Question

Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level of service to customers: The average number of customers waiting in line to begin service should not exceed 1; at least 95 percent of the time, the number of customers waiting in line should not exceed 6 (a) Determine how well these guidelines are currently being satisfied. (b) Evaluate how well the guidelines will be satisfied a year from now if no change is made in the number of tellers. Problem 5. Janet is planning to open a small two-bay car-wash operation, and she must decide how much space to provide for waiting cars. Janet estimates that customers would arrive ran domly (i.e., 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 3 minutes. Compare the expected fraction of potential customers that will be lost because of inadequate waiting space if (a) 2 spaces, and (b) 4 spaces were provided

Answer 1

Answer 5

Part (a)

Part (b)

4 spaces

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