A Waiting-Line Problem That Cannot Be Modeled by Standard Distributions

question 53

Essay

A waiting-line problem that cannot be modeled by standard distributions has been simulated. The table below shows the result of a Monte Carlo simulation. (Assume that the simulation began at 8:00 a.m. and there is only one server.
$$\begin{array} { | c | c | c | c | } \hline \text { Customer Number } & \text { Arrival Time } & \text { Service Time } & \text { Service Ends } \\\hline 1 & 8 : 06 & 2 & 8 : 08 \\\hline 2 & 8 : 07 & 10 & 8 : 18 \\\hline 3 & 8 : 12 & 10 & 8 : 28 \\\hline 4 & 8 : 24 & 11 & 8 : 39 \\\hline 5 & 8 : 30 & 5 & 8 : 44 \\\hline\end{array}$$
a. What is the average waiting time in line?
b. What is the average time in the system?

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Definitions:

Invincibility Fable

A cognitive bias often observed in adolescents and young adults, characterized by the belief that they are immune to common dangers and risks.

Deductive Reasoning

A process of reaching a decision through the harmony of multiple propositions that are commonly taken as factual.

Hypothetical Reasoning

The cognitive process of thinking about situations that are not directly observed or real and exploring possible outcomes.

Inductive Reasoning

A method of reasoning in which specific observations or data are used to form a general conclusion or hypothesis.