In a queueing system, customers arrive once every 3 minutes (standard deviation=4) and services take 2 minutes (standard deviation =6.3) ( Do not round intermediate calculations . Round your answer to three decimal places) What is the average number of customers in the system? customers
Answers
Final answer:
In a queueing system with customer arrivals every 3 minutes and service times of 2 minutes, the average number of customers in the system is calculated to be approximately 0.667
Explanation:
To calculatethe average number of customers in the system, we can use Little's Law, which states that the average number of customers in a stable queueing system is equal to the average arrival rate multiplied by the average time spent in the system.
First, we need to calculate the average arrival rate. Since customers arrive once every 3 minutes, the arrival rate is 1 customer per 3 minutes or 1/3 customers per second.
The total service time is 2 minutes, and the standard deviation is 6.3. Therefore, the average service time is 2 minutes.
Using Little's Law, we multiply the average arrival rate (1/3 customers per minute) by the average service time (2 minutes) to obtain the average number of customers in the system.
Average number of customers in the queue = (1/3) × 2 = 2/3 ≈ 0.667
Read more about standard deviaton at:
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If we sketch a scatter plot for this situation, notice that the time goofing off would be on the x-axis and Diaco's grade would be on the y-axis.
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No correlation
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