Empire Building on the Internet

So you want to build yourself an empire on the Internet.  You have a great idea for a new product, you scrape together some money, get a web site built, and open your first Internet storefront.  Time to conquer the competition.  Things start off well.  Your site makes a splash, people love your product, and they start coming in droves.  One problem: your site can't handle the load.

Waiting time for a queuing system (Brian Tung)

You've just encountered the harsh realities of queuing theory. Imagine you own a bakery, and you employ one clerk to staff the store.  The clerk is fairly efficient and takes about a minute to handle a customer.  Some customers will take longer, because they have a special order.  If two customers arrive within 30 seconds of each other, clearly the second will have to wait until the first one is finished.  If customers keep arriving quickly, a line will form.  Queuing theory says that if customers start arriving close to the capacity of the store (1 customer per minute), delays will quickly grow and waiting time will become infinite.  The remarkable thing is that this happens before the store reaches its capacity, because some customers take longer to service than one minute, and because sometimes customers arrive sooner than the average.  The same situation holds whether you run a bakery, a web server, or a highway.  (See Brian Tung's excellent blog entry explaining why this happens for freeway traffic.)