A Small Store Is Trying to Determine If Its Current

question 22

Essay

A small store is trying to determine if its current checkout system is adequate. Currently, there is only one cashier, so it is a single-channel, single-phase system. The store has collected information on the interarrival time, and service time distributions. They are represented in the tables below. Use the following two-digit random numbers given below to simulate 10 customers through the checkout system. What is the average time in line, and average time in system? (Set first arrival time to the interarrival time generated by first random number.
$$\begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } \text { Interarrival } \\\text { time (minutes) }\end{array} & \text { Probability } & & \begin{array} { c } \text { Service time } \\\text { (minutes) }\end{array} & \text { Probability } \\\hline 3 & .25 & & 1 & .30 \\\hline 4 & .25 & & 2 & .40 \\\hline 5 & .30 & & 3 & .20 \\\hline 6 & .20 & & 4 & .10 \\\hline\end{array}$$ Random numbers for interarrival times: 07, 60, 77, 49, 76, 95, 51, 16, 14, 85
Random numbers of service times: 57, 17, 36, 72, 85, 31, 44, 30, 26, 09

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Definitions:

Parabola

A symmetrical plane curve formed by the set of all points equidistant from a fixed point (focus) and a fixed straight line (directrix).

Upward

Directed or moving towards a higher place or position.

Downward

Describes the direction that is towards a lower position or level.

Graph

A visual representation of data or mathematical functions, often displayed within a coordinate system.