The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

Spare capacity allocation using shared backup path protection for dual link failures

This paper extends the spare capacity allocation (SCA) problem from single link failure [1] to dual link failures on mesh-like IP or WDM networks. The SCA problem pre-plans traffic flows with mutually disjoint one working and two backup paths using the shared backup path protection (SBPP) scheme. The aggregated spare provision matrix (SPM) is used to capture the spare capacity sharing for dual link failures. Comparing to a previous work by He and Somani [2], this method has better scalability and flexibility. The SCA problem is formulated in a non-linear integer programming model and partitioned into two sequential linear sub-models: one finds all primary backup paths first, and the other finds all secondary backup paths next. The results on five networks show that the network redundancy using dedicated 1+1+1 is in the range of 313-400%. It drops to 96-181% in 1:1:1 without loss of dual-link resiliency, but with the trade-off of using the complicated share capacity sharing among backup paths. The hybrid 1+1:1 provides intermediate redundancy ratio at 187-310% with a moderate complexity. We also compare the passive/active approaches which consider spare capacity sharing after/during the backup path routing process. The active sharing approaches always achieve lower redundancy values than the passive ones. These reduction percentages are about 12% for 1+1:1 and 25% for 1:1:1 respectively

Exploring the benefit of rerouting multi-period traffic to multi-site data centers

In cloud-like scenarios, demand is served at one of multiple possible data center (DC) destinations. Usually, the exact DC that is used can be freely chosen, which leads to an anycast routing problem. Furthermore, the demand volume is expected to change over time, e.g., following a diurnal pattern. Given that virtually all application domains today rely heavily on cloud-like services, it is important that the backbone networks connecting users to the DCs are resilient against failures. In this paper, we consider the problem of resiliently routing multi-period traffic: we need to find routes to both a primary DC and a backup DC (to be used in the case of failure of the primary one, or of the network connection to it), and also account for synchronization traffic between the primary and backup DCs. We formulate this as an optimization problem and adopt column generation, using a path formulation in two sub-problems: the (restricted) master problem selects "configurations" to use for each demand in each of the time epochs it lasts, while the pricing problem (PP) constructs a new "configuration" that can lead to lower overall costs (which we express as the number of network resources, i.e., bandwidth, required to serve the demand). Here, a "configuration" is defined by the network paths followed from the demand source to each of the two selected DCs, as well as that of the synchronization traffic in between the DCs. Our decomposition allows for PPs to be solved in parallel, for which we quantitatively explore the reduction in the time required to solve the overall routing problem. The key question that we address with our model is an exploration of the potential benefits of rerouting traffic from one time epoch to the next: we compare several (re) routing strategies, allowing traffic that spans multiple time periods to i) not be rerouted in different periods, ii) only change the backup DC and routes, or iii) freely change both primary and backup DC choices and the routes toward them