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Virtual Network Embedding Survey

Explore the challenges of mapping virtual networks onto physical resources, including node and link capacities, with an overview of embedding complexity, solutions, and optimization strategies in network virtualization.

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Virtual Network Embedding Survey

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  1. To map virtual networks onto physical network resources. Lilin Zhang Virtual Network Embedding Survey

  2. A starter example • Substrate Network node capacity is limited (indicated as integers in square box); • SN link capacity is infinite; • VNR (Virtual Network Request) arrives along the time, each VNR has VN node demands indicated; • After each VNR's arrival/departure, the remaining SN node capacity is updated (at t1, t2, t3, and t4); • After the departure of VNR1 and the arrival of VNR3, remapping (at time t4) is performed to make room for VNR3.

  3. Complexity of VNE • VNE, with constraints on virtual nodes and virtual links: NP-hard. • Reduced to the NP-hard multi-way separator problem. • D.G.Andersen. "Theoretical Approaches to Node Assignment" (2002).CMU Computer Science Department.Paper #86. http://repository.cmu.edu/compsci/86/ • VLinkE, with all virtual nodes already mapped, to optimally allocate a set of virtual links to single substrate paths: NP-hard. • Becomes an offline load balancing routing problem where the source and destination are the ingress and egress nodes of each Vlink and each flow has a unit demand. • Reduced to the NP-hard unsplittable flow problem (i.e., integer flow assignment in multi-source/sink flow network). • J.Kleinberg. “Approximation algorithms for disjoint paths problems”. Ph.D. Dissertation, MIT, 1996. • S.Kolliopoulos and C.Stein. “Improved approximation algorithms for unsplittable flow problems”. In Foundations of Computer Science, 1997.

  4. Complexity of VNE • VNE, with constraints on virtual nodes and virtual links: NP-hard. • Reduced to the NP-hard multi-way separator problem. • D.G.Andersen. "Theoretical Approaches to Node Assignment" (2002).CMU Computer Science Department.Paper #86. http://repository.cmu.edu/compsci/86/ • VLinkE, with all virtual nodes already mapped, to optimally allocate a set of virtual links to single substrate paths: NP-hard. • Becomes an offline load balancing routing problem where the source and destination are the ingress and egress nodes of each Vlink and each flow has a unit demand. • Reduced to the NP-hard unsplittable flow problem. • J.Kleinberg. “Approximation algorithms for disjoint paths problems”. Ph.D. Dissertation, MIT, 1996. • S.Kolliopoulos and C.Stein. “Improved approximation algorithms for unsplittable flow problems”. In Foundations of Computer Science, 1997.

  5. Naive solution to VNE • A naive way to perform VN assignment is to treat Vnode mapping and Vlink mapping as two independent sub-problems and solve them sequentially. • Cons: the optimality of Vnode mapping and optimality of Vlink mapping cannot be achieved at the same time via the naive solution. • e.g., two ways of embedding 6 pairs of connected Vnodes onto three SN nodes: Optimal node embedding – i.e., SN nodes are least loaded, but both SN links are provisioned with 4 Vlinks, more than the 3Vlinks-scenario on the left. Optimal link embedding – i.e., SN links are least loaded, but the centre SN node is over-provisioned with 6 Vnodes.

  6. Y.Zhu, M.Ammar. “Algorithms for Assigning Substrate Network Resources to Virtual Network Components”. INFOCOM 2006

  7. INFOCOM 06 • To fight against the cons of naive solution, this study considers both SN node and SN link loads while embedding new VNR. • Assume infinite capacity of substrate nodes and links to avoid VNR admission control, i.e., the SN network keeps accepting arriving VNR's, and the research focuses on how to embed them optimally. • Y.Zhu, M.Ammar. “Algorithms for Assigning Substrate Network Resources to Virtual Network Components”. INFOCOM 2006. • Introduce a new metric to measure to performance of embedding – node/link stress ratio • Substrate node stress at time t, , is the # of virtual nodes that are assigned to the substrate node • Substrate link stress at time t, , is the # of virtual links whose substrate path passes through the substrate link Global graph metric: quantify the node stress Global graph metric: quantify the link stress

  8. INFOCOM 06 Cont'1 • The VN assignment for the i-th VN is formulated as: • is the time instance immediately after the i-th VNR arrival. are weights to tradeoff the optimization prone to node-efficiency or to link-efficiency, determined by specific application scenarios. • Two solutions: • VNA-I (V1 basic VN assignment taking the entire VN as one entity) it follows the sequential process: (1) select a cluster of SN nodes as embedding candidates (2) perform a one-to-one mapping for Vnodes (3) run shortest-distance path algorithm to determine Vlinks • In Step (1), the 1st SN node is identified through: • In Step (1), all subsequent SN node are identified through: • In Step (2), the one-to-one mapping is done in the way that Vnode of higher degree are mapped to SN node of higher NR. • This solution aims at minimizing the maximum node stress (node-opt) A multiplication of SN node stress and its direct link stress Count the distance to all previously assigned Vnodes, i.e., assume “fully-connected VN” ,regardless the actual VN topology

  9. INFOCOM 06 Cont'2 • VNA-I (V2 - subVN subdivide the entire VN into a set of star sub-VN's) • For unconstrained subVN, perform VNA-1(V1) • For centre-constrained subVN, perform VNA-1(V1) and select subsequent SN nodes using • For center-unconstrained subVN, perform VNA-1(V1) • VNA-I (V3 - link-opt to optimize link stress) • VNA-I (V4 - adaptive) • Iterate between node-opt solution and link-opt solution based on the network condition • Upon the arrival of i-th VNR, if , do link-opt; otherwise, do node-opt (1 )Divide and Conquer (2) didn’t assume “full graph”, but use the actual VN topology to compute A summation of SN node's direct link stress A ratio of the sum of SN node distance to all previously assigned Vnode

  10. Infocom 06 Cont'3 • VNA-II (with reconfiguration) • Propose a selective reconfiguration scheme: reconfig critical VNs, in order to reduce the maximum link/node stress. • Example of four VNs: the 2-node diamond VN is non-critical; all other VNs are critical (the maximum link stress is 3). • (a) the embedding before reconfig; (b) the embedding if one critical VN is reconfiged; (c) the embedding if the non-critical VN is reconfiged (max link stress remains the same)

  11. INFOCOM 06 Cont‘4 • VNA-II (with reconfiguration) • Global marking: identify critical SN nodes and links; all VNs that are using these nodes or links are marked for reconfig • Per VN reconfig • use VNA-I (V1 or V2 or V3) Didn’t prove if the “per VN” algorithm will converge

  12. INFOCOM 06 Cont‘5 • Simulation setting (no-blocking VNE) • SN network – 100 nodes, 316 links, random topology generated by GT-ITM [1996] • VN networks (offline setting, i.e., the VNR arrival is known beforehand) • arrive in Poisson process at rate , • lifetime exponentially distributed with average time units, • Size is uniformly distributed from 2~10, • Random topology, link probability = 0.5 • Experiment #1: Effects of VNR loads • changing the VN arrival rate, compare the VN assignments of VNA-I (V1), VNA-I (subVN), VNA-I (adaptive), least-load (always select least stressed SN node for Vnode and connect Vnodes using shortest distance path algorithm)

  13. INFOCOM 06 Cont‘6 • Experiment #2: VN assignment without reconfiguration - Benefits of subVN scheme. • changing the link probability in VN topology, and compare the Max-link-stress of VNA-I (V1-basic) vs. VNA-I (V2 - subVN) • The SubVN algorithm over-performs the VNA-I (V1 – basic) • The difference decreases as the VN topology becomes denser • Reason is that VNA-I (V1 -basic) scheme assumes the VN is a fully connected graph; yet VNA-I (V2 – subVN) has no such assumption, uses the actual VN topology and splits it into a set of star-subgraphs.

  14. INFOCOM 06 Cont‘7 • Experiment #3: VN assignment without reconfiguration - the effectiveness of adaptive optimization strategy • change the potion use of link-opt and node-opt in VNA-I (V4-adaptive) • The VN assignment algorithms with different values of form distinctive clusters Ratio of maximum node stress Ratio of maximum link stress

  15. INFOCOM 06 Cont‘8 • Experiment #4: VN assignment with reconfiguration - varying the reconfig threshold The reconfig threshold controls the ratio of VNs that are allowed to do reconfig: = 0 means only the VNs using the highest stressed substrate nodes/links are allowed to reconfigure; = 1 means all VNs are allowed to reconfigure. In (c), the increase in VN reconfig ratio between threshold [0.4,0.5] indicates that if allows 50% of VN to reconfig, the actual reconfig ratio jumps from 40% to 90% dramatically. The phenomenon shows that 50% of VNs locate on most lightly loaded SN links (not necessarily on lightly loaded SN nodes). It explains the strange bump in (b) between threshold [0.4,0.5]. Since the actual reconfig ratio is 90% when =0.5, a majority of VNs are reconfigured hence the max link stress drops for the segment where threshold is [0.4,0.5]

  16. INFOCOM 06 Cont‘9 • Experiment #5: VN assignment with reconfiguration – the effects of reconfiguration period • From (a) and (b), the performance of VNA-II adaptive scheme is in the middle for maximum node/link stress. • From (c), the less frequent reconfigure events, the less cost (nearly exponentially decreasing with the reconfig period)

  17. INFOCOM 06 Cont‘10 • Experiment #6: VN assignment on different network settings – effect of different SN networks • The denser of the SN network, the better performance all kinds of VNA schemes can achieve. • The absolute difference between different VNA schemes diminishes as the SN network becomes denser.

  18. INFOCOM 06 Cont‘11 • Experiment #7: VN assignment on different network settings – effects of the size of VN

  19. INFOCOM 06 Cont‘11 • Experiment #8: VN assignment on different network settings - multidomain SN topology • Setting: 124 nodes, 510 links, 4-node transit domain, each transit node attached by three 10-node stub domain. • VNA schemes performs better than least-load scheme: the lowest stress may be scattered in different domains, least-load algorithm will select them for a single VNR, leading to highly loaded transit-stub links 10-node stub domain 10-node stub domain 10-node stub domain

  20. In all previous papers before 2013, there is a common assumption that the SN network is fault-free, i.e., the underlying InP network remains operational at all times. The fault-free assumption is removed in the following paper, which considers a variant of VNE in the scenario where the SN network is error-prone (more specifically, the assumption is that the underlying SN network has single link failure in a certain distribution?). M.R.Rahman, R.Boutaba, “SVNE: Survivable Virtual network Embedding algorithms for network virtualization”. IEEE Transactions Network and service management, 2013. The fault-free assumption is removed in the following paper, which considers a variant of VNE in the scenario where the SN network is error-prone (more specifically, the assumption is that the underlying SN network has single link failure in a certain distribution?). The protection against single SN link failure is to dedicate a certain percentage of bandwidth on each SN link for backup.

  21. IEEE Transactions 2013 • VNE in the presence of arbitrary substrate node and link failures. • M.R.Rahman, R.Boutaba, “SVNE: Survivable Virtual network Embedding algorithms for network virtualization”. IEEE Network and service management, 2013. • Deal with single substrate link failure, not multiple link failures due to its low probability of occurrence. • Do not deal with node failure. Because any node failure leads to the adjacent link failures, to address the link failure is thus a priority. • Related work on VNE • Only consider the off-line version of VNE • Or assuming infinite capacity of SN nodes and links to avoid admission control • All in common assume the SN network to be operational at all times • Related work on survivability in IP-over-WDM • The design of IP-over-WDM is an offline problem • The objective is to ensure all nodes remain connected in presence of failure. • Unique in SVNE • The objective is to ensure all Vlinks are intact • Maximize the long term revenue for InP, and minimize the long term penalty of InP due to single SN link failure.

  22. IEEE Transactions 2013 Cont'1 • Solution to online SVNE (two phases of decoupled node embedding and link embedding) • For each incoming VNR, node embedding heuristics is greedy • After Vnode embedded, the Vlink embedding is done via path selection • SVNE model and formulation • SN network: a weighted graph , each SN node has cpu and location attributes: and . Each SN link has two endpoints and bandwidth attribute: . • VN: a weighted graph , each Vnode has cpu and location requirements: and . Each Vlink has bandwidth and delay requirements: and . • Resource consumption: finite SN node and link resources. Do not accept a VNR unless there are adequate resource to serve it (i.e., a naive admission control scheme - progressively consuming all SN network). The capacity of residual SN node is defined: . The capacity of residual SN link is defined: . • Both capacity values are updated (1) after successfully embedding a VNR; (2) each departure of a VNR; (3) each SN link failure occurrence; and (4) after its repair. • For each SN link of bandwidth , percentage of the bandwidth is for primary VNE, percentage of the bandwidth is reserved for backup use. In total

  23. IEEE Transactions 2013 Cont'2 • SVNE model and formulation • Revenue function where is the lifetime of the VNR . C1 and C2 are weights factors in calculating the revenue from bandwidth and cpu usage. • Penalty function is the Vlink set affected by the failure of MTTR( ) is the mean time to repair for failed SN link . db(v) is the difference between v's requested bandwidth and the actual bandwidth supplied by InP. • Objective function • are the VNR sequence. are the sequence of failed SN links. • Restoration model • Local link restoration: for each SN path , each SN link in the path has a backup detour • End-to-end path restoration: survivable flow from SN node u to v consists of a primary flow of value f and a link-disjoint secondary flow of the same value f.

  24. IEEE Transactions 2013 Cont'3 • Heuristics for SVNE • Proactive policy (provision redundant resource, i.e., for each Vlink, provision a primary flow and a secondary flow) • Objective: min subject to Variables: Primary capacity constraint is link-path indicator variable, =1 if = 0 otherwise. secondary capacity constraint is the primary flow value on the simple path p for the virtual link v. Primary bandwidth constraint secondary bandwidth constraint Link-disjoint constraint ?

  25. IEEE Transactions 2013 Cont'4 • Heuristics for SVNE • Proactive policy – using two sequential linear programming Objective #1 min Subject to Objective #2 min Subject to Minimize the SN usage for primary flows Primary capacity constraint Primary bandwidth constraint Minimize the SN usage for secondary flows, and the costs due to violating Vlink bandwidth requirement is a boolean variable, keeps track of the SN links that have been used for primary flow. It is used to keep primary flow and secondary flow link-disjoint, i.e., = 1 means SN link s has been used for a primary flow. The algorithm fist assigns bandwidth for primary flows and marks the SN links used. Marking a SN link is equivalent to deleting it while assigning bandwidth for backup flows. The algorithm is online, since it finds an embedding for each new VNR. The algorithm is expected to perform worse than an optimal offline algorithm.

  26. IEEE Transactions 2013 Cont'5 • Heuristics for SVNE • Hybrid policy • Before VNR arrival, InP computes backup detour for each SN link; • Upon VNR arrival, InP first embeds the Vnodes using existing heuristics, then embeds the Vlinks using multi-commodity flow algorithm; Objective min subject to • When a SN link fails, InP reroutes all affected flows along their backup detours. Objective min subject to is the amount of bandwidth allocated on path p for Vlink v. Primary capacity constraint Primary bandwidth constraint is the amount of rerouted bandwidth on detour. Secondary capacity constraint Recovery constraint

  27. IEEE Transactions 2013 Cont'6 • Heuristics for node embedding • Greedy node embedding solve , where is a product of residual bandwidth and cpu capacity of x and the sum of its adjacent link residual bandwidth. Map Vnode to x and iterate. • D-ViNE algorithm (a node embedding algorithm based on mixed integer programming, not elaborated in the paper, referred to their 2009 Infocom paper) • Heuristics for path selection • K-shortest path algorithm (extension of Dijkstra's): static path selection - set the path for each Vlink and the path remains constant during the lifetime of the VNR. • Performance Evaluation • Simulation environment • Random-graph network topology, Poisson process for VNR arrival, Poisson process for single SN link failure. • GNU linear programming toolkit (glpk) to solve all LP on Ubuntu 12.04 on Windows 7; Intel i5, 8GB RAM. • SN network 50 nodes (p=0.5); cpu and bandwidth are limited (uniformly distributed between 50~100) • Varying the parameter in the simulation. • VNR network size is a uniform r.v. between 2~20, (p=0.5 fixed); bandwidth requirement is a uniform r.v. between 0~50; penalty for a Vlink v is a uniform r.v. Between 2~15.

  28. IEEE Transactions 2013 Cont'7 • Performance Evaluation • Business profit. BLIND algorithm – recomputes a new link embedding for each VN affected by the SN link failure. Proactive algorithm – provision redundant resource, for each Vlink provision primary flow and secondary flow. Hybrid algorithm – first compute backup detour for each SN link, embed the VNR as the decoupled node/link mapping, reroute to backup detour upon single SN link failure. is the percentage of the SN link reserved for primary flow allocation. is the ratio of SN link failure arrival rate to VNR arrival rate, i.e.,

  29. IEEE Transactions 2013 Cont'8 • Performance Evaluation • Acceptance ratio. The acceptance ratio is calculated by the # of VNR admitted and the # of failed VNs, e.g. An accepted Vlink is embedded on a SN link who later fails, the VN is considered as a failed request.

  30. IEEE Transactions 2013 Cont'9 • Performance Evaluation • Responsiveness to failures • Performance Evaluation • Bandwidth efficiency Proactive algorithm – pre-reserves additional BW for each Vlink during embedding phase. Hybrid algorithm – does not pre-reserve BW during embedding, but pre-selects detour for each SN link and only allocates the BW when a SN link failure occurs.

  31. IEEE Transactions 2013 Cont'10 • Performance Evaluation • Specific VN topology The relative performance is unchanged for two specific VN topologies – Hub-and-spoke and Mesh network: Hybrid algorithm > Proactive algorithm > Blind algorithm.

  32. IEEE Transactions 2013 Cont'11 • Performance Evaluation • Effect of k (the number of shortest paths to be computed) The highest profit is achieved by hybrid policy with DviNE node embedding algorithm. Insight is that the performance metrics against k are affected by the selected node embedding scheme

  33. Last paper (Infocom 2006) addresses an online VNE problem, i.e., the VNRs arrive along the time. It proposed a new metric – SN link/node stress, and optimizes a linear combination of the link stress and node stress in the objective. Two kinds of algorithms are proposed: VNE without reconfiguration and VNE with reconfiguration. The latter algorithm needs to have the global knowledge of the SN network topology and embedding loads. I.Houidi, W.Louati, and D.Zeghlache, “A distributed virtual network mapping algorithm”, IEEE ICC, 2008. The contribution of the next paper is to decentralize the VNE embedding among SN nodes. In order to exchange local information, a VN Mapping protocol is therefore proposed for the efficient message-passing between the agent-based SN nodes.

  34. ICC08 • One objective: to efficiently assign VNs to specific SN nodes and links in distributed heuristic manner, while minimizing the network cost. • Two assumptions • a. the SN network resource (e.g., CPU, bandwidth) is unlimited to accept and handle all VN requests • b. all VN requests are defined and known in advance (i.e., offline problem)

  35. ICC08 Cont' 1 the star-decomposition is the same as what proposed in Infocom 2006 • “preprocessing” the VN topology • Decompose the VN into star-based subgraphs : • Find the highest capacity Vnode as the center of the star • All of its direct neighbours in the VN are the leaf • Remove this star (center and leaf) from the VN and repeat to find the next star. • VN mapping algorithm • For each VN star-based decomposition, find the SN node with maximum available resource and map it to the star center • Identify the set of SN nodes to be the leaf nodes of the star decomposition, based on Shortest-Path algorithm and the capacity of the SN node • Remove the SN nodes and path assigned to the above star • Move on to the next VN star decomposition, and find the next SN node as its star center. • VN mapping protocol • The VN mapping is distributed: each SN node designated as the star center will be responsible for selecting and mapping its own star decomposition. All the star center SN nodes communicate/interact with each other to complete the VN mapping. • Protocol messages: MSG (exchange node capacity among SN nodes), START, NOTIFY, NEXT, STOP

  36. ICC08 Cont' 2 • Distributed VN mapping algorithm • Decompose the VN topology into star like clusters • Start with one star cluster at a time, • Each SN node keeps an up-to-date sorted list of all available SN nodes and their current capacity • find the SN node of maximum capacity (root) to be mapped to the center of the star cluster • Use shortest-path algorithm to identify the SN nodes connected to the root, of maximum capacity • The Vnode of higher capacity demand is mapped to the SN node of higher available capacity • Upon finishing the mapping of 1st star cluster, the root SN node sends NEXT msg to all SN nodes • A next root node is to be found, i.e., repeat from (3)

  37. ICC08 Cont' 3 • Performance Evaluation platform • GRID5000 A real SN network emulator (different topologies available) • Java agent development framework (implement the distributed algorithm) • Agents are deployed on GRID5000 to emulate the SN nodes and to handle the VM mapping algorithm. • Performance evaluation • The overhead incurred by the node capacity sorting operation The time overhead caused by sorting the node capacity increases exponentially when the SN topology has over 80 nodes The # of messages exchanged caused by sorting the node capacity increases exponentially with the size of the SN network

  38. ICC08 Cont' 4 • The overhead incurred by the use of shortest-path algorithm • Blue – Full mesh SN topology; Red – partial mesh SN topology The absolute difference in time overhead between full mesh and partial mesh increases as SN size grows The absolute difference in # of msgs exchanged between full mesh and partial mesh increases as SN size grows

  39. ICC08 Cont' 5 • The overhead incurred by the use of distributed VN mapping algorithm • A single VN request: consists of 25 Vnodes in two topologies: full mesh and partial mesh • Calibre with centralized VN mapping algorithm In the centralized VN mapping, the central coordinator needs to gather parameters (of SN nodes and links) globally. In the distributed VN mapping, less overhead is due to that each SN node is already aware of the parameters of its direct neighbour SN nodes and links

  40. ICC08 Cont' 6 • The time overhead incurred by the use of distributed VN mapping algorithm • On the left: 10 VN requests • each consists of 25 Vnodes • On the right: re-assign a VN in face of a SN node/link failure

  41. Summarize so far: [Infocom06] proposes centralized VN mapping schemes: with/without VN reconfiguration [ICC08] proposes to decentralize VN mapping in that each SN node once chosen to be mapped to the center of the VN star decomposition, is responsible to choose a set of connected SN nodes to be mapped as leafs of that star decomposition. M.Chowdhury, F.Samuel, R.Boutaba, “Polyvine” policy-based virtual network embedding across multiple domains”, ACM SIGCOMM 2010. Both papers in previous concern the VN mapping in a single domain. The next two papers extend it to propose VN mapping across multiple domains. The common approach of the two is to decouple the inter-domain mapping and intra-domain mapping. Both use the idea of partitioning the end-to-end VNR into several sub-graphs. The difference is the approaching of graph partitioning. [SIGCOMM 2010] implements a simple “starting with seed InPs and passing onto next hop InPs” way for each InP to determine on their own to embed the largest connected component from the received VN topology. [CFI ACM 2011] makes use of the min k-cut algorithm, Gomory-Hu Trees, to partition the end-to-end VNR into multiple subgraphs.

  42. SIGCOMM10 • The intra-domain algorithm of VNE is extended to multiple administrative domains. • M.Chowdhury, F.Samuel, R.Boutaba, “Polyvine” policy-based virtual network embedding across multiple domains”, ACM SIGCOMM 2010. • Difference between intra-domain VNE and inter-domain VNE • For intra-domain VNE, typical assumption is the full knowledge of SN topology; typical objective is SN node/link attributes. • For inter-domain VNE, usually no global topological knowledge of all participant SN; two typical objects are : • How to partition the end-to-end VN request into K sub-graphs to be embedded onto K SN networks; • How to embed to inter-connection between K sub-graphs onto the inter-domain SN paths • SN network model Control Network

  43. SIGCOMM10 Cont'1 • VN model and Embedding assignment : Meta-VN request topology One possible InP-level embedding InP#2 has no embedded Vnode, but is still in the embedding for the inter-domain connection purpose VN Network K-th sub-graph is the set of VN links crossing domain boundaries

  44. SIGCOMM10 Cont'2 • Decentralized embedding • The end-to-end VNR is sent to multiple InPs to begin with • The embedding process starts from the initial InP receivers and propagates to other InPs. • Embedding protocol • Six messages: EMBED(Req_id, InPSet), SUCCESS(Req_id, M, InPSet), FAILURE(Req_id, errorDesc), CONNECT(Req_id, , InPSet), RELAY(Req_id, G, InPSet, InP#), ACK(Req_id) • Sample embedding process (right plot) • How InP works • Local embedding: use intra-domain VNE algorithm to decide which part of an end-to-end VNR to embed locally and embed it (i.e., this is the authors' answer to the question #1 of inter-domain VNE – how to partition the end-to-end VN request into K sub-graphs) • Forwarding: forward the rest of the VNR to other InPs • Back-propagation: upon completely embedding or no available InPs to send forwarding to, return SUCCESS or FAILURE message • How to choose the InPs to forward the remaining VNR?

  45. SIGCOMM10 Cont'3 • Location aware forwarding • informed forwarding based on (a) hierarchical address of the SN nodes (2) prices announced by the other InPs (3) reputation score of the InPs • Hierarchical addressing: • Vnode – NA.CA.* • SN node – NA.CA.ON.Toronto • Location awareness protocol • Every InP informs its neighbor InPs of the address of its SN nodes along with prices. • Each InP maintains a Location DB • In steady state, each InP knows about all the InPs

  46. SIGCOMM10 Cont'4 SP: Service provider, the one who generates the VN requests. • Numerical evaluation setting • 100 InPs, each consists of 80~100 SN nodes, 540~600 SN links on average (random graph topology) • Each SN node has CPU units uniformly ranging from 1 ~ 100 CPU units • Each SN link has 100 bandwidth units • InP performs a naive greedy node and link mapping to embed the largest possible connected component from the VNR received • Afterwards, InP randomly chooses a Vnode from the remaining VNR to forward • InP chooses the top 3 InPs from its Location DB to forward. • VNR drop if reaching 12-hop max among InP propagation • In the evaluation setting, only the embedding process is implemented and evaluated • the price propagation or the selection based on lowest-price are not implemented • The performance of the mapping of inter-connection between K VNR sub-graphs onto the inter-domain SN paths is not considered (i.e., didn't answer to the question #2 of inter-domain VNE - How to embed to inter-connection between K sub-graphs onto the inter-domain SN paths ) • Experiment #1 – node mapping and hop count • VNR has 50 Vnodes and 200 Vlinks (random graph topology) • The first InP that received the complete VNR embeds the largest # of Vnodes • The # of embedded Vnodes decreases exponentially as the remaining VNR forwarded along • Reason is uncertain: (a) the random graph topology (b) simple greedy algorithm

  47. SIGCOMM10 Cont‘5 • Experiment #2 – node mapping and VNR size • Observe the # of Vnodes being embedded by the immediate InP contacted by the SP • Varying the size of VNR from 10~70 Vnodes • Each VNR is a generated sparse random graph, with n Vnodes and 4*n Vlinks • Observation: the # of Vnodes mapping by the first-hop InP grows linearly with the VNR size. Experiment #3 – InPs involved in a successful mapping Same setting as Experiment #2 Observation: the # of InPs that have Vnodes embedded onto their SN nodes grows linearly with the size of VNR.

  48. The last paper, SIGCOMM2010, introduces the two challenges of inter-domain VNE: (1) how to partition the end-to-end VNR into K sub-graphs for K InPs to embed (2) how to efficiently use the inter-domain SN links to embed the inter-connection Vlinks of the K sub-graphs. Yet in its experiments, the authors evaluated numerical relations using random graph topology and simple greedy embedding algorithm within each InP. Further, their answer to the challenge #1 is delegated to intra-domain VNE, i.e., the intra-domain VNE decides which part of the end-to-end VNR to embed locally. And there was no explicit answer to the challenge #2 in the paper. Y.Xin, I.Baldine, A.mandal, C.Heermann, J. Chase, and A. Yumerefendi. “Embedding virtual topologies in networked clouds”, International conference on Future Internet Technologies (CFI) ACM , 2011. The next paper also consider the VNE across distributed sites – embedding over multiple cloud sites. Unlike the paper SIGCOMM2010, this paper explicitly answered the question – how to partition the end-to-end VNR, via using a minimum k-cut algorithm. However this is a 4-page short paper, absent of formulation details.

  49. CFI ACM 11 • The intra-domain algorithm of VNE is extended to geo-distributed cloud computing environments. • Y.Xin, I.Baldine, A.mandal, C.Heermann, J. Chase, and A. Yumerefendi. “Embedding virtual topologies in networked clouds”, International conference on Future Internet Technologies, 2011. • The paper distinguish between Cloud providers and Transit network providers (provides inter-cloud virtual network services, such as on-demand QoS-guaranteed paths) • Contributions: • ORCA, a broker-based architecture to federate multiple resource providers (including cloud sites) • [NEuca] An extension to Eucalyptus cloud middleware. It embeds the VN within a cloud site by using the VLAN technology • The software and its deployment testbed provide a platform to experiments with different approaches to VNE problem in a multi-domain environment with brokers. [NEuca] “GENI-ORCA Control Framework,” http://geni-orca.renci.org

  50. CFI ACM 11 Cont'1 • Inter-cloud VNE model • Physical infrastructure: clouds interconnected by transit providers • VN request: with BW requirement on each link. Each Vnode is provisioned as a VM • Embedding solution: . Each cloud site provisions VMs and Vlinks within its cloud domain. represents the Vlinks between two VN partitions mapped in two clouds and . • Cost function: a linear weighted sum of (1) cost of embedding Vnodes (2) cost of embedding Vlinks within a cloud site (3) cost of embedding Vlinks over transit networks across cloud sites: Where the individual costs are: • Upon VNR arrival, 1st question is whether to assign the VN to a single cloud site or partition it across multiple clouds. is the available VM resources in cloud site is the available network resources in cloud site The proof was based on the cost function of embedding Vnodes alone.

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