minutes.
Quick Oil provides a single-channel automobile oil change and lubrication service.Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars perhour. Assume that arrivals follow a Poisson probability distribution and that servicetimes follow an exponential probability distribution. a. What is the average number of cars in the system? b. What is the average time that a car waits for the oil and lubrication serviceto begin? c. What is the probability that an arrival has to wait for service? *Please solve for a-c typing or neatly writing all your work/steps and answers on paper, NO EXCEL* thank you !
A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 11 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee urn? b. How long would you expect it to take to get a cup of coffee? c. What percentage of time is the urn being used? d. What is the probability that three or more people are in the cafeteria? e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? f.If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?
6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. (a) Use the Excel sheet to evaluate how well the guidelines will be satisfied a year from now if no change is made in the number of tellers.
6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. a)Use the Excel sheet to determine how many tellers will be needed a year from now to completely satisfy these guidelines.
A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. 3. Find the proportion of the time that the employee is busy. 4. Find the average number of people receiving and waiting to receive information. 5. Find the average number of people waiting in line to get information.
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
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
new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Find the probability that the employee is idle. Find the proportion of the time that the employee is busy. Find the average number of people receiving and waiting to receive some information. Find the average number of people waiting in line to get some information. Find the average time a person seeking information spends in the system. Find the expected time a person spends just waiting in line to have a question answered (time in the queue).
An average of 12 jobs per hour arrive at our departmentalprinter.a Use two different computations (one involving thePoisson and another the exponential random variable) todetermine the probability that no job will arrive duringthe next 15 minutes. b What is the probability that 5 or fewer jobs will ar-rive during the next 30 minutes?
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.