Question

The following presents a calculation based on Little's Law. Choose the correct option.

A Unisa library has adopted a policy whereby there should never be more than 10 students waiting at the counter where library books are issued. It takes the library assistant on average 3 minutes to issue the books to the student. The library policy further makes provision that a student should not wait longer than 6 minutes in the queue. Using Little’s Law, calculate how many library assistants should be at the counter issuing books.
a. 1 library assistant
b. 2 library assistants
c. 3 library assistants
d. 4 library assistants

Answer 1

Using Little's Law and the information provided, the calculation suggests that 5 library assistants are required to meet the policy requirements, but this is not an available option. The closest correct option from the given choices is 4 library assistants.

Step-by-step explanation:

The question involves applying Little's Law, which relates the average number of customers in a system (L), the average arrival rate (λ), and the average time a customer spends in the system (W), given by the formula L = λW. To ensure that no student waits longer than 6 minutes, we need to find the number of library assistants required to serve the students within this time frame, considering that one assistant takes 3 minutes on average to issue books to a student.

Let's denote the maximum number of students in the queue as L (which is 10 according to the policy), and the maximum waiting time as W (which is 6 minutes). If it takes 3 minutes to serve one student, an assistant can serve λ = 1/3 students per minute.

We use Little's Law to find the arrival rate: λ = L/W. Substituting the given values, λ = 10 students / 6 minutes = 5/3 students per minute. Since one assistant can serve 1/3 of a student per minute, we divide the total arrival rate by the rate per assistant to find the number of assistants needed. Hence, (5/3) / (1/3) = 5, which means 5 assistants are needed to meet the policy requirements. However, this is not one of the provided options, thus indicating a possible mistake in the options provided or the setup of the scenario.

It's important to note that the library policy states a student should not wait more than 6 minutes, so the average service rate needs to be high enough to meet this requirement. With the provided options, we must choose the highest number of library assistants available which is:

d. 4 library assistants

The calculation shows that considering a service time of 3 minutes per student and a maximum waiting time of 6 minutes, a significantly higher number of library assistants than the provided options would be needed. Thus, the best choice from the given options is 4 library assistants, though it should be noted that this may not fulfill the policy's requirements as per the calculation.