Instructions for this demo are down below.
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The applet above simulates a queuing situation. It starts with a newly opened service, with no one being served or waiting. Once you start the simulation, the green indicator in the n column shows how many customers are currently in the system, updated once each simulated second.

Click on the Go button to start the clock.

The slider below the Go button regulates the speed. With the slider to the far right, the display updates in real time, so one simulated second equals one actual second. Move the slider to the left to speed up the simulation.

Lambda is the expected number of arrivals per hour. Each second, the probability is lambda/3600 of an arrival during that second. Each arrival increments n, the number in the system.

Mu is the expected service rate per hour. If there is someone being served, the probability is mu/3600 of a service completion during that second. Each service completion decrements n, the number in the system.

The Seconds of n column shows how long the system has had each number of customers present since you started it. The Proportion column shows what proportion of time the system has had each number of customers present. Each Proportion is Seconds of n divided by total seconds since the system started. The Proportions are updated once each simulated minute. Also calculated is L, the average number of people in the system since it started.

Click on the Stop button to stop the clock.

The longer this runs, the closer the proportions should get to the theoretically predicted proportions in the right column. However, this convergence can take a very long time, especially if lambda and mu are small.

To change lambda or mu, type in the lambda or mu text box. Then press Enter while the cursor is in one of the boxes. The table resets to 0 and the clock stops when lambda or mu are changed. Click on the Go button to start the clock.