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:

Conditioning

A learning process in which an individual's behavior becomes dependent on the occurrence of a stimulus in its environment.

Survive

To continue to live or exist, especially in spite of danger, hardship, or after experiencing a life-threatening situation.

Reproduce

The biological process by which living organisms produce offspring, either sexually or asexually.

Generalization

The process of applying information or conclusions from specific instances to broader contexts or general situations.