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Consider a post office with two employees and a single waiting line. On average, the inter-arrival time is 6 minutes. Standard deviation of inter-arrival time is 3.94 minutes. Average service time is 5 minutes. Standard deviation of service time is 2.83 minutes.

a. What is the arrival rate? What is the service rate per employee?
b. What is the utilization of each employee?
c. What is the average time a customer waits for service?
d. What is the average number of customers waiting to be served?
e. What is the average number of customers being served?
f. What is the average number of customers in the system?
g. What is the average time a customer spends in the system?

User Swapab
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1 Answer

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Final answer:

a. The arrival rate is 1/6 customers per minute. The service rate per employee is 1/5 customers per minute. b. The utilization of each employee is 0.8333. c. The average time a customer waits for service is 5 minutes.

Step-by-step explanation:

a. The arrival rate is calculated by taking the average of the inter-arrival time. In this case, the average inter-arrival time is 6 minutes, so the arrival rate is 1/6 customers per minute.

The service rate per employee is calculated by taking the inverse of the average service time. In this case, the average service time is 5 minutes, so the service rate per employee is 1/5 customers per minute.

b. The utilization of each employee is calculated by dividing the arrival rate by the service rate per employee. In this case, the utilization of each employee is (1/6)/(1/5) = 5/6 = 0.8333.

c. The average time a customer waits for service can be calculated using Little's Law. Little's Law states that the average number of customers in the system (including those being served) multiplied by the average time a customer spends in the system is equal to the arrival rate. In this case, the average number of customers in the system is the utilization of each employee, which is 0.8333. The arrival rate is 1/6 customers per minute. Therefore, the average time a customer waits for service is (0.8333)/(1/6) = 5 minutes.

User Brett Gregson
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