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:

Ligamentum Arteriosum

A small fibrous band that connects the pulmonary artery to the aorta, a remnant of the fetal circulation.

Celiac Trunk

A major artery originating from the abdominal aorta that supplies blood to the stomach, spleen, liver, and other organs of the upper abdomen.

Pulmonary Trunk

A major blood vessel that carries blood from the heart to the lungs for oxygenation.

Abdominal Aorta

The portion of the aorta that passes through the abdomen, supplying blood to the abdominal organs.