Many of a bank's customers use its automatic teller machine to transact business after normal banking hours. During the early eveninghours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using aPolsson distribution. Each customer spends an average of 85 seconds completing his or her transactions. Transaction time isexponentially distributed.a. Determine the average time customers spend at the machine, Including waiting in line and completing transactions. (Do not roundIntermediate calculations. Round your answer to the nearest whole number.)Average time|minutesb. Determine the probability that a customer will not have to wait upon arriving at the automatic teller machine. (Round your answer to2 decimal places.)Probabilityc. Determine the average number of customers waiting to use the machine. (Round your answer to 2 decimal places.)Average numbercustomers

Given: The customers arrive at a rate of one every other minute. hence, inter-arrival time = 2…

Answered: Many of a bank's customers use its…

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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Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Eachcustomer spends an average of 90 seconds completing his or her transactions. Transaction time isexponentially distributed. Determine the following:a. The average time customers spend at the machine, including waiting in line and completingtransactionsb. The probability that a customer will not have to wait upon arriving at the automatic tellermachinec. The average number waiting to use the machine
Twenty-one customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 2 minutes to fill each order (following a negative exponential distribution). The Waiting Line Table is provided below and also we know that ... a) What is the average number of customers in the queue? Using the table, the average number of customers in the queue is ______ customers (round your response to four decimalplaces). b) How long will a person wait in line on average? The average time a person spends in the queue is ______ minutes(round your response to two decimal places). c) If Andy's wife joins him in serving meals (at the same speed as Andy), how will your answers to parts a and bchange? Using the table, the new average number of customers in the queue is _________ customers (round your response to four decimal places). The new average time a person spends in the…

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