A residential line might typically see three calls of three minutes a day, made at more or less random times, while a business line might see more than 20 of slightly longer duration. The resource sharing increases beyond the local switch, as traffic is concentrated on to a hierarchical global network, and only in the local loop do we all need a dedicated connection.

This analysis was characterised by A.K. Erlang, a Danish telephone pioneer working around 1917, and has become holy writ, involving negative exponential distributions and queueing theory. Simply put: as the number of users grows, the more resource aggregation is possible, and the longer you are on the phone, the more likely you are to hang up. Historically, two-hour calls are rare.

Some years ago, a discussion with a computer network team brought home to me just how much the telephone network might have to change. Computer users had complained about the lack of bandwidth and latency, while measurements had established the LAN (local area network) loading to be 25 per cent. This figure turned out to be the average over a full day.

It was then discovered that the average loading for one-hour periods could exceed 55 per cent; while 10-minute periods returned 95 per cent. The real shock came when the one-minute figure revealed loadings in excess of 300 per cent. Here was the problem, a now obvious oversight; a massive peak to mean ratio never experienced in telephone networks.

This problem has since become much worse with the emergence of the Internet. Highly correlated network activities have seen the peak to mean ratio increase rapidly to create the World Wide Wait. While the bit transport problem can be solved by providing more bandwidth, a more holistic approach might be to examine network protocols and topologies. We might then simultaneously relieve the strain on routers, switches and servers.

A growing problem for telephone networks is the hold times associated with Net access from fixed and mobile terminals. Instead of three minutes, the average can now be hours, or in the case of polling systems, less than a minute.

The Erlang model fails under these extremes because the underlying assumptions are wrong, and resource sharing on a grand scale breaks down. Lots of people making very long calls to a local server rapidly clog up the switching fabric for normal users. This also results in the balance of local and long-distance calls being distorted.

On a personal level, users find they cannot make calls, and miss calls when they are online longer than they think. The solution? Well, it appears that most of us just have to get a second phone line.

But this is only the start. Network computing, and TV access to the Net through set-top boxes, will introduce new online activities that could swell the population of users very fast. The problem will be the lack of sharing, and it looks like we need a new Mr Erlang - and a new network model.

Peter Cochrane holds the Collier Chair for the Public Understanding of Science & Technology at the University of Bristol. His home page is:
http://cochrane.org.uk