Resource Allocation in Network Virtualization Jie Wu Computer

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

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

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

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

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

Embedding Examples

Virtualization Examples

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

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

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

Scheduling of Network Updates l Schedulability l Extension ¡ Introducing intermediate steps

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

Extensions: Virtual Backbone l Mapping VNs onto a shared substrate (Lu and Turner’ 06) ¡ Backbone-star, a complete graph, a ring or a star l 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 l 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

Challenges l 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 l Different models ¡Static ¡Dynamic (long-term statistical guarantees) l Qo. S ¡ Different provisioning models

Qo. S-based Slice Provisioning l Safe vs. Unsafe ¡ In terms of available network resource l Qo. S-based slice provisioning ¡ Slice reservation in unsafe areas l 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

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

Virtualization in SDNs l Virtualization of controller in SDNs l Multiple controllers ¡Disjointed ¡Overlapped (token-based access control) l Controller placement

Hose Model in DCNs l 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) l Minimizing the combined utilization ¡To provide flexibilities for new VM requests (elasticity)

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

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

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