Consider a bank with two tellers. Service times by each teller are exponentially distributed with mean of 1 hour per customer. Customers also arrive with an exponential interarrival times with mean of 1 hour. Suppose a customer has just arrived at 2pm: a. What is the probability that the next customer will arrive between 3:00 pm and 4:00 pm? b. If no customer arrives before 4:00 pm, what is the probability that the next customer will arrive between 4:00 pm and 5:00 pm? c. What is the probability that the number of arrivals between 2:00 pm and 4:00 pm will be more than one?

Consider a bank with two tellers. Service times by each teller are exponentially distributed with mean of 1 hour per customer. Customers also arrive with an exponential interarrival times with mean of 1 hour. Suppose a customer has just arrived at 2pm: a. What is the probability that the next customer will arrive between 3:00 pm and 4:00 pm? b. If no customer arrives before 4:00 pm, what is the probability that the next customer will arrive between 4:00 pm and 5:00 pm? c. What is the probability that the number of arrivals between 2:00 pm and 4:00 pm will be more than one?

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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