Sunday, June 13, 2004

Is the matrix in you?

After a long break, I took up my pen, nee mouse, and pointed it to Just when I thought I had seen it all, I came across this group of sites, the matrix sites, of which is one. This entirely legal, clever and resourceful venture offers quick get-rich schemes, electronics items at unbelievably cheap prices, and the like. But of course, there is a catch, and a good one at that. You have to wait in a queue for every item. The queue policy is that for every N persons joining the queue for item x, the person at the head of the queue wins item x. For the next person to win x, N more have to join the queue, and so on.

The interesting part is to see how this system behaves. Its easy to see that the tail of the queue grows much faster than the head shrinks. In the limiting case, the queue size is unbounded. But what does this translate to in terms of average queue length, waiting times etc? While I won't go into a rigorous analysis, here's a simple scenario. One product on sale on is the 40 GB Apple iPod, for ONLY $115. For this product, N=7. So, for every 7 customers joining the queue, the person at the head of the queue gets an iPod, for $115. Now, 7 more people have to join for the next person to get his iPod, and so on.

When I checked, the queue was 500 persons long. So, if I joined now, I would get my iPod only after these 500 got theirs. But this would require that 500 * 7 = 3500 more customers join the queue after me. But when I checked, I saw that 20 new customers join the queue every month. At this rate, I would have to wait 3500 / 20 = 175 months = 175 / 12 = 16 years! Not exactly a breeze, this queue... Even doubling / tripling the joining rate doesn't help too much. Seems like I have to look elsewhere for my iPod.

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