2014 International Conference on Computing, Networking and Communications (ICNG)
Design of Reliable Virtual Infrastructure Using Local Protection l
Hao Dit, Vishal Anand2, Hongfang Yut, Lemin Lit, Dan Liaol3 and Gang Sunl3 Key Lab of Optical Fiber Sensing and Communications (Ministry of Education), University of Electronic Science and Technology of China, Chengdu, China 2Department of Computer Science, The College at Brockport, State University of New York, USA 3Institute of Electronic and Information Engineering in Dongguan, UESTC, China {dihao, yuhf, gangsun, liaodan }@uestc.edu.cn,
[email protected]
constraints of the underlying substrate network. The works in [4-8] study the VI mapping problem without considering substrate failures. More recently reliable or survivable VI mapping is studied [9-15], where backup computing and bandwidth resources are reserved for possible substrate failures.
Abstract-Network virtualization technology wherein multiple virtual
infrastructures
underlying
(VIs)
infrastructure
is
are the
supported key
enabler
on
the
same
of
the
cloud
computing paradigm. However, due to the resource sharing, even a single server failure in the substrate will affect all the VIs mapped on to it. Thus, backup resources should be reserved
In this paper, we study reliable VI mapping over multiple clusters of servers (i.e., data centers). The servers in a cluster are located in multiple racks, which are interconnected by switches and routers [16]. The clusters can be geographically distributed and interconnected over a wide area network, such as a federated computing and network system (FCNS) [17]. The cooperation among clusters can meet the ever-increasing demands of data-intensive applications, where the applications are geographically separated over cluster, i.e., VI nodes are mapped onto different clusters. Server failures in different racks of a cluster can be assumed to be independent [14,15], since servers in different racks can be connected to different switches and power supplies. In this study we assume that each physical server in a cluster has a known failure probability and each VI request has a desired reliability that has to be guaranteed. The reliability of a VI request is defined as the probability of all VI nodes remaining in operation [15]. This work is different from previous studies in [14,15] that study reliable VI mapping in a geographically limited single location or cluster that is not distributed over the wide-area network. Furthermore, in these works the reliability of a VI request is guaranteed while backup VI nodes are shared by all protected VI nodes. This sharing can reduce the required number of backup VI nodes, but the total backup bandwidth is very large. In the process of reducing the required computing backup resources by sharing backup VI nodes, a lot of backup VI links are needed to connect the neighbors of the protected VI nodes with each shared backup VI node to protect primary VI links. The cost of bandwidth is not a critical factor in [14,15] since the bandwidth cost is quite cheap in a cluster [18]. However, this sharing approach does not apply when reliable VI mapping is considered over geographically separate clusters since the bandwidth cost in a wide-area network is much higher than that in a single cluster. Hence, the bandwidth cost must be taken into consideration while mapping VI requests over multiple geographically separated clusters.
intelligently to provide cost-effective VI reliability. In this paper, we study the problem of reliable VI mapping over multiple clusters. We propose a local protection scheme to minimize the total reliable mapping cost, i.e., each VI node is protected in a local cluster so that the high backup bandwidth cost on the wide area network can be avoided. We present our local protection based reliable VI mapping algorithm (LP-RVIM) to minimize the mapping cost for VIs with protection. Through simulations we show that our LP-RVIM algorithm
can
efficiently
reduce
the
mapping
costs
when
compared to other VI mapping algorithms.
Keywords: virtual infrastructure reliability; multiple clusters; local protection
1.
INTRODUCTION
Network virtualization [1,2] allows multiple virtual infrastructures (VI) to coexist on a shared substrate network. Network virtualization enables the development and deployment of new and different technologies and networking paradigms on the same underlying substrate network. Thus, virtualization can help diversify the Internet and prevent its ossification. Furthermore, by using the cloud computing paradigm [3] network virtualization enables application providers to rapidly deploy applications and services on the substrate network without the responsibility and large costs associated with maintaining the substrate network. In such a network virtualization environment each application or service request can be modeled as a VI request, which consists of a set of virtual nodes connected by virtual links. The VI nodes and links of a VI request indicate the computing (e.g., CPU, memory) and bandwidth resource requirements of the application that is specified as the VI request. To deploy an application, each VI node is assigned to a physical machine in the form of virtual machine (VM), and each VI link is assigned to a substrate link/path. Thus, the VI mapping problem can be defined as: mapping the VI request onto the underlying substrate network while satisfying the resource requirements of the VI request subject to the resource
In this study, we develop the local protection based reliable VI mapping algorithm (LP-RVIM) that protects geographically distributed VI requests across multiple clusters while
This research was partially supported by the National Grand Fundamental Research 973 Program of China under Grant (No. 2013CB329103 ), Natural Science Foundation of China grant (No. 61271171, No. 61001084 ), Sichuan Youth Science and Technology Fund (No. 2012JQ0020 ), Program for New Century Excellent Talents in University (No.NCET-11-0058 ), the Fundamental Research Funds for the Central Universities (ZYGX2010J002, ZYGX2012J004, ZYGX20IOJ009 ), Guangdong Science and Technology Project (2012B090500003, 2012B091000163, 2012556031 ), and Science and Technology Research Projects of Chongqing Municipal Education Commission under Grant KJ120523.
978-1-4799-2358-8/14/$31.00 ©2014 IEEE
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2014 International Conference on Computing. Networking and Communications (ICNG)
guaranteeing the desired VI reliability. The algorithm aims to minimize the total computing and bandwidth cost. In order to avoid the above mentioned high backup bandwidth cost in the wide-area network LP-RVIM protects primary VI nodes in local clusters, i.e., a primary VI node and the corresponding backup VI nodes are assigned in different racks in a cluster.
a, band c connected by three VI links. The values in the rectangles close to the nodes are the required capacities of VI nodes, and the values close to the VI links are the required bandwidths. Each VI node is mapped onto a facility node. In particular, it is assigned to a physical server in a rack of a cluster, in the form of VM. All VI nodes in a request are mapped onto diffe rent facility nodes. Each VI link is mapped onto a substrate link/path or a set of substrate paths with path splitting which allows a VI link to be split over multiple substrate paths. Fig. l(a) shows the mapping of the VI request in Fig. l(b) on the substrate.
The rest of the paper is organized as follows. Section II describes reliable VI mapping over multiple clusters using local protection. Section III describes the LP-RVIM algorithm. Section IV presents the simulation results, and Section VI concludes the paper. II.
PROBLEM STATEMENT
C.
In this section we describe the problem of reliable VI mapping over multiple clusters and local protection. A.
Substrate Network
We model the substrate network as an undirected graph Gs (Vs, Es), where Vs and Es are the sets of clusters and substrate links connecting the clusters, respectively. Each cluster is represented by a facility node. In a cluster, there are multiple racks. The set of racks on the facility node ns is denoted by K(ns), and the total available capacity (e.g., CPU) of the rack kon the facility node nsE Vs is denoted by CsCns, k). The available bandwidth on the substrate link ls{i, j)EEs between two facility nodes i andj is represented by BsCts). The unit capacity costs of facility nodes and links are denoted by utAns) and UL(lS), respectively. r20,20,20,29Y
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(a) Substrate
(b) A VI request
Each physical server in a cluster (i.e., on a facility node) is assumed to be failed with a known probability. If a server is failed, all VMs (i.e., VI nodes) running on it are affected. We assume that the failure probabilities of servers in a cluster are the same, and the failure probabilities of servers in different racks of a cluster or in different clusters are independent. The probability of server failure on the facility node ns is denoted by denoted by pens). D.
Reliable
VI Mapping
In this work, reliability guarantee for VI requests is provided. VI reliability is the probability of all VI nodes of the VI request remaining in operation, and the failure probability of each primary VI nodes is equal to that of the server in which it is assigned. If the primary VI mapping cannot guarantee the desired VI reliability, backup VI nodes should be added to improve the reliability. If a backup VI node protects a primary VI node, the primary VI node can be replaced by the backup VI node after the failure of the server to which the primary VI node is assigned. The reserved computing capacity for the backup VI node is the same as that of the protected VI node. Note that backup VI nodes also may fail due to server failures. To isolate the failures of primary and backup VI nodes, they should be assigned in different racks. In addition, primary VI links should also be protected if their end nodes are migrated. Backup VI nodes and links are also to be mapped onto facility nodes and substrate paths. E.
Problem Statement
Given: a substrate network Gs, a VI request Gv.
Fig. 1. Example of primary VI mapping
Question: how to jointly allocate computing and bandwidth resources, comprising of primary and backup resources, such that the total cost of reliable VI mapping, i.e., the total cost of reserved computing and bandwidth resources is minimized?
Fig. l(a) shows a substrate network with 6 facility nodes A through F, each with 4 racks. The lines connecting the facility nodes represent the substrate links. The values in the bracket next to a node are the available computing capacities of racks on the facility node, and the values on the links are the available bandwidth capacities.
B.
Server Failures
If the backup VI node and the protected primary VI node are in different clusters, i.e., on different facility nodes, backup VI links (on the wide-area network) connecting the backup VI node and the neighbors of the protected VI node are necessary. And the total bandwidth capacity of the backup VI links is very large [15], leading to high bandwidth cost. As shown in Fig.2 (a) if the server failure probabilities on all facility nodes are l.0% and the desired VI reliability is 99.999%, two backup VI nodes (r I and r2) are needed for the VI request in Fig.1 (b) (as shown in [15]). In addition, a number of backup VI links have to be
VI Request
Similarly, we denote a VI request by an undirected graph Gv (Vv, Ev), where Vv and Ev are the sets of VI nodes and links respectively. The required computing capacity (CPU) of the VI node nvE Vv is represented by Cv(nv). Accordingly the required bandwidth on the VI link l v( i,j) EEv between two VI nodes i andj is represented by Bv(lv). The desired VI reliability is denoted by rv. Fig.1 (b) shows a VI request with 3 VI nodes =
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2014 International Conference on Computing. Networking and Communications (ICNG)
than rv 1\ 1/ l Vvi . The desired VI reliability can be guaranteed if all the VI nodes in the request are protected as described above.
added to protect primary VI links for node recovery/migration [14]. * 0:2] 3
):] 3
4
[!]
For example, the server failure probabilities on all facility nodes and the desired VI reliability of the VI request in Fig.l(b) are 1.0% and 99.999% (the same as the example in Fig. 2(a»). As shown in Fig. 2(b), if the VI nodes are protected in different racks on the local facility nodes, there should be two backup VI nodes for each VI node (as in (3)), i.e., one primary VI node and two backup VI nodes are needed in total for mapping each VI node in the request. Compared with sharing backup VI nodes across multiple clusters (as in Fig.2(a»), the link mapping cost of local protection is reduced at the price of increasing the node mapping cost, and the total reliable mapping cost can be reduced.
[NJ
�
5
c
(b) Local protection
(a) Shared backup VI
Fig. 2. Example of a reliable VI request
In this study, we propose that primary VI nodes are protected in local clusters, i.e., local protection, such that the backup bandwidth in the wide-area network can be avoided.
III.
The reliability of the VI node nvE Vv, denoted by r(nv) (0 � r(nv) � 1) is the probability of nv remaining in operation. If a primary VI node for nv is mapped onto the facility node ns, its failure probability is denoted as pens). Then, r(nv) is I-p(ns) with no protection. And the reliability of the VI request Gv is denoted by rel(Gv). Since the VI nodes in the request are to be mapped onto different facility nodes, the reliabilities of the VI nodes are independent. Thus, rel(Gv) is calculated as in (1).
rel(Gv)
=
IT r(nv)
THE LP-RVIM ALGORITHM
The problem of mapping VI requests even without reliability considerations is known to be NP-hard [4]. Thus we develop the local protection based reliable VI mapping algorithm (LP-RVIM) to efficiently minimize the reliable VI mapping cost with low time complexity. LP-RVIM II map Gv � (Vv, Ev)and backup VI nodes onto Gs � (VS, Es) I' A�0M�0 2 while (�I < IVv I) 3: select a VI node i E Vv- A, adjacent to the VI nodes in A Ilwhen A �0 ,a VI node in Vv is selected. 4: for all sE Vs- Mwith enough capacity for i II C,{i) �Cs(s , k), k �I, 2,... NB(s) + I, 5: COST(s) � (NB(s) + 1 ) C * ,.(i) u * ,�s)/1 NB(s)is calculated as in (3 ) 6: forh(i,j)EEv,jEA 7: find minimal cost path pC!;) for Iv using the Dijkstra's algorithm 8: if no available path then 9: COST(s) � += 10: else 11: COST(s) �COST(s) + I CB(/V)*UL(/s)
(1)
nvEVv
The reliability rel(Gv) should not be smaller than the desired VI reliability rv. To ensure that rv is guaranteed, r(nv) of each VI node nvE Vv is to be improved to rv 1\ 111 Vvi for local protection. While using local protection for nvE Vv, the primary VI node and m corresponding backup VI nodes (denoted by nB/, nB2 , . . . , nBm) are to be mapped onto the same facility node ns, and Cv(nv)= Cv(nBI)=Cv(nB2)=" . =Cv(nBm)' Note that primary and backup VI nodes are to be assigned in different racks in a cluster, thus the reliabilities of the primary VI nodes and the backup VI nodes are independent. The reliability r(nv) is improved as in (2) with the m backup VI nodes.
'sEp(fV)
12: end if 13: end for 14: end for 15: ns�arg min COST (s) SEVs-M
16: if no available nsor COST(s) �+=for all nodes in Vs- Mthen 17: return False 18: end if 19: map i and the backup VI nodes for it onto ns ,and map h(i,j)EEv,jEA on the paths as line II 20: put i into A, and put nsinto M 21: end while 22: return Truell Successful mapping
(2)
Fig. 3. The LP-RVIM algorithm
As in (2), the failure of at most m VI nodes among all the primary and backup VI nodes (m+ l VI nodes) on the facility node nv can be tolerated. For example, the VI node nv is mapped onto ns of which pens) is 99.0%. If there is one backup VI node protecting nv, the reliability r(nv) is improved to 99.99%.
The racks on each facility node ns is sorted in descending of the available capacity, i.e., Cs(ns, 1):::: Cs(ns, 2):::: . . :::: . Cs(ns, n) (n = IK(ns)!). Since the bandwidth cost in a cluster is quite cheap [18], the bandwidth cost in a cluster is not considered. The procedure of LP-RVIM is shown in Fig.3. In each step of LP-RVIM, a primary VI node, the backup VI nodes for it, and the associated VI links (line 6) are mapped so as to minimize the computing and bandwidth cost (lines 5, 11). To
If the VI node nvE Vv is mapped onto the facility node ns, the required number of backup VI nodes is denoted by NB(ns) (calculated as in (3)), which ensures that r(nv) is not smaller
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2014 International Conference on Computing. Networking and Communications (ICNG)
minimize the bandwidth cost the VI links are mapped onto minimal cost paths. Further, before mapping a primary or backup VI node onto a facility node we must make sure there are enough computing resources on that facility node.
B.
All the IVvi VI nodes in the VI request are iterated over, and at most IVvI-1 paths are found using Dijkstra's algorithm in each iteration. The time complexity of the Dijkstra's algorithm is O(lVi). Thus, the time complexity of the LP-RVIM algorithm is 0(1 vllVsl\ IV.
SIMULATION RESULTS
For each VI request, VI node pairs are randomly connected by a VI link with probability 0.5. The capacities of the VI nodes and links vary according to a uniform distribution from 10 to 50 units. The desired reliability is 99.999%. Fig. 5-7 show the average mapping cost of LP-RVIM and ViPXi with varying size of VI requests. The total node mapping cost is the total cost of the reserved computing resources for primary and backup VI nodes. The total link mapping cost is the total cost of the reserved bandwidth for primary and backup VI links. And the total mapping cost is the sum of node mapping cost and link mapping cost.
In this section, we present our simulation results. We compare the mapping costs of our algorithm LP-RVIM with i) MIP solved by CPLEX 10.0 (denoted as MIP) and ii) the reliable VI mapping algorithm with backup VI node sharing for all protected (primary) VI nodes [14] (denoted as ViPXi). In ViPXi, a primary VI node can be recovered by any one backup VI node, and the primary VI nodes and backup VI nodes are not mapped onto the same facility nodes. The associated backup VI links are added (as in Fig. 2(a».
Small Substrate Network
A.
Large Substrate Network
We use the 46 node, 76 link US network topology with average nodal degree of 3.3, the 27 node, 41 link England topology with average nodal degree of 3.0 and the 55 node, 103 link China topology with average nodal degree of 3.7 as substrate networks to test the working of our LP-RVIM algorithm. We assume that there are 8 racks on each facility node, and the computing capacity of each rack is 1000, and the bandwidth capacity of each substrate link is 8000. The unit costs of node and link capacity are both 1. The server failure probability on each facility node is 1.0%.
Since solving the MIP is intractable, LP-RVIM is compared with MIP on a small substrate network.
01) 2000 .5. 1800 go 1600 E 1400 .g 1200 g 1000 '0 800 :g 600 400 ¢: 200 .J-..:6� 8
We use a small substrate network with 10 nodes and 15 links, shown as Fig. 4. There are 4 racks on each facility node, and the computing capacity of each rack is 200 units. The bandwidth capacity of each substrate link is 400 units. The unit costs of node and link capacity are both 1, and the failure probability of each server on the facility nodes is 1.0%.
u "
�10 -1�2 � 14-� 16-
�-
Number of
VI
-
-
nodes in a VI request
Fig. 5. The total node mapping cost for US topology
01)16000 ·5.14000 go12000 ..:; 10000 ;.§ 8000 '0 6000 "§ 4000 � 2000 ¢: 0 �----��-----� 6 10 12 14 16
Fig. 4. The 10 node topology
For each VI request, VI node pairs are randomly connected by a VI link with the probability of 0.5. The capacities of the VI nodes and links vary according to a uniform distribution from 10 to 30. The desired VI reliability is assumed to be 99.99%. The number of VI nodes in a VI request varies from 2 to 6. Table 1 shows the average mapping cost from using the MIP optimization and the LP-RVIM algorithm. From the table it can be seen that the mapping cost of LP-RVIM is close to the optimum. In particular, the LP-RVIM algorithm can give time and cost efficient mapping results that are at most 8% more costly than the time consuming MIP optimization. Thus the LP-RVIM algorithm is cost efficient in providing local protection. TABLE
l.
Number of VI nodes in a VI request
Fig. 6. The total link mapping cost for US topology
16000
"§ 14000
�12000 '[10000
! 4000 :��� §
�
TOTAL MAPPING COSTS FOR A SMALL SUBSTRATE NETWORK
Size
MIP
LP-RVIM
Size
MIP
LP-RVIM
2
136.5
136.5
5
400
413.2
3
225.2
225.2
6
489.4
527.3
4
317
327.1
I-
2000 0
8
10
12
14
16
Number of VI nodes in a VI request Fig. 7. The total reliable mapping cost for US topology
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2014 International Conference on Computing, Networking and Communications (ICNG)
18000 816000 .?f14000 §t12000 � 10000 t:: 8000 "8 6000 B " 4000 t: 2000 t:
o
cost. The LP-RVIM algorithm aims to minimize the total reliable mapping cost. We compare the LP-RVIM algorithm with various other mapping algorithms in the simulations. Our simulation results show LP-RVIM can reduce the mapping cost by using local protection.
6
8
10
12
14
In our future work, we will study the resource sharing in each cluster between different VIs, in order to further reduce the reliable mapping cost.
16
Number of VI nodes in a VI request
REFERENCES
Fig. 8. The total reliable mapping cost for England topology
6
8
10
12
14
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16
Number of VI nodes in a VI request Fig. 9. The total reliable mapping cost for China topology
From Fig. 5-7, we observe the following.
The link mapping cost of sharing backup VI nodes is much higher than the node mapping cost. Fig.5 and Fig.6 show that the link mapping cost of ViPXi is much higher than the node mapping cost. This is because a large number of backup VI links are needed while primary VI nodes are protected by the shared backup VI nodes. As the size of VI requests increases, the link mapping cost is 6 to 20 times that of the node mapping cost.
[8]
The node mapping cost using local protection is higher than that from sharing backup VI nodes. As shown in Fig.5,
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[9]
the node mapping cost of LP-RVIM is higher than that of ViPXi. This is because local protection needs larger backup computing capacity than sharing backup VI nodes (as in Fig. 2).
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The link mapping cost using local protection is lower than that from sharing backup VI nodes. As shown in Fig.6,
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the link mapping cost of LP-RVIM is higher than that of ViPXi. This is because that backup VI links on the wide-area network are avoided using local protection (as in Fig. 2).
The total mapping cost using local protection is lower than that achieved from sharing backup VI nodes. Fig. 5
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and Fig. 6 show than the reduced link mapping cost of LP RVIM is much higher than the increased node mapping cost. As shown in Fig. 7-9, the total reliable mapping cost of LP RVIM is much lower than that of ViPXi for different topologies. This shows that local protection is more cost efficient than sharing backup VI nodes for reliable VI mapping over multiple clusters. V.
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CONCLUSION
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In this paper, we present the local protection based reliable VI mapping algorithm (LP-RVIM) for reliable VI mapping over multiple clusters, avoiding the high backup bandwidth
[18] hltps:l/aws.amazon.comlec2/pricing
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