Distributed optimization of multi-commodity routing in Software-Defined Networks Mathieu Leconte, Ioannis Steiakogiannakis, Georgios Paschos France Research Center, Huawei Technologies Co. Ltd PGMO Days 2016

Optimization in multi-controller SDN Inter-controller communication protocols (e.g., ONOS, OpenDayLight-SDNi) “Public” memory Private memory Higher data rates & densification will carry the increased traffic at the access Backhaul links will get congested (these include links from base stations to small cells) Meeting throughput & latency targets of 5G requires mitigating such congestion Is edge-caching suitable to solve these issues? SDN moving towards partially distributed control logic more distributed Fast, optimal solutions What can we achieve? Can we retain optimality & fast operation? Optimal is too slow, operate in very sub-optimal regimes

Min-cost multi-commodity routing Edge formulation O(KV) constraints O(KE) variables Path formulation O(K+E) constraints many variables, but O(K+E) active variables Minimize cost Serve demands Capacity constraints Flow conservation Large problem size V  1000 nodes, E  10000 edges, K  100000 demands Sparse methods are required

Prior art & contributions Fully centralized methods interior point method  non-sparse column generation (modified-cost shortest path) + simplex  sparse, fast in practice Fully distributed methods backpressure-like  too slow Our contributions Fast partially distributed methods preserving sparsity

Separating the problem into multiple domains Minimize sum of intra-domain costs Serve demands in source domain Capacity constraints inside domains Flow conservation at domain borders Dantzig-Wolfe decomposition Intra-domain problems + coupling constraints at domain borders

Handling flow agreement at domain borders Penalize flow imbalance with Lagrange multipliers Modified costs for intra-domain MCF Subgradient method to update multipliers: Flow imbalance  increase of multiplier Exchange of border flow information between neighboring domains Still decomposes into column generation + simplex O(K+E(D)) active variables in each domain  sparse method in each domain

A sparse partially distributed solution Inter-domain: subgradient update of Lagrange multipliers Lagrange multipliers for border edges Intra-domain: column generation + simplex for modified-cost MCF Column generation + simplex inside domains Fast and sparse Subgradient between neighboring domains Quite slow

Faster inter-domain updates Replace subgradient with higher-order method Non-smooth problem  no guarantee of speed-improvement Augmented Lagrangian Inter-cluster updates: Subgradient  parallel proximal ADMM Intra-cluster modified MCF: linear simplex  quadratic simplex More complex problem inside domains We can still use column generation  still sparse original cost 1st-order flow-imbalance penalty 2nd-order flow-imbalance penalty

Fast & sparse partially distributed solution Inter-domain: parallel proximal ADMM update of Lagrange multipliers Lagrange multipliers + neighboring flow + previous flow for border edges Intra-domain: column generation + quadratic simplex for modified-cost quadratic MCF Much improved speed Slightly less sparse

To sum-up Min-cost MCF = one basic problem for traffic engineering Combination of centralized & distributed techniques In practice, constrained paths (delay, node-inclusion, protections, optical,…) SDN opens up new optimization challenges “More optimal” solutions within reasonable time due to more centralization Many traditional problems need to be revisited, many new problems as well