tomers per hour and interarrival times are exponentially distributed? Josh's Hot Dogs is a one-person hot dog stand, and normally gets about 10 customers per hour. Assuming that Josh can serve one customer in about 3 minutes, calculate the stand's queuing characteristics. What is the probability that there is more than one customer in the system, at any given time? Do you think Josn has an acceptable queuing system? Change the arrival rate at Josh's Hot Dogs in Question 9 to 6 customers per hour. What impact does ths la on the queuing characteristics? What is the probability that there is more than one customer in the system 9. SU12 gniueup6 gniybusa ow 1o uorl ne bn drieniu&a 10.
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- Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = fill in the blank 1 What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = fill in the blank 2 What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = fill in the blank 3Melanie 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 lineSunset 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…A study-aid desk staffed by a graduate student has been established to answer students’questions and help in working problems in your OSCM course. The desk is staffed eighthours per day. The dean wants to know how the facility is working. Statistics show thatstudents arrive at a rate of four per hour and the distribution is approximately Poisson.Assistance time averages 10 minutes, distributed exponentially. Assume population andline length can be ini nite and queue discipline is FCFS.Before a test, the arrival of students increases to six per hour on the average. What willthe new average line length be?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…
- 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?Doña Blanca plans to open a small car wash and must decide how much space to allocate to waiting cars. She estimates that customers will arrive randomly (Poisson process) at an average rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers will take their car elsewhere. The total time attributable to washing a car has exponential distribution with mean 3 minutes. Compare the fraction of potential customers lost due to lack of waiting space if a) 2 and b) 4 spaces (in addition to the wash location) are provided.In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the utilization? Note: Round your answer to 3 decimal places. What is the expected number of customers in the system (L)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the system (W)? Note: Express the waiting time in hours, round your answer to 3 decimal places. What is the expected number of customers in the queue(Lq)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the queue(Wq)?
- Currently, Commercial Banks have 1 unit of ATM machines to meet customer needs. It is known that there is an average of 12+x customers in the system. Then it is also known that the average time spent by someone in the system is 10 minutes. Assume that the system follows M/M/1. The Commercial Bank operational manager is considering whether it is necessary to add 1 unit of ATM machine. What are your considerations? To strengthen the consideration, compare the queue length, queue length, and utilities before and after adding an ATM machine? Note: x denoted by the last number of my ID Number.Example, if my ID number is 2602296545, then the number used are “5”Last National Bank is concerned about the level of service at its single drive-in window. A study of customer arrivals during the window’s busy period revealed that, on average, 20 customers per hour arrive, with a Poisson distribution, and they are given FCFS service, requiring an average of 2 minutes, with service times having a negative exponential distribution. a. What is the expected number of customers waiting in queue? b. If Last National were using an automated teller machine with a constant service time of 2 minutes, what would be the expected number of drive-in customers in the system? c. There is space in the drive for three cars (including the one being served). What is the probability of traffic on the street being blocked by cars waiting to turn into the bank driveway? d. Last National is considering adding tellers at the current drive-in facility. It has decided on $5 per hour as the imputed cost of customer waiting time in the system. The hourly cost of a teller is $10.…The Minute Stop Market has one pump for gasoline, which can service 10 customers per hour (Poisson distrib-uted). Cars arrive at the pump at a rate of 5 per hour (Poisson distributed). a. Determine the average queue length, the average time acar is in the system, and the average time a car must wait.b. If, during the period from 4:00 P.M. to 5:00 P.M., thearrival rate increases to 12 cars per hour, what will bethe effect on the average queue length?