Resolve the Virtual Network Embedding Problem: A Column Generation Approach

1. Resolve the Virtual Network Embedding Problem: A Column Generation Approach Qian Hu, Yang Wang, Xiaojun Cao Department of Computer Science Georgia State University Atlanta, GA, 30303

2. What is Network Virtualization? • ISP Decoupling: Infrastructure Providers (InPs) and Service Providers (SPs) • InPs: manage the physical infrastructure • SPs: operate virtual network, offer E2E user services • A programmable infrastructure • InPs resources efficient utilization • Hardware, energy, recovery • SPs can deploy services fast • No high initial investments on the infrastructures • Flexible deployment • Disruptive technologies deployed by InPs will not affect supported services

3. Virtual Network Embedding Problem Given the virtual network (VN) request GV = (NV , LV ), and substrate network GS = (NS , LS ), Objective: Map the VN with least cost Constraints: Node Computing: One virtual node mapped onto one substrate node No two virtual nodes share the same substrate node; Link/path bandwidth capacity One virtual link mapped to substrate links or path(s) Others such as location, protection

4. Bridging SP and InP: Virtual Network Embedding Virtual Network: the logical network of SP 4 8 5 8 6 3 Substrate Network: the physical network of InP 20 2 20 20 5 26 30 20 40 30 20

5. Literature Work Virtual Network Embedding (VNE): NP-Complete Optimal solutions from link-based ILP [Chowdhury etc, INFOCOM’09] Extensive computational time Not practical Heuristic approaches Relaxation of link-based ILP [Chowdhury etc, INFOCOM ’09] Others[e.g., Lischka etc, ACM VISA’09] Not optimal Not sure how far away from optimal

6. Major Contributions of Our Work Propose path-based ILP model for VNE problem Propose a column generation process Integrated with a branch-and-bound framework Resolve the VNE problem optimally in practice Obtain sub-optimal results with guaranteed performance (with branch-and-bound)

7. Network Embedding: Network Flow Model Virtual Network 1 1 Virtual Network Embedding => Multi-commodity Flow problem a a 2 2 3 3 c b c b c 5 4 4 5 1 Substrate Network 2 3 a 4 5 auxiliary edge: connect a virtual node to eligible substrate nodes b

8. Path-based ILP Formulation Amount of Flow on Path p Exponential number of paths c Link is not overloaded 1 2 3 Xa,2 Each commodity is satisfied Xa,4 5 a Node Assignment 4 Traffic only on the link to the “mapped” node Primal b

9. Path-based Formulation-Primal and Dual :ye :λk :yi :yI exponential # path choices => exponential # of constraints :ΠI,i Primal Dual Fact 1: OPT(P) = OPT(D-P)

10. Column Generation to try path selection PO: set of optimal paths P’: path space we look at P: potential exponential path space P’ Target: OPT(P’) =OPT(P) PO P P’ PO Q1: Is P’ optimal? Q2: Which path to add to P’ ? P

11. Q1: P’ optimal? & Q2: which path to add to P’ Exponential # of Constraints (D-P) Solution with some Constraints (D-P’) OPT(D-P’) P’ Q3: Check Exp. # of constraints? Feasible for other constraints in P? Q1 PO No Add the constraint’s corresponding path to P’: Q2 P Yes OPT(D-P’) =OPT(D-P) OPT(P’) = OPT(P) OPT(D-P’) = OPT(P’) >= OPT(P) = OPT(D-P)

12. Check all the Constraints: Shortest Path Problem Weight for auxiliary edge WI,i=ΠI,i c Wc-1 Weight for substrate links We = ye+ce Wc-3 1 W1-2 W1-3 Wa-2 Wa-2+W1-2+Wc-1≥λk W1-4 2 3 a W3-4 W2-4 W3-5 Wa-4 W4-5 4 5 Rational: if the shortest path of each commodity satisfies, all the paths satisfy. Wb-5 Wb-4 b

13. Overall Framework Theorem 1: The process to identify a set of optimal paths is Polynomial. Obtain a subset P’ Solve the D-P’ Solution feasible for D-P NO Increase P’ YES Solution for D-P Found

14. Performance Evaluation Simulation Setting Virtual network node number [2-10] Substrate network node number [10-50] Average connectivity 50% Virtual network link/node capacity [1-20] Substrate network link/node capacity [1-50] Compared Approaches Link-based ILP (from prior work Infocom’09) Path-based ILP ILP P-VNE Relaxed Path-based ILP ILP P-VNE’ k=1 ILP P-VNE’ k=2 ILP P-VNE’ k=3

15. Optimality Comparison Both P-VNE and Link-based ILP achieve optimality Increasing k improves the performance for relaxed P-VNE P-VNE has considerable less computational time than Link-based ILP Increasing k also increases time Over small k may leads to infeasible solution Resource Consumption (ce=1) QoS (ce=latency of e)

16. Summary What is Network Virtualization? Virtual Network Embedding and Network Flow Model Path-based VNE Model Column Generation Approach

17. Questions? Resolve the Virtual Network Embedding Problem: A Column Generation Approach Qian Hu, Yang Wang, Xiaojun Cao Thank you!