OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty

Abstract

We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and a routing is sought with a fair performance for any feasible traffic matrix in the polyhedron. The problem accurately reflects real world networks, where demands can only be estimated, and models one of the main traffic forwarding technologies, Open Shortest Path First (OSPF) routing with equal load sharing. This is an NP-hard problem as it generalizes the problem with a fixed demand matrix, which is also NP-hard.We prove that the optimal oblivious routing under polyhedral traffic uncertainty on a non-OSPF network can be obtained in polynomial time through Linear Programming. Then we consider the OSPF routing with equal load sharing under polyhedral traffic uncertainty, and present a compact mixed-integer linear programming formulation with flow variables. We propose an alternative formulation and a branchand-price algorithm. Finally, we report and discuss test results for several network instances.

Multi-objective routing and wavelength converter allocation under uncertain traffic

“…So, at each portion of the solution space, distinct routes were calculated. To face the same problem, Altin et al [53] proposed a polyhedral model with a scale factor that generates trade-off solutions between robust solution and other solutions with a more conservative robustness level. This approach was based on studying the robustness price [52,54,55].…”

Robust optimisation for risk-averse multi-period inventory decision with partial demand distribution information

“…More recently, Pishvaee, Rabbani, and Torabi (2011) propose a close-loop supply chain network for demand belonging to a box uncertainty set. Gallego, Ryan, and Simchi-Levi (2001), Sungur, Ordónez, and Dessouky (2008), Zhu andFukushima (2009), Altın, Belotti, andPınar (2010), and Baron, Milner, and Naseraldin (2011) have also employed these uncertain sets to denote demand or financial risk uncertainties.…”

Oblivious OSPF routing with weight optimization under polyhedral demand uncertainty

“…Consequently, Fortz and Thorup [22, 24] launch the idea of managing link weights so as to make an efficient use of network resources and improve performance. Since then, determining the link metric and hence the routing paths so as to optimize some design criteria like link‐utilization or routing cost has been the focus of the most recent research on OSPF routing [2, 25, 29, 30, 32, 38].…”

“…However, the additional benefits of these methods are not for free since excessive modifications might ruin the consistency and dependability of network operations. At this point, off‐line methods based on optimizing over a set of traffic matrices have started to win adherents [2, 5, 6, 9, 29].…”

“…Mulyana and Killat [29] deal with the weight setting problem for OSPF routing, where traffic uncertainty is described by a set of outbound constraints. Finally, Alt \documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*} \mathcal{i}\end{align*}\end{document}n et al [2] study polyhedral demand uncertainty with OSPF routing under weight management and provide a compact MIP formulation and a Branch‐and‐Price algorithm.…”