1. Resource Allocation in Network Virtualization Jie Wu Computer and Information Sciences Temple University

2. Road Map 1.Motivation and Applications 2.Tracing Back: Embedding 3.Basic Models 4.Extensions 1.Hose model 2.Virtual backbone 5.Looking Forward: Other Fields 6.Conclusions

3. 1. Motivation Network virtualization (Peterson, Shenker, and Turner’04)  A number of virtual networks (VNs) co-exist over the same physical network (PN) (substrate network)  VN: a group of nodes that are connected, with bandwidth reserved in the underlying network Implementation: RSVP and MPLS

4. Applications Coexistence Flexibility Manageability Scalability Isolation Heterogeneity ISP = SP + InP SP: Service Provider InP: Infrastructure Provider SDN  Programmable switches and routers than (using virtualization) can process packets for multiple isolated networks Virtualization  Data center networks (DCNs)

5. 2. Tracing Back: Embedding Embedding (E) of tasks (G) in processors (G’) Dilation of an edge of G is the length of the path in G’ onto which an edge of G is mapped. Dilation of E is the maximum edge dilation of G. Expansion of G is the ratio of the number of nodes in G to the number of nodes in G’. Congestion of E is the maximum number of paths containing an edge in G’, where every path represents an edge in G. Load of an E is the maximum number of tasks of G assigned to any processor of G’.

6. Embedding Examples

7. Virtualization Examples

8. 3. Basic Models Embed VNs in PN  Subject to CPU (node) and bandwidth (link) constraints General VN embedding  NP-hard (multiway separator problem) Special VN embedding (fixed nodes)  Multicommodity flow problem

9. Minimum Cost Multicommodity Flow Multicommodity flow  Capacity constraints, flow conservation, demand satisfaction Minimum cost  Sum of a(u, v) f(u, v) on edge (u, v) Integer flow: hard Fractional flows: solvable (Yu et al 06)  Path split  Path migration

10. Scheduling of Network Updates Dionysus (Jin et al’14)  Loop freedom  Congestion freedom Special constraint  A link must occur after an update that removes an existing flow Dynamic scheduling  Dependency graph (Resource allocation graphs)

11. Scheduling of Network Updates Schedulability Extension  Introducing intermediate steps

12. 4. Extensions: Hose Model (Duffield, Goyal, and Greenberg’99) Hose: aggregate traffic to and from endpoints in a VN Routing structures  Pipe  Ingree (Egree) tree  Shared tree  Mesh E.g. X (in 3), Y (out 2), and Z (out 2) using a Steiner tree

13. Extensions: Virtual Backbone Mapping VNs onto a shared substrate (Lu and Turner’06)  Backbone-star, a complete graph, a ring or a star Connected dominating set (CDS) (Wu and Li’99)  A subset (V) of nodes such that all other nodes not in V have at least one neighbor in V Resilience (Dai and Wu’05)  K-covered CDS: each node has k CDS nodes in its 1-hop neighborhood (including itself)  K-connected CDS: can tolerate k-1 faults and still connected

14. Challenges Different models  Static  Dynamic (long-term statistical guarantees) QoS  Different provisioning models Different measurements  Minimization of weighted sum of maximum values of node and link stress  Minimization of long term average value of the weighted sum of bandwidth and CPU revenue

15. QoS-based Slice Provisioning Safe vs. Unsafe  In terms of available network resource QoS-based slice provisioning  Slice reservation in unsafe areas Other extensions  K-hop CDS: A subset V such that each node not in V can reach a node in V within k hops  K-spanner: A spanning subgraph S in which every two vertices are at most k times as far apart in S than on G

16. 6. Looking Forward: Other Fields Virtualization in data center networks  Virtual machines (VMs) assignment in physical machines (PMs)  Subject to CPU and network bandwidth constraints Virtualization in DSN  Hadoop scheduling: map, shuffle, and reduce

17. Virtualization in SDNs Virtualization of controller in SDNs Multiple controllers  Disjointed  Overlapped (token-based access control) Controller placement

18. Hose Model in DCNs Elasticity (Li, Wu, and Blaisse’12)  The CPU / bandwidth utilization is the ratio of the used CPU / bandwidth among all PMs / links  The combined utilization is the maximal one of the CPU and bandwidth utilizations (bottleneck) Minimizing the combined utilization  To provide flexibilities for new VM requests (elasticity)

19. Hose Model in DCNs (cont’d) Iterative stack up Layer by layer recursive placement  CPU bottleneck: load balancing placement  Link bottleneck: load unbalancing placement

20. Conclusions Allocation  centralized vs. distributed Reconfiguration  migration and dynamic scheduling Survivability and Flexibility  resource overprovisioning and controlled slicing Other Applications  SDNs and DCNs

21. Future Challenges Performance guarantee Deterministic vs. statistic Resource discovery and allocation Cooperation and competition between IPs Heterogeneity and diversity of infrastructure