B. A bank has only one counter for its customers. Suppose that the customers to the bank arrive at random with exponential inter arrival time and their mean inter arrival time is 10 minutes. Suppose the counter takes on an average 15 minutes to serve the customer and this also follow an exponential distribution. a) What percentage of time the bank counter is busy? b) On the average, how many customers are in the system? c) On the average, how many customers are in the queue waiting for the service? d) How long a customer will take to be out of the service system after being served? e) How long a customer to wait before being served? f) What is the probability that there are at most three customers in the system?

B. A bank has only one counter for its customers. Suppose that the customers to the bank arrive at random with exponential inter arrival time and their mean inter arrival time is 10 minutes. Suppose the counter takes on an average 15 minutes to serve the customer and this also follow an exponential distribution. a) What percentage of time the bank counter is busy? b) On the average, how many customers are in the system? c) On the average, how many customers are in the queue waiting for the service? d) How long a customer will take to be out of the service system after being served? e) How long a customer to wait before being served? f) What is the probability that there are at most three customers in the system?

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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