Monday, October 13, 2008

DCII 13.10.08

Erlang was a Danish mathematician who first solved the problem of provisioning for telephone networks by computing the relationship between the call arrival statistics, the capacity, and the "call blocking probability" (i.e. chance that there isn't a single call's worth of capacity on any circuit to the destination for your call). N.B. as well as being independent random arrivals, calls are mostly short (3 mins) and local (one hop), so hierarchical capacity assignment is straightforward. Of course, there are "flash crowds" (a.k.a. "Mother's Day" events), which do not follow these statistics, and generally lead to higher than usual call blocking.

Leland, Willinger and others were the first to report the (then surprising) non-poisson nature of Internet traffic in their rightly celebrated sigcomm 93 paper - this somewhat went against received telephone network wisdom that traffic was I.I.D and therefore characterized by the Poisson distribution. This, of course, describes the aggregate traffic characteristics - most traffic is TCP-based, and a single source's behaviour is described by Padhye's equation

THe Telephone networks were designed, top down, by large national monopolies and their topology was created by network design equations. The Internet has grown in a decentralised way, and so its topology is a result of a number of natural (demographic) forces and is described better as a (nearly) scale free graph, whose node degree distribution follows a power law - many other systems are like this (e.g. authorship graphs, the web page link topology, the appearance of actors in films (kevin bacon etc). This also has interesting properties in terms of resilience to failure and attack, and reflects an ancient truth about society which network scientists call "preferential attachment" and social scientists call "rich get richer".

Errata: I am corrected about use of Mobile Phones on planes in landing in HK - apparently, it isn't allowed there yet - this was something I was told a few years back, and was by someone from the far east but perhaps it wasn't HK _ perhaps Beijing?
Anyway, key point is that the main objection is from cell phone providers worried about network overload from roaming, handover and beaconing traffic rather than the specifics of where - two CS solutions are 1). predictive handover and 2). aggregate signaling (e.g. via a small "microcell" on the plane).

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