Many of a bank’s customers use its automatic teller machine to transact business after normalbanking hours. During the early evening hours in the summer months, customers arrive at acertain location at the rate of one every other minute. This can be modeled using a Poissondistribution. Each customer spends an average of 90 seconds completing his or hertransaction. Transaction time is exponentially distributed.A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?

Question

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. Each customer spends an average of 90 seconds completing his or her
transaction. Transaction time is exponentially distributed.

A) Identify the Queuing Model and sketch the system.

B) What is the arrival rate?

C) What is the service rate?

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Step 1

The arrival rate is 1 per minute and a Poisson distribution is assumed. The service time is 90 seconds or 1.5 min. So the service rate is 1/1.5 (number of customers per min) and the distribution is exponential. Since the number of service boot...

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