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

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

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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United Raiders Drive-In Market has one checkout counter where one employee operates the cash register. The combination of the cash resister and the operator is the server in this queuing system; the customers who line up at the counter to pay their selections form the waiting line. Customers arrive at a rate of 24 per hour according to a Poisson distribution, and service times are on average equal to 2 minutes per customer. What is the number of customers waiting in the queue on average?
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…
Sunset Airlines is concerned about the level of service for its check-in procedure. Currently, a single clerk spends an average of 3 minutes per passenger checking luggage and issuing boarding passes. Passengers arrive at the rate of 15 per hour. Make all the assumptions of M/M/1 model. Submit your answers to the following questions. Show your work. (a) What is the utilization of the clerk? (b) What is the average number of passengers in service? (c) What is the average number of passengers in the waiting line? (d) What is the average waiting time in line of a passenger? (e) What is the average time spent in the system of a passenger? (f) What is the average number of passengers in the system? (g) What is the probability of having more than 2 passengers in the system? (h) What is the probability of having no passenger in the waiting line? (i) If the clerk is replaced by a self-serve ATM with a constant service time of 3 minutes, what would be the average waiting time in line of a…
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…
McBurger’s fast-food restaurant has a drive-through window with a single server who takes orders from an intercom and also is the cashier. The window operator is assisted by other employees who prepare the orders. Customers arrive at the ordering station prior to the drivethrough window every 4.5 minutes (Poisson distributed), and the service time is 2.8 minutes (exponentially distributed). Determine the average length of the waiting line and the waiting time. Discuss the quality of the service.
Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business if 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If a single teller is used, find: 1. The average time in line 2. The average number in the line 3. The average time in the system 4. The average number in the system 5. The probability that the bank is empty 6. CEO Benjamin Neve is considering a second teller (who would work at the same rate as the first) to reduce waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting line in half. If the second teller is added, find the new answers to #1 through 6.
To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on the average, 10 persons per hour request a test. Blood pressure measurements can be made following the queuing (waiting line) model we have studied with an average service time of five minutes each. a) What is the expected average number waiting in line for the testing booth? b) What is the average amount of time that a person can expect to spend waiting in line? c) On average, how long will a person spend in the system (waiting for the testing booth and having the blood pressure test)? d) What is the probability that a person arriving will have to wait for the testing booth?
During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.7 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan's management would like to evaluate two alternatives: Use one consultant with an average service time of 8 minutes per customer. Expand to two consultants, each of whom has an average service time of 10 minutes per customer. If the consultants are paid $19 per hour and the customer waiting time is valued at $29 per hour for waiting time prior to service, should Agan expand to the two-consultant system? No What is the total cost for each scenario? Round your answers to the nearest cent. The total cost for the first scenario where there is one consultant with an average service time of 8 minutes per customer is $ fill in the blank 2 . The total cost for the second scenario where there are two consultants with an average service time of…
A student arrive in a photocopy service. There is only one photocopy operator, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem? Select one: a. 2.28 minutes b. 4.35 minutes c. 3 minutes d. 1 minute
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.9 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. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. If required, round your answers to four decimal places. Lq = fill in the blank 1 L = fill in the blank 2 Wq = fill in the blank 3 hours W = fill in the blank 4 hours Pw = fill in the blank 5 Service goals dictate that an arriving customer should not wait for service more than an average of 6 minutes. Is this goal being met? If not, what action do you recommend? If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean service rate? If required, round your answer to one…