Internet's Critical Path Horizon

TL;DR

This paper investigates how routing depth affects internet traffic efficiency, revealing a critical transition point where traffic flow becomes highly efficient due to the network's small-world structure.

Contribution

It identifies a critical path horizon in internet routing, showing how reaching the network diameter optimizes traffic flow based on realistic topological models.

Findings

Traffic exhibits a phase transition at the network diameter

Routing near the critical path horizon enhances efficiency

Internet likely operates close to this optimal transition point

Abstract

Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be minimized by choosing appropriate routing strategies. But what are the requirements of routing depth in order to optimize the traffic flow? In this paper we analyse the behavior of Internet traffic with a topologically realistic spatial structure as described in a previous study (S-H. Yook et al. ,Proc. Natl Acad. Sci. USA, {\bf 99} (2002) 13382). The model involves self-regulation of packet generation and different levels of routing depth. It is shown that it reproduces the relevant key, statistical features of Internet's traffic. Moreover, we also report the existence of a critical path horizon defining a transition from low-efficient traffic to highly efficient flow. This transition is actually a direct consequence of the web's small world architecture exploited by the routing algorithm. Once routing tables reach the network diameter, the traffic experiences a sudden transition from a low-efficient to a highly-efficient behavior. It is conjectured that routing policies might have spontaneously reached such a compromise in a distributed manner. Internet would thus be operating close to such critical path horizon.