please answer in 30 mins. if drivers wanting to fill up their cars arrive randomlyat another gas station across the street at a rate of45 customers per hour. On average the service timeis 3 minutes to pump has and pay, and variesexponentially. One of the 5 pumps malfunctions.The cars will drive to each pump to fill up the gas. Ifthe pump is used, they will wait in line at eachpump. In this case, if we use the hour as ameasurement when we use M/M/s model to solvethis problem what are the mean arrival rate, meanservice rate, and number of servers?

Answered: Image /qna-images/answer/e984bd45-6e9e-4462-ac9f-f53cf15df986.jpg

Answered: if drivers wanting to fill up their…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.4: Important Queueing Relationships

Problem 6P

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Please solve this in excel. Ray is planning to open a small car-wash operation for washing just one car at a time. He must decide how much additional space to provide for waiting cars. Ray estimates that customers would arrive according to a Poisson input process with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean of 2 minutes. Suppose that Ray makes an average $4 per served customers. Moreover, each car space rented for waiting costs $800 per month. Ray is planning to run the car-was for 200 hours every month. 2. How much space should Ray provide for the waiting cars in order to maximize his expected net profit? (By net profit, we mean profit from car-wash operations minus the rental cost)
At a fashion retailer, there are 3 cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It has been estimated that the arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 17 minutes. Suppose that customers form a single line. What is the average length of the line (i.e., average number of customers in the waiting line)? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.
The First American Bank of Rapid City has one outside drive-up teller. It takes the teller an average of 4 minutes to serve a bank customer. Customers arrive at the drive-up window at a rate of 12 per hour. The bank operations officer is currently analyzing the possibility of adding a second drive-up window, at an annual cost of $20,000. It is assumed that arriving cars would be equally divided between both windows. The operations officer estimates that each minute’s reduction in customer waiting time would increase the bank’s revenue by $2,000 annually. Should the second drive-up window be installed?
Zimmerman’s Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: The average time in the line. The average number in the line. The average time in the system. The average number in the system. The probability that the bank is empty.

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