Please do not give solution in image format thanku 41. What is the average time in minutes that a customer must wait in line before being served?Round your answer to three decimal places.A. 0.019B. 0.074C. 1.123D. 4.456 A returns desk at a department store has a single queue for the customers. There are threeemployees to serve the customers. Each employee can serve one customer in an average time of5 minutes. Customers arrive at an average rate of 20 per hour. This system fits the "multiple-server, single waiting line (with infinite calling population)" model. The average number ofcustomers in this entire system is 2.041.

Customer arrival rate refers to the frequency at which customers arrive at a particular location,…

Answered: 41. What is the average time in 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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The Swedish Bakery gets an average of 8 customers per hour. Tim Gonzales, the server, can serve a customer in 5 minutes on average. The arrival rate follows a Poisson distribution, and service time is exponentially distributed. What is the average number of customers in the system? If your answer is not an integer, keep two decimal points. What is the average waiting time in the queue (in minutes)? If your answer is not an integer, keep two decimal points.
Customers arrive at the company's service office at an average of one every 20 minutes. Their requests take, on average, 15 minutes to be processed. The service counter is staffed by only one employee, who works six hours per day. Assume Poisson arrivals and exponential service times. What model should you use? What percentage of time is the employee idle? How long is the waiting line, on average? How much time, on average, does a customer spend waiting in line? What is the probability that an arriving customer, just before entering the office, will find at least one other customer waiting in line?
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 11 customers per hour and an average service rate of 14 customers per hour. The average length of time customers will spend in the system is: a. 15.71 minutes b. 20 minutes c. 0.2619 minutes d. 0.3333 minutes
At a particular service operation, customers form a single queue that operates on a first-come, first-served basis. There is one server. Customers arrive at the rate of 12 per hour. Using the current technology in place, the server can process 15 customers per hour. Upgrades to the technology, as listed below, would allow the server capacity to increase. For example, an expenditure of $1,000 would allow the server to process 16 customers per hour. The manager wishes to insure that the time the average customer must spend in the system is less than or equal to 10 minutes. What is the minimum amount of money the manager must spend on technology to meet that standard? $1,000 service is 16 customers per hour $3,000 service is 17 customers per hour $5,000 service is 18 customers per hour $7,000 service is 20 customers per hour $10,000 service is 22 customers per hour…
Many of a bank’s customers use its automated banking machine (ABM). During the early eveninghours in the summer months, customers arrive at an ABM at the rate of one every other minute(assume Poisson). Each customer spends an average of 99 seconds completing the transaction.Transaction times are exponentially distributed. Assume that the length of the queue is not aconstraint. Determine the average time customers spend at the machine, including waiting in line and completing transactions. Determine the probability that a customer will not have to wait upon arrival at the ABM. Determine the utilization of the ABM.
A request for assistance at the reference desk at a library is submittedat an average rate of 9 per hour (Poisson distribution). At the reference desk, there is only one librarianand he can serve customers in 6 minutes on average (exponential distribution). Calculate according tothe queuing model M/M/1:1. Server utilization2. Expected number of customers in queue3. Expected waiting time of customer in queue

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41. What is the average time in minutes that a customer must wait in line before being served? Round your answer to three decimal places. A. 0.019 B. 0.074 C. 1.123 D. 4.456