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

question 8

Essay

A waiting-line problem that cannot be modelled 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.) Why do you think this problem does not fit the standard distribution for waiting lines? Explain briefly how a Monte Carlo simulation might work where analytical models cannot.
$$\begin{array} { | c | c | c | c | } \hline \text { Customer Number } & \text { Arrival Time } & \text { Service Time } & \text { Service Ends } \\\hline 1 & 8 : 05 & 2 & 8 : 07 \\\hline 2 & 8 : 06 & 10 & 8 : 17 \\\hline 3 & 8 : 10 & 15 & 8 : 32 \\\hline 4 & 8 : 20 & 12 & 8 : 44 \\\hline 5 & 8 : 30 & 4 & 8 : 48 \\\hline\end{array}$$

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Definitions:

Chi-Square Test

A statistical test used to determine if there is a significant association between two categorical variables.

Expected Cell Counts

Predicted frequencies in cells of a contingency table in statistics, assuming that the null hypothesis is true.

Observed Cell Counts

The actual frequencies or numbers of observations recorded or categorized in each cell of a contingency table in statistical analysis.

Two-Way Table

A tabular method to display the frequency of occurrence of variables that are categorized along two dimensions.