The System

$[$Source: Shannon$]$ We want to simulate the checkout in a small store $($say$,$ a small gift shop$).$ One cashier, one line of customers waiting for service. We are interested in determining the average time a customer spends ln the system $($both waiting and being serviced$)$ and the percentage of time that the checkout clerk is not occupied with work.

Let$$s assume that

the time between arrivals of the customers is uniformly distributed from $1$ thru $10$ minutes $($for simplicity we round off all times to the nearest whole minute$).$

the amount of time required to service each customer is also uniformly distributed from $1$ through $6$ minutes.

To simulate the system, we need to generate an artificial experience that would be characteristic of the situation. In other words, we need an artificial way to generate customer interarrival times and service times based on the distribution assumptions above. One way to do this is to obtain ten poker chips and a single die. Number the poker chips from $1$ to $10,$ put them in a hat, and mix them up by shaking the hat. By drawing a poker chip out of the hat and reading off the number, we represent the time between the arrival of the present customer and the next one. Rolling the die and reading off the number on its face would represent how long it takes to service the customer currently at the checkout.

By repeating this process, we can generate a stream of customer arrivals and service times. The problem then reduces to being simply one of bookkeeping. This is done manually for $20$ customers in the "Simulating By Hand" lecture notes and using MS Excel in the "Simulation Using Spreadsheets" lecture notes.