One More Weight is Enough: Toward the Optimal Traffic Engineering with OSPF

Traffic Engineering (TE) leverages information of network traffic to generate a routing scheme optimizing the traffic distribution so as to advance network performance. However, optimize the link weights for OSPF to the offered traffic is an known NP-hard problem. In this paper, motivated by the fairness concept of congestion control, we firstly propose a new generic objective function, where various interests of providers can be extracted with different parameter settings. And then, we model the optimal TE as the utility maximization of multi-commodity flows with the generic objective function and theoretically show that any given set of optimal routes corresponding to a particular objective function can be converted to shortest paths with respect to a set of positive link weights. This can be directly configured on OSPF-based protocols. On these bases, we employ the Network Entropy Maximization(NEM) framework and develop a new OSPF-based routing protocol, SPEF, to realize a flexible way to split traffic over shortest paths in a distributed fashion. Actually, comparing to OSPF, SPEF only needs one more weight for each link and provably achieves optimal TE. Numerical experiments have been done to compare SPEF with the current version of OSPF, showing the effectiveness of SPEF in terms of link utilization and network load distribution

IceCube and HAWC constraints on very-high-energy emission from the Fermi bubbles

The nature of the $\gamma$-ray emission from the \emph{Fermi} bubbles is unknown. Both hadronic and leptonic models have been formulated to explain the peculiar $\gamma$-ray signal observed by the Fermi-LAT between 0.1-500~GeV. If this emission continues above $\sim$30~TeV, hadronic models of the \emph{Fermi} bubbles would provide a significant contribution to the high-energy neutrino flux detected by the IceCube observatory. Even in models where leptonic $\gamma$-rays produce the \emph{Fermi} bubbles flux at GeV energies, a hadronic component may be observable at very high energies. The combination of IceCube and HAWC measurements have the ability to distinguish these scenarios through a comparison of the neutrino and $\gamma$-ray fluxes at a similar energy scale. We examine the most recent four-year dataset produced by the IceCube collaboration and find no evidence for neutrino emission originating from the \emph{Fermi} bubbles. In particular, we find that previously suggested excesses are consistent with the diffuse astrophysical background with a p-value of 0.22 (0.05 in an extreme scenario that all the IceCube events that overlap with the bubbles come from them). Moreover, we show that existing and upcoming HAWC observations provide independent constraints on any neutrino emission from the \emph{Fermi} bubbles, due to the close correlation between the $\gamma$-ray and neutrino fluxes in hadronic interactions. The combination of these results disfavors a significant contribution from the \emph{Fermi} bubbles to the IceCube neutrino flux.Comment: 9 pages, 4 figures, to appear in PR