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In a truck-loading operation, the arrival rate for loading trucks is 13 trucks per hour, and the average service time is 3.7 minutes. What is the mean time between arrivals (in minutes)?

Answer :

The mean time between arrivals, or interarrival time in a truck-loading operation, given an arrival rate of 13 trucks per hour, is roughly 4.615 minutes.

The primary concept of this question lies in the field of operations management, particularly in queuing theory, an area of mathematics. The arrival rate, denoted usually by λ (lambda), represents the number of clients that arrive at the system per unit of time.

Given that the arrival rate here is 13 trucks per hour, the mean time between arrivals, also known as interarrival time or waiting time, can be found by the inverse of the arrival rate.

To convert the arrival rate from trucks per hour to trucks per minute, because there are 60 minutes in an hour, divide 13 trucks per hour by 60 to get an arrival rate of approximately 0.2167 trucks per minute.

Therefore, the mean time between arrivals is the reciprocal of this value, which is approximately 4.615 minutes. This means, on average, a new truck arrives every 4.615 minutes.

Learn more about the topic of Queuing Theory here:

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