The Lunch Counter at a Small Restaurant Has Difficulty Handling

Essay

The lunch counter at a small restaurant has difficulty handling the lunch business. Currently, there is only one cashier in a single-channel, single-phase system. The restaurant has collected information on the interarrival time, and service time distributions from past lunch hours. 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.
$$\begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } \text { Interarrival } \\\text { time (minutes) }\end{array} & \text { Probability } & & \begin{array} { c } \text { Service time } \\\text { (minutes) }\end{array} & \text { Probability } \\\hline 1 & .20 & & 1 & .20 \\\hline 2 & .20 & & 2 & .30 \\\hline 3 & .30 & & 3 & .30 \\\hline 4 & .20 & & 4 & .20 \\\hline 5 & .10 & & & \\\hline\end{array}$$
Random numbers for interarrival times: 32, 73, 41, 38, 73, 01, 09, 64, 34, 44
Random numbers of service times: 84, 55, 25, 71, 34, 57, 50, 44, 95, 64