Consider a Single-Line, Single-Server Waiting Line System

question 17

Essay

Consider a single-line, single-server waiting line system. Suppose that there is only physical space for 2 units in the system (one in line and one being served). The arrival rate λ is 80 people per hour. The manager, Johnny Three Toes, has the choice among workers of different speeds to be the server. He wants to save money by hiring the slowest server that will result in an average number of units in the system (L) equal to 2.
a) Using Johnny Three Toes' strategy, what will the server's service rate per hour () need to be?
b) What is the probability of having 3 or more units in the system?
c) What is wrong with Johnny Three Toes' strategy?

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Definitions:

Difference Score

The result of subtracting one quantity from another, often used to measure change or effects in experimental designs.

T-test

A statistical test used to determine if there is a significant difference between the means of two groups, which may be related in certain features.

Critical Value

A threshold value in statistical testing used to determine whether to reject the null hypothesis.

Alpha

The threshold of significance in hypothesis testing, representing the probability of committing a Type I error.