2,071 research outputs found
Internet routing paths stability model and relation to forwarding paths
Analysis of real datasets to characterize the local stability properties of the Internet routing paths suggests that extending the route selection criteria to account for such property would not increase the routing path length. Nevertheless, even if selecting a more stable routing path could be considered as valuable from a routing perspective, it does not necessarily imply that the associated forwarding path would be more stable. Hence, if the dynamics of the Internet routing and forwarding system show different properties, then one can not straightforwardly derive the one from the other. If this assumption is verified, then the relationship between the stability of the forwarding path (followed by the traffic) and the corresponding routing path as selected by the path-vector routing algorithm requires further characterization. For this purpose, we locally relate, i.e., at the router level, the stability properties of routing path with the corresponding forwarding path. The proposed stability model and measurement results verify this assumption and show that, although the main cause of instability results from the forwarding plane, a second order effect relates forwarding and routing path instability events. This observation provides the first indication that differential stability can safely be taken into account as part of the route selection process
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
In this paper we study balanced growth path solutions of a Boltzmann mean
field game model proposed by Lucas et al [13] to model knowledge growth in an
economy. Agents can either increase their knowledge level by exchanging ideas
in learning events or by producing goods with the knowledge they already have.
The existence of balanced growth path solutions implies exponential growth of
the overall production in time. We proof existence of balanced growth path
solutions if the initial distribution of individuals with respect to their
knowledge level satisfies a Pareto-tail condition. Furthermore we give first
insights into the existence of such solutions if in addition to production and
knowledge exchange the knowledge level evolves by geometric Brownian motion
Routing Regardless of Network Stability
We examine the effectiveness of packet routing in this model for the broad
class next-hop preferences with filtering. Here each node v has a filtering
list D(v) consisting of nodes it does not want its packets to route through.
Acceptable paths (those that avoid nodes in the filtering list) are ranked
according to the next-hop, that is, the neighbour of v that the path begins
with. On the negative side, we present a strong inapproximability result. For
filtering lists of cardinality at most one, given a network in which an
equilibrium is guaranteed to exist, it is NP-hard to approximate the maximum
number of packets that can be routed to within a factor of O(n^{1-\epsilon}),
for any constant \epsilon >0. On the positive side, we give algorithms to show
that in two fundamental cases every packet will eventually route with
probability one. The first case is when each node's filtering list contains
only itself, that is, D(v)={v}. Moreover, with positive probability every
packet will be routed before the control plane reaches an equilibrium. The
second case is when all the filtering lists are empty, that is,
. Thus, with probability one packets will route even
when the nodes don't care if their packets cycle! Furthermore, with probability
one every packet will route even when the control plane has em no equilibrium
at all.Comment: ESA 201
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