Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 4.0 per hour. It will take Benny an average of 12 minutes to give a haircut. Based on these figures, find the following: a. The average number of customers waiting. (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.) Average number of customers waiting b. The average time a customer waits. (Round your answer to 2 decimal places.) Average waiting time minutes

Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 4.0 per hour. It will take Benny an average of 12 minutes to give a haircut. Based on these figures, find the following: a. The average number of customers waiting. (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.) Average number of customers waiting b. The average time a customer waits. (Round your answer to 2 decimal places.) Average waiting time 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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Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from…
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 4.0 per hour. It will take Benny an average of 11 minutes to give a haircut. Based on these figures, find the following:a. The average number of customers waiting. (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.) b. The average time a customer waits. (Round your answer to 2 decimal places.) c. The average time a customer is in the shop. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) d. The average utilization of Benny’s time. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)
92 Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 2.5 per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: a. The average number of customers waiting Note: Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places. b. The average time a customer waits. Note: Round your answer to 2 decimal places. c. The average time a customer is in the shop. Note: Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following a The average number of customers waiting b. The average time a customer waits.
Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a) Compute the average number of cars in line.
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following:a. The average number of customers waiting.b. The average time a customer waits.c. The average time a customer is in the shop.d. The average utilization of Benny’s time.
Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a.Compute the average number of cars in line. b.Calculate the value of probability that there are no car in the system. c.Compute the average time that a car spends in the system.
A small town with one hospital has 4 ambulances to supply ambulance service. Requests for ambulances during nonholiday weekends average 0.70 per hour and tend to be Poisson-distributed. Travel and assistance time averages 2.50 hours per call and follows an exponential distribution Use Table 1. a. Find system utilization. (Round your answer to the nearest whole percent. Omit the "%" sign in your response.) System utilization % b. Find the average number of customers waiting. (Round your answer to 3 decimal places.) Average number of customers c. Find the average time customers wait for an ambulance. (Round your answer to 3 decimal places.) Average time hour d. Find the probability that all ambulances will be busy when a call comes in. (Round intermediate calculations to 3 decimal places and final answer to 2 decimal places.) Probability
Melanie is the manager of the Clean Machine car washand has gathered the following information. Customers arriveat a rate of eight per hour according to a Poisson distribution.Th e car washer can service an average of ten cars per hour withservice times described by an exponential distribution. Melanie isconcerned about the number of customers waiting in line. She hasasked you to calculate the following system characteristics:(a) Average system utilization(b) Average number of customers in the system(c) Average number of customers waiting in line
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.6 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. (a) Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. (Round your answers to four decimal places. Report time in hours.) ?=?=Lq=L=Wq= hW= hPw= (b) Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? (Round your answer to one decimal place.) Wq (in minutes) = min, which is than the desired wait time, so the goal met. What action do you recommend? (Select all that apply.) Increase the mean service rate.Decrease the mean service rate.There is no need to change the current operating parameters.Hire another…
Drivers who come to get their licenses at the Department of Motor Vehicles have their photograph taken by an automated machine that develops the photograph onto the license card and laminates the complete license. The machine requires a constant time of 4 minutes to prepare a complete license. The interarrival time between two drivers is 6 minutes distributed exponential. a) What type of queuing model this system follow ? b) Determine the average length of the waiting line. c) Determine the average waiting time.