How big is big?


tsuchiya@gateway.mitre.org
Tue, 7 Apr 87 13:37:11 EST


I am doing some routing research which requires that I predict the
performance of a new sort of routing hierarchy for networks of
virtually unlimited numbers of nodes. I need to also state the
diameters of these large networks. I am therefore curious as
to what people think the diameter of very large networks will be.
For those who care to consider it, then, please make a guess at the
following:

What should be the diameter of networks with
        10,000 nodes?
        100,000 nodes?
        1,000,000 nodes?

Rules:
1. A node is a switching point, such as an IMP or a gateway. Hosts don't
    count (DEC people call hosts nodes).
2. Consider any single piece of transmission as a hop. This includes
    Ethernets, single wires, and a single satellite hop, but does not
    include transit through a DDN or even bridged Ethernets.
3. This does not include ALL connectivity, only connectivity that can
    be used for transit routing. For instance, we at MITRE have both
    a MILNET and an ARPANET connection two machines on the same Ethernet.
    However, since we do transit traffic between the two, we cannot be
    considered a hop. (Actually, this third point is a little tricky,
    since physical connectivity can be blocked in many ways at many levels,
    and in different ways for different users.
    People may answer the question assuming both physical and logical
    connectivity if they wish. I just happen to be more interested in
    logical connectivity.)
4. ANSWER TO ME DIRECTLY. Do not answer over the interest list. I
    don't want people's guesses to be biased by other guesses they have
    seen. I will post a summary of this (assuming I get any interest)
    in a few days.
5. Prizes for most accurate guesses will be awarded. First prize is
    full veto power over all ISO and CCITT standards. Second prize is
    AT&T long lines and 1000 fuzzballs. Third prize is AT&T long
    lines and 2000 fuzzballs. Prizes will be awarded when the actual
    diameters of said networks are discovered.

        Paul Tsuchiya tsuchiya@gateway.mitre.org
        The MITRE Corp. tsuchiya@mitre-gateway.arpa



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