Question

A branch of mathematics called queuing theory gives a formula for the average length of a line given guest arrivals and front desk associate service time. The formula is p2 / (2 x (1 - p)) where p = average guest arrivals per minute / guests served per minute. If the average guest arrivals per minute is 10 and guests served per minute is 11. What is the average line length? (Compute p to 3 decimals places. Round answer to the nearest whole number.)

Answer 1

The average line length is approximately 3.

Step-by-step explanation:

To find the average line length, we need to calculate the value of p and then use it in the formula. First, we calculate p by dividing the average guest arrivals per minute (10) by the guests served per minute (11). This gives us p = 10/11 = 0.909 to 3 decimal places.

Now, we can substitute the value of p into the formula: p^2 / (2 x (1 - p)). Plugging in the value of p, we get 0.909^2 / (2 x (1 - 0.909)). Calculating this expression, we find that the average line length is approximately 3.