I was reading Andrew Odlyzko and Benjamin Tilly’s new paper on network scaling on the plane to the US last week. In brief, it challenges the widely-repeated (even my me!) laws-of-thumb for network scaling:
In their place they propose a nlog(n) scaling property, and have some empirical and anecdotal evidence to support it. It also starts to capture the idea that most possible connections (or options to connect) have negligible or negative value (as noted previously).
The crux of the paper is the implication that this has for peering, as greatly more benefit accrues to the smaller partner when two dissimilarly sized networks join together. This is an important observation that holds up under many circumstances even if the nlog(n) formula is wrong. It means that the big guys get to charge the small guys for interconnect. Yes, we sort-of knew this already; but the insight is that you can’t have asymmetric charging and simultaneously have the above 3 laws hold true. Something has to give.
Much as I admire the contribution of this paper, it somehow feels incomplete.
Firstly, it doesn’t account for differences between broadcast, P2P, and group forming networks. Surely there should be some influence from the nature of the network on its scaling properties?
In a related fashion, it says nothing about the rate of change of adoption or growth of networks (as opposed to absolute, static value). Do group-forming networks grow faster? Both the traditional “laws” and the proposed new one just feel like they’re operating at too simplistic a level. I suspect that the effect of eliminating “membranes” in networks that constrain connectivity is a dynamic process that is better modelled in the first or second order derivative. Networks mostly grow via little local explosions of adoption. Maybe different rules apply for organic vs. orchestrated growth?
Lastly, and more importantly, it continues to confuse the value of a network to its owners with that of its users. It there’s one lesson of the Stupid Network, it’s that there’s a massive increase in consumer surplus. The value to users diverges from that to owners. You can’t measure user value by looking at industry revenue.
Consider when two networks merge under some roaming, interconnect or collaboration agreement. Now the customer has a choice of two places to buy service for the merged whole. (The case of fixed network access and no choice is the exception, not the rule; most networks are mobile or virtual.) This erodes pricing power. Whether or when that pricing power erodes quicker than new chargeable value is created, I don’t know. This supplier choice aspect isn’t in the model.
I have to admit I’m pretty unread in the economics of networks and peering, but it looks like there’s a lot of work still to be done. I look forward to seeing a more definitive paper on the matter.
Posted by Martin Geddes at 02:21 PMTrackBack URL for this entry:
http://www.telepocalypse.net/cgi-sys/cgiwrap/mgeddes/MT/mt-tb.cgi/440.
I'm sure you would enjoy: The Economics of Network Industries by Oz Shy; it's is just great!
Posted by: at April 11, 2005 03:28 PM