Scaling Properties of the Internet Graph
Computer Science Department
Carnegie Mellon University
Pittsburgh, PA 15213
As the Internet grows in size, it becomes crucial to understand how
the speeds of links in the network must improve in order to sustain
the pressure of new end-nodes being added each day. Although the
speeds of links in the core and at the edges roughly improve accord-
ing to Moore’s law, this improvement alone might not be enough.
Indeed, the structure of the Internet graph and routing in the net-
work might necessitate much faster improvements in the speeds of
key links in the network.
In this paper, using a combination of analysis and extensive sim-
ulations, we show that the worst congestion in the Internet in fact
scales poorly with the network size (
is the num-
ber of nodes), when shortest-path routing is used. We also show,
somewhat surprisingly, that policy-based routing
erbate the maximum congestion when compared to shortest-path
Our results show that it is crucial to identify ways to alleviate this
congestion to avoid some links from being perpetually congested.
To this end, we show that the congestion scaling properties of the
Internet graph can be improved dramatically by introducing mod-
erate amounts of redundancy in the graph in terms of parallel edges
between pairs of adjacent nodes.
Categories and Subject Descriptors
]: Network Architecture and Design
power-law distribution, congestion, shortest path routing, policy
The Internet grows in size every day. As time progresses, more
end-hosts are added to the edge of the network. Correspondingly,
to accommodate these new end-hosts, ISPs add more routers and
links. History has shown that the addition of these links maintains
the power law properties of the Internet topology . The addition
of new end-hosts places a greater load on the network as a whole.
Fortunately, the improvement of network technology, operates over
the same time period.
We expect the network links at the edge
and core of the network to improve by a similar performance factor
as the growth of traffic over time, since they both typically follow
similar Moore’s Law-like technology trends.
Unfortunately, due to the topology of the network and behavior
of Internet routing, the increase in load may be different on differ-
ent links. As a result, it may be necessary for the speed of some
hot-spot links in the network to improve much more quickly than
If this is true, then these parts of the network are likely
to eventually become bottlenecks and the network has poor scal-
ing properties. In such a situation, we would either need to adjust
the routing behavior, remove the power law nature of the topology