# VDC Planner: Dynamic Migration-Aware Virtual Data Center Embedding for Clouds

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4 that indicates whether virtual node n can be embedded in physical node n. For example, VMs can only be embedded in physical machines rather than switches. Thus, if a virtual node n from VDC i is a virtual server, we have x i n n = n N s and x i n n = 1 n N m where N s and N m are the sets of physical switches and physical machines respectively (i.e., N = Ns N m ). Note that the placement constraint can also describe whether a switch can be embedded exclusively in physical switches or in physical servers or in both types of equipments. The following equation captures the placement constraint: x i n n x i n n i I,n n, n N (12) To ensure embedding of every virtual node n, we must have: x i n n = 1 i I,n N i (13) n N In our model, we also define y n as a boolean variable that indicates whether physical node n is active. A node is active if a virtual node of the a VDC runs on the physical node. This implies the following constraints must hold: y n x i n n i I,n N i, n N (14) y n 1 b l f i l l s n l i I, n N,l L i, l L (15) y n 1 b l f i l l d n l i I, n N,l L i (16) Finally, we also to consider the migration cost. In our formulation, we treat migration cost as a one-time embedding cost. The one-time embedding cost gn n i of a virtual node n of VDC i, which is currently embedded in node m N in substrate node n N is given by: mig(n, m, n) if n m gn n i = if n = m if n is currently not embedded where mig(n, m, n) denotes the cost of migrating virtual node n from substrate node m to substrate node n. Thus, when a virtual node n is already embedded but needs to be migrated from m to n, the one-time embedding cost is equal to the migration cost. This cost is equal to zero when n is already embedded in the physical node n (i.e., m = n). Its value is also zero when the node n is embedded for the first time. Let p n denote the cost in dollars of leaving the node n active, the goal of the migration-aware embedding can be stated by finding an embedding that achieves min ( y n p n + k K n γ n x i n ng n n), i (17) N i I n N i n N subject to equations (7) - (15). Here, γ n is a weight factor that captures the tradeoff between the migration cost and operational cost. Even though the migration-aware embedding problem is easier than the original online embedding problem, it is still difficult to solve as it still generalize a multidimensional bin packing problem. Figure 1: VDC Planner Architecture IV. VDC PLANNER In order to reduce the complexity of the online VDC embedding problem, we have designed VDC Planner, a framework that provides cost-effective VDC embedding in production data centers. Instead of solving the online problem directly, VDC Planner divides the overall problem into several usage scenarios, such that each scenario can be solved effectively and efficiently. We describe hereafter the overall architecture as well as our heuristic algorithms for each scenario. A. Architecture The architecture of VDC Planner is shown in Figure 1. It consists of the following components: VDC Scheduler: Upon receiving a VDC request from a SP, the VDC Scheduler is responsible for scheduling the VDC on the available physical machines. If there is no feasible embedding in data center, the request is kept in a scheduling queue until the SP decides to withdraw it. Different from existing VDC embedding algorithms, our VDC scheduler leverages migration to improve the revenue gain from embedding VDC requests. Resource Monitor: The Resource Monitor is in charge of monitoring the physical and virtual data centers. It also notifies the VDC scheduler if a failure of any physical or virtual node occurs in the physical data center. VDC Consolidation Module: The VDC Consolidation Module consolidates the VDCs over time in order to

5 reduce resource fragmentation (i.e., residual capacities in physical machines and network components that are not capable of scheduling any VDC components). VDC consolidation improves the overall resource utilization of data center and maximizes the number of machines that can be turned off. Our strategy for reducing the complexity of migration-aware VDC embedding is to divide the overall problem into several scenarios, such that each scenario can be easily addressed. Figure 2 illustrates the scenarios we consider for VDC Planner. They can be described as follows: Initial VDC Embedding: A tenant submits a new VDC request and the scheduler has to map it onto the physical data center. When the data center is heavily loaded, it may be impossible to directly embed the VDC due to lack of space. In this case, VM migration can adjust previous resource allocations in order to accommodate the new request. VDC Scaling: A tenant requests the topology of VDC to be dynamically scaled up and down. For example, if the tenant runs a web application in the data center and it experiences a demand spike, the tenant can submit a request to increase the resource allocation of his VDC. Migration can also be used to increase the chance of satisfying the embedding request, while minimizing the total bandwidth usage for satisfying the requests. Dynamic VDC Consolidation: As VDCs continuously enter and leave the system, the VDC embedding can become obsolete and suboptimal. We believe it is beneficial to re-optimize the embedding of VDCs at run-time in order to achieve better server and network consolidation. Overtime, this allows more physical servers and network components (e.g., switches and ports) to be turned off to save energy cost [9]. We have developed two heuristic algorithms to support the above scenarios. The first heuristic is designed for migrationaware VDC embedding. It leverages migration to handle VDC embedding as well as scaling up requests. The second heuristic is designed for dynamic VDC consolidation. It also utilizes migration to improve utilization and save energy. We describe each heuristic separately in the following subsections. B. Migration-Awaref VDC Embedding Heuristic We describe now our heuristic for migration-aware VDC embedding. Given a VDC embedding request (either an initial embedding or scaling up request), the goal is to find a feasible embedding of the request that incurs minimal migration cost. Our heuristic is depicted by Algorithm 1. Intuitively, upon receiving a VDC request i, the algorithm first sorts the physical machines based on whether they are active or inactive. It then sort virtual nodes in the request based on their size. Specifically, for each n N i, we define its size size i n as size i n = r R w r c ir n, (18) Figure 2: Scenarios for dynamic VDC embedding where w r is a weight factor for resource type r. The intuition is that size i n measures the difficulty of embedding node n. Accordingly, w r is selected based on the scarcity of resource type r R. After sorting all virtual nodes in N i according to size i n, our algorithm then tries to embed each node in the sorted order, based on whether it is connected to any embedded nodes. For each selected node n N i and each physical node n N, the algorithm computes the embedding cost cost i (n, n) as: cost i (n, n) = γ n (mig(n, m, n)+migother(n, n)) + d( n, n) b (n,n) (19) n N i :(n,n) L i where the last term represents the communication distance d( n, n) weighted by the bandwidth requirement b (n,n) between n and the other node n N i that is embedded on physical node n. If a particular n is not embedded, d( n, n) is set to zero. The intuition here is to minimize the communication distance between virtual nodes in order to reduce bandwidth consumption. In the long run, it also allows more physical network devices to be turned off. Finally, MigOther(n, n) is the cost of migrating away the VMs not belonging to G i on n in order to accommodate n on n. This is similar to the migration plans defined in Entropy. Formally, we denote by loc( n) the set of virtual nodes hosted on physical node n. Let mig(ñ, n) denote the minimum cost for migrating away ñ loc( n) to another node that has capacity to host ñ with minimum distance. Computing MigOther(n, n) becomes a problem of migrating away a set of node Ñ located on n such that there is enough capacity to accommodate n on n, while minimizing the total migration cost: min xñmig(ñ, n) xñ {,1} ñ loc( n) s. t. ñ loc( n) xñc jr ñ cir n r R This problem generalizes a minimum knapsack problem [4], which is NP-hard. We adopt a simple greedy algorithm to

6 Algorithm 1 Algorithm for embedding VDC request i 1: Sort N based on their states (active or inactive) 2: S N i 3: repeat 4: Let C S be the nodes that are connected to already embedded nodes 5: if C == then 6: Sort S according size i n defined by equation (18). 7: n first node in S 8: else 9: Sort C according size i n defined by equation (18). 1: n first node in C 11: end if 12: for n N in sorted order do 13: Compute embedding cost cost i (n, n) according to equation (19). If not feasible, set cost i (n, n) =. 14: end for 15: if cost i (n, n) = n N then 16: return VDC i is not embeddable 17: else 18: Embed n on the node n N with the lowest cost i (n, n). 19: S S\n 2: end if 21: until S == { } solve the problem. In particular, for a virtual node ñ loc( n) that belongs to VDC j, we compute a cost-to-size ratio rñ: rñ = mig(ñ, n) r R wr c jr ñ (2) Then, we sort loc( n) based on the values of rñ, and greedily migrate away rñ in the sorted order until there is sufficient capacity to accommodate n on n. The total migration cost of this solution produces M igother(n, n). If there is no feasible solution, we set MigOther(n, n) =. Lastly, for a selected node n, once the embedding cost cost i (n, n) is computed for every n N, we embed n on the node with the minimum value cost i (, n). The algorithm repeats until all nodes in N i are embedded, or cost i (n, n) =, which indicates VDC i is not embeddable. As for the running time of the algorithm, line 4 takes O(n) time to complete as it essentially partitions the physical machines into active and inactive machines. Line 6 and 9 take O( N i ) time to execute assuming the number of resource types is constant. Line 13 requires running the greedy algorithm for the minimum knapsack problem. Assume each physical node can host at most n max virtual nodes, the running time of the greedy minimum knapsack problem is O( N n max ). The remaining lines each takes O(1) time to run. Thus the total running time of the algorithm is O( N i N n max ). C. Dynamic VDC Consolidation Algorithm The previous heuristic leverages migration to maximize the number of number of VDC requests. However, as VDC Algorithm 2 Dynamic VDC Consolidation Algorithm 1: Let S represent the set of active machines 2: repeat 3: Sort S in increasing order of U n according to equation (21). 4: n next node in S 5: S loc( n) 6: Sort S according to size i n defined in equation (18). 7: for n S do 8: n next node in S. Let i denote the VDC to which n belongs 9: Run Algorithm 1 on VDC i over S\{ n}. 1: end for 11: cost( n) the total cost according to equation (17) 12: if cost( n) p n then 13: Migrate all virtual nodes according to Algorithm 1 14: Set n to inactive 15: end if 16: S S\{ n} 17: until U n C th requests can scale down and leave the system over time, a large number of physical nodes may become under-utilized. In production data centers, this typically happens at night time, where the number of VDC requests becomes low. In this case, we would like to dynamically consolidate VDCs such that a large number of physical machines can be turned off. We point out that VDC Planner merely tries to minimize the number of active machines used by VDCs. Deciding the number of machines to be turned on a particular time is a different problem that has been studied extensively (e.g., [16]). Thus existing techniques can be readily applied to control the number of active machines. Our migration-aware dynamic VDC consolidation algorithm is represented by Algorithm 2. Specifically, the algorithm first sort the physical nodes in increasing order of their utilizations. For each n N, we define the utilization U n as the weighted sum of the utilization of each type of resources: U n = r R i I n N i :n loc( n) w r c ir n c r n, (21) The intuition here is to select the nodes with lowest utilization as candidate for consolidation. Once physical nodes are sorted, for each physical node we sort virtual nodes n loc(n) according their size size i n. Let i denote the VDC n belongs to. We then run Algorithm 1 on VDC i with physical nodes excluding n. This will find an embedding where n is not used, (i.e., n has been migrated to different physical node). Once all the virtual node has been migrated, we compute the cost of the solution according to equation (17) and compare it to the energy saving, which is represented by p n. If the total saving is greater than the total cost of the solution, migration is performed and n becomes inactive. Otherwise, the algorithm proceeds to the next physical node n in the list until the

7 2 2 1 Intantaneous Income Gain (%) Time (hour) Number of VDCs Gain (%) Time (hour) CDF Baseline Migration-Based Queuing Delay (second) (a) Instantaneous income gains (b) Gain in acceptance ratio (c) Gain in terms of queuing delay Figure 3: Migration-aware embedding vs. baseline algorithm cluster is sufficiently consolidated (i.e., all the machines in the cluster have reached a threshold C th. Using the algorithm, the VDC consolidation component is able to make dynamic consolidation decisions that considers migration cost. Finally we analyze the running time of the algorithm. Line 3 takes O( N ) time to complete assuming the number of resource types is constant. Line 6 takes O(n max log(n max )) time to complete. Line 9 runs algorithm 1, which takes O( N i N n max ) time to complete. Line 13 takes O(n max ) time to finish. The remaining lines each takes O(1) time to complete. Thus the total running time of the algorithm is O( N 2 log N + N n 2 maxn max ) assuming the maximum of virtual nodes per VDC is N max. Lastly, we need to answer the question that when should VDC consolidation be performed at run time. A naïve solution is to perform VDC consolidation periodically. However, we have found that periodic consolidation may not be beneficial when request arrival rate is high. In this case, even if we can reduce the number of active machines for a particular time instance, the high arrival rate of new VDC requests will force more machines to be active, rendering the consolidations effort ineffective. Motivated by this observation, we perform VDC consolidation only when arrival rate is low over a period of time (i.e., below a threshold λ th requests per second over T minutes). Even though more sophisticated techniques such as predicting the future arrival rate allows for more accurate consolidation decisions, we have found this simple policy achieves a good balance between migration cost and energy cost at run time in our experiments. V. EXPERIMENTS We have implemented VDC Planner and evaluated its performance through simulation studies. Specifically, we have simulated a data center with 4 physical machines organized in 4 racks. The topology used in our experiment is the clos topology described in VL2 [7], which provides full bisection bandwidth in the data center network. To implement this topology, we have also added 4 top-of-rack switches, 4 aggregation switches as well as 4 core switches in our topology. In our experiments, VDC requests arrive following a Poisson distribution with an average rate of.1 requests per second during night time and.2 requests per second during day time. This reflects the time-of-the-day effect where resource demand is higher during day time. For convenience, we set γ n = 1, and λ th =.15. In practice, the value of λ th can be obtained through experience. The number of VMs per VDC is generated randomly between 1 and 2. In our simulations, each physical machine has 4 CPU cores, 8GB of memory, 1GB of disk space, and contains a 1Gbps network adapter. The size of each VM for CPU, memory and disk are generated randomly between 4 cores, 2GB of RAM and 1GB of disk space, respectively. The bandwidth requirement between any two VMs that belong to the same VDC is generated randomly between and 1Mbps. Furthermore, the lifetime of VDCs follows an exponential distribution with an average of 3 hours. In our implementation, a VDC can wait in the queue for a maximum duration of 1 hour after which it is automatically withdrawn. In our first experiment, we evaluated the revenue gain achieved when using the migration-aware embedding algorithm compared to a baseline algorithm similar to Second- Net that does not consider VM migration and energy-aware VDC consolidation. Let R m and R n denote the infrastructure provider s income over a period of time using the migrationaware algorithm and the baseline algorithm, respectively. The revenue gain is defined as G m/n = 1 R m R n 1. (22) The same formula is used to compute the gain in terms of request acceptance ratio (i. e. successfully embedded VDC requests divided by the total number of received VDC requests), and the number of inactive machines. Figure 3a and Figure 3b show the instantaneous revenue gain and the increase in acceptance ratio, respectively. Every point in each figure represents the gain over a 1 minute interval. It can be seen that from midnight till the morning, the migrationaware algorithm is providing the same revenue as the baseline approach. However, during the day time when resource demand is high, the migration-aware embedding algorithm can achieve an increase up to 17% in revenue gain over the baseline approach. This is expected since during idle periods (e. g., night time), it is easy to embed VDC requests given the

8 Number of Machines reduced (%) Time (hour) (a) Migration-aware algorithm Number of Machines reduced (%) Time (hour) (b) Migration-aware embedding + consolidation Figure 4: Change in number of machines ample free capacities in the data center. However, when the cluster is busy, it becomes difficult to embed VDC requests directly. In this case, migration-aware approach is able to leverage migration to find more embeddable VDCs. This result is also confirmed by Figure 3b which shows an improvement of 1% in terms of VDC requests acceptance ratio during busy periods. We also compare the queuing delay experienced by the VDC requests. Figure 3c compares the cumulative distribution function (CDF) of scheduling delays achieved by each of the studied algorithms. It is clear that the migration aware approach significantly reduces the average scheduling delay. In particular, our algorithm can reduce the scheduling delay by up to 25%. On the other hand, even though the migration-aware embedding algorithm is able to improve InP s revenue, at the same time it also uses more physical machines to host embedded VDCs than the baseline algorithm, as shown in Figure 4a. Therefore, we also implemented the dynamic VDC consolidation algorithm as described in Section IV-C to reduce the number of physical machines used. Compared to Figure 4a, Figure 4a shows that percentage reduction in number of machines can reach 14% when the consolidation algorithm is applied along with the migration-aware embedding. The benefit is apparent especially at night (8pm to midnight) when VDCs are leaving the system. We also notice that, by reducing the number of active machines, consolidation also improves the income as defined in Eq. 5. Combining consolidation with the migration-aware embedding technique, we found on average VDC Planner achieves a 15% increase in net income compared to baseline algorithms that resembles the existing algorithms proposed in the literature (e.g., SecondNet). VI. CONCLUSIONS Driven by the need to support network performance isolation and QoS guarantee in public clouds, recently a number of research proposals have proposed to allocate resources to SPs in the form of virtual data centers that include both guaranteed server resources and network resources. A key challenge that needs to be addressed in the context is dynamic VDC embedding problem, which aims at optimally allocating both servers resources and data center networks to multiple VDCs to optimize total revenue, while minimizing the total energy consumption in the data center. However, despite recent studies on this problem, none of the existing solutions have considered the problem in a dynamic and online setting, where migrations can be utilized to flexibly and dynamically adjust the allocation of physical resources. In this paper, we have described VDC Planner, a migrationaware dynamic virtual data center embedding framework that aims at achieving high revenue while minimizing the total energy cost over-time. Our framework supports various scenarios, including VDC embedding, VDC scaling as well as dynamic VDC consolidation. Through simulation experiments, we show our proposed approach is able to achieve higher net income as well as lower scheduling delay compared to existing solutions in the literature. REFERENCES [1] Hitesh Ballani, Paolo Costa, Thomas Karagiannis, and Ant Rowstron. Towards predictable datacenter networks. in Proceedings of ACM SIGCOMM, August 211. [2] MF. Bari, R. Boutaba, R. Esteves, L. Granvilley, M. Podlesny, M. Rabbani, Q. Zhang, and M. F. Zhani. Data center network virtualization: A survey. IEEE Communications Surveys and Tutorials, Aug [3] T. Benson, A. Akella, A. Shaikh, and S. Sahu. Cloudnaas: a cloud networking platform for enterprise applications. In Proceedings of the 2nd ACM Symposium on Cloud Computing, page 8. ACM, 211. [4] T. Carnes and D. Shmoys. Primal-dual schema for capacitated covering problems. Int. Prog. and Combinatorial Optimization, 28. [5] Mosharaf Chowdhury, Muntasir Raihan Rahman, and Raouf Boutaba. Vineyard: virtual network embedding algorithms with coordinated node and link mapping. IEEE/ACM Trans. Netw., 2(1):26 219, 212. [6] Nabeel Farooq Butt, Mosharaf Chowdhury, and Raouf Boutaba. Topology-awareness and reoptimization mechanism for virtual network embedding. In IFIP International Conference on Networking, 21. [7] A. Greenberg, J.R. Hamilton, N. Jain, S. Kandula, C. Kim, P. Lahiri, D.A. Maltz, P. Patel, and S. Sengupta. VL2: A Scalable and Flexible Data Center Network. 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