Queues are comprised of customers joining, waiting and then being served. There are two random processes here: arrivals, and serving time, which in this case are both Poisson processes. There can be one or more servers. A handy notation for this is: M/M/n, where the first M describes customer arrival, the second M server processing time, and the n the number of servers.
In this applet, there are 150 queues, each one M/M/5, with a customer arrival rate 
of 20 per second, and a server rate 
of 3 per second.
As each customer gets served, their dot turns red, and all the customers shuffle up one. When serving is finished, the dot disappears. As the server has become free, the next customer is served.
This first attempt demonstrates the variation that can occur. Currently, the queues move to the right if serving outpaces arrival. The next step is to have them wait at a particular point, and then moving off when a server is free, with those behind moving up to fill the space.
More queue models to follow, though not sure what their arrival rate will be…