In a queueing system, customers arrive once every 4 hours (standard deviation = 7) and services take 3 hours (standard deviation =4.9).(Do not round intermediate calculations. Round your answer to three decimal places.)What is the average number of customers in the queue?customers

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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[Queuing Theory - Operation research] The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following: (a) probability that the system is idle (b) average number of customers in the system (c) amount of time a customer should expect to wait before service (d) probability that a customer will have to spend more than 15 minutes in the queue
At a book store, one customer arrives every 4 minutes. The bookstore has one cashier, and it takes 3 minutes to serve one customer with a standard deviation of 4.9. The arrival process has a standard deviation of 7. What is the average number of customers in the queue
In an M/MA queueing system, the arrival rate is 5 customers per hour and the service rate is 9 customers per hour. If the service process is automated (resulting in no varlation in service times but the same service rate), what will be the resulting performance measurements? (Round your answers to 3 decimal places.) a. What is the utilization? Ubization b. What is the expected number of customers in the system (L)? Number of customers c. What is the expected walting time (in hours) for the system (W? Waiting timetin nours)
Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?
In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle? What is the probability of having exactly 4 customers in the system? What is the probability of having 4 or fewer customers in the system?
Please try to solve in 30 minute A queueing system has an arrival rate of 45 visitors per hour (standard deviation of 24) and a service rate of 35 visitors per hour (standard deviation of 20). What is the cofficientvof variation of the service rate .
In a queueing system, customers arrive once every 3 hours (standard deviation = 4) and services take 2 hours (standard devlation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the system (in hours)? hours
In a queueing system, customers arrive once every 3 hours (standard devlation = 4) and services take 2 hours (standard deviation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the system? customers
What is the answer in this number 2?
At a book store, one customer arrives every 6 minutes. The book store has one cashier, and it takes 4 minutes to serve one customer with a standard deviation of 5.9. The arrival process has a standard deviation of 8. (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the queue? customers
In an M/MA queueing system, the arrival rate is 8 customers per hour and the service rate is 11 customers per hour. (Round your answers to 3 decimal places.) a. What is the probability that the server will be idle? Probability b. What is the probability of having exactly 4 customers in the system? Probability c. What is the probability of having 3 or fewer customers in the system? Probability

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In a queueing system, customers arrive once every 4 hours (standard deviation = 7) and services take 3 hours (standard deviation = 4.9). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the queue? customers