Globecom 2014 Workshop - Cloud Computing Systems, Networks, and Applications
Survivable Mapping for Multicast Virtual Network under Single Regional Failure Dan Liao1,2, Gang Sun1,2, Vishal Anand3, Kexiang Xiao1 1
Key Lab of Optical Fiber Sensing and Communications (Ministry of Education), University of Electronic Science and Technology of China, Chengdu, China 2 Institute of Electronic and Information Engineering in Dongguan, UESTC, China 3 Department of Computer Science, the College at Brockport, State University of New York, USA E-mail:
[email protected] [email protected]
provisioning strategy that intelligently uses the resources of the substrate network is significant to both users and infrastructure providers (InPs). How to efficiently map/embed a VN request onto the substrate network is always a challenging problem in network virtualization. Most existing researches on the problem of VN provisioning/mapping only consider the case of unicast service oriented VN requests [5-8], and accordingly aim at designing efficient provisioning strategies for such VN requests. However, in some practical use cases, the applications or services must be abstracted as multicast service-oriented virtual network requests. Multicast virtual networks are expected to support many real-time or interactive applications with diverse performance requirements, such as video-conferencing, distributed database replication, and online games. Thus, a multicast virtual network (MVN) has a tree like topology with a source node at the root and destination nodes at the leaves of the tree. In real world applications such as real-time applications multicast service-oriented virtual network requests have delay constraints on the MVN links. Therefore, in this work, we consider the transmission delay constraint of each MVN link while mapping it onto the substrate route which consists of substrate links. Furthermore, due to the shared nature of network virtualization, even small failures in the substrate network will interrupt a large number of MVN requests hosted on it. Therefore, how to guarantee the operation of a mapped MVN request while the substrate network failing is a challenging problem in MVN provisioning. In this work we study the problem of how to implement the mapping for MVN requests with considerations of the survivability, i.e., the survivable MVN mapping (SMVNM) problem. Since the optimal VN embedding problem is NP-hard [3], we propose heuristic algorithms to solve the mapping problem in a reasonable amount of time as well as achieving better results. We evaluate the performance of our heuristics by conducting extensive simulation experiments under various scenarios.
Abstract: Recent research on virtualization has focused on developing various solutions for the problem of mapping a virtual network (VN) onto the substrate network. However, these solutions and associated algorithms are only efficient for constructing unicast service-oriented virtual networks, and generally not applicable to the cases of multicast service-oriented virtual networks (MVNs). Furthermore, there has been very limited work on the survivable MVN mapping (SMVNM) problem, which is important while considering multicast traffic. In this research, we discuss SMVNM problem while considering regional failures of the substrate network and propose an efficient algorithm for solving this problem. We validate and evaluate our framework and algorithms by conducting extensive simulations on realistic network under various scenarios, and by comparing with existing approaches. The simulation results show that our approach outperforms existing solutions.
Key words: multicast virtual network; regional failures; failure-aware; mapping; cloud-based datacenters
I. INTRODUCTION The traditional Internet structure faces many challenges due to the explosive increase and diversification in user demands and Internet services. Network virtualization is a new paradigm that can introduce flexibility in the Internet and prevent its ossification. Network virtualization technology allows multiple heterogeneous virtual networks (VNs) to share the resources of the same underlying substrate network [1]. Cloud computing services and applications are commoditized and delivered in a manner similar to traditional utilities such as water, electricity, gas, and telephony. Users can access applications or services and infrastructure resources provisioned by cloud-based data centers by using thin clients without having to know the actual location and characteristics of the resource, or how they are delivered. Infrastructure as a service (IaaS), software as a service (SaaS) and platform as a service (PaaS) are the three main categories of cloud computing service models. IaaS is a service provisioning model in which an infrastructure provider (InP) typically owns and leases substrate network resources to support various operations using a usage-based pricing model. The service provider (SP) rents resources from one or many InPs to serve the end users. Network virtualization plays an important role in cloud computing and serve as a key enabler for cloud computing [2]. A network virtualization environment (NVE) [3] [4] consists of shared resource (i.e., substrate network with resource capacity) and virtual network (VN) requests which are abstracted from divers applications or services. Since multiple VN requests could be hosted by the same substrate network and for sharing the resources of the same underlying substrate network, an efficient cloud resource
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II. PROBLEM STATEMENT AˊMulticast VN (MVN) Request A XVHU¶Vservice or application request with quality of service (QoS) demands (i.e., link bandwidth, delay, delay variation, node resource, and etc.) submitted to a cloud-based datacenter can be abstracted as a multicast virtual network request. We model the multicast virtual network request as an undirected weighted graph GV ( NV , EV , CN , CL , CD , CDV ) , where NV {v1, v2 ..., vt } denotes nodes of the MVN, where t is the number of MVN nodes and EV
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authors assume a set of possible regional failures R is given. As mentioned ach regional failure r R will simultaneously destroy one or more substrate nodes and links, denoted by G(r ) ( Nr , Er ) , where Nr N S and Er E S . If we allocate
indicates the set of MVN links. CN represents the node resource constraint and CL {x1, x2 .....x|E |} represents link bandwidth V
constraint, respectively. We also use xev
to denote the
bandwidth required by virtual link ev EV . We use CD and CDV to denote the constraints on the maximum delay and delay variation [9] of substrate paths to host the virtual links. For each multicast virtual node nv NV , we assume H (nv ) is the amount of node resources requested from a specific MVN node. Figure 1 (a) gives an example of MVN request. In this example, a is the root node and b and c are leaf nodes of the MVN request. The numbers in the rectangles next to the MVN nodes represent the resources demands of nodes and the numbers next to the MVN links represent the requested link bandwidth resources/delay/delay variation .
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D. MVN Mapping Under Single Regional Failure The procedure of mapping a MVN request GV onto a substrate network GS with survivability against any single regional failure r in this research includes four steps: initial MVN request mapping, backup substrate nodes, backup substrate paths, MVN request migration. First we map the MVN request without consideration of any possible regional failure. We need to allocate a separate substrate node and required computing resources for each MVN node of the MVN request, as well as find paths and reserve required bandwidth resource to transmit data among the MVN nodes. Assume that the number of MVN nodes is N1, and then exactly N1 substrate nodes are allocated in this initial request mapping. In this work, in order to map a MVN request onto a substrate network with survivability against any single regional failure, we assume that if a substrate node ns1 initially assigned for a MVN node v is within the failed region, we need at least another backup substrate node ns2 outside the failed region to remap this MVN node v. Note that the choice of the backup substrate node(s) depends on the failure scenario, and the selected backup substrate node may be within another failure region. To ensure that such a substrate node can be found in the event of a regional failure, we allocate it before a failure actually happens. Since a regional failure may cause multiple substrate nodes allocated for initial MVN request mapping to fail, a sufficient set of backup substrate nodes have to be pre-assigned. Similarly, we also need to pre-assign enough backup bandwidth resource on the substrate links to support the communication between the MVN nodes under any single regional failure. Particularly, if a MVN node v is to be remapped at a pre-assigned spare substrate node, we must set up new spare path(s) between that spare substrate node and other surviving substrate nodes. Figure 2 gives an example of MVN mapping under regional failure. In this example MVN nodes a, b and c are initially (under no failures scenario) mapped onto the substrate nodes B, C and A communicating through substrate link B-C and B-A, respectively. Regional failure r1 destroys substrate nodes D and E, as well as destroys substrate links C-D, D-E, B-E, E-F which do not influence the initial mapping, thus we need no backup nodes and links resource for recovering from this failure. Regional failure r2 destroys substrate nodes A and F, as well as destroys substrate links A-B, A-F, E-F. The substrate network remaps the MVN request such that the MVN node c is now mapped onto substrate node E, and MVN nodes a and b are still mapped onto B and C.
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the resource from G(r ) to the MVN request, we must reserve resource from regions which do not include r for the MVN request to recover from regional failure r. Figure 2 (b) shows an example of regional failures. There are two regional failures r1 and r2 in this example. We can see that G(r1) ( Nr1 , Er1 ) , where Nr1 = {D, E} and Er1 = {C-D, D-E, B-E, E-F}, as well G(r 2) ( Nr 2 , Er 2 ) where Nr2 = {A, F} and Er2 = {A-B, A-F, E-F}.
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(b) Substrate Network
Fig. 1 Example of MVN mapping without regional failure(s)
B. Substrate Network The substrate network consists of multiple or multi-data centers spread across multiple geographical locations that are interconnected by a network. Similar to the MVN request described above, we model the substrate network as a weighted undirected graph GS ( N S , E S , C L , C N ) . Where N S and E S represent the set of substrate nodes and the set of substrate links, respectively. C N and C L denote the node the attributes of substrate nodes and substrate links, respectively. The typical attributes of substrate nodes denote node resource (such as CPU, memory, storage, and etc.) capacities. The typical attributes of substrate links include bandwidth capacity and transmission delay. For each substrate node ns N S , which is able to provision node resource for any MVN node, the amount of available node resource capacity and the cost of per unit of node resource is denoted as c(ns ) and p(ns ) , respectively. For each substrate link es E S , we define the amount of available link resource capacity, the cost per unit of link resource and transmission delay as b(es ) , p(es ) and d (es ) , respectively. Figure 1 (b) presents an example of a substrate network, where the numbers in rectangles next to the nodes represent the amount of available node resources/cost of per unit resource of the nodes and the numbers next to the links represent the available link resource/cost of per unit resource/transmission delay of links.
CˊRegional Failure A regional failure in the substrate network will simultaneously destroy one or more substrate nodes and/or links. In [10], the
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Thus, now the new paths are B-E and B-C. Accordingly, we have to migrate the MVN node c from A to E and migrate communications on MVN link c-a from B-A to B-E for recovering from regional failure r2. Regional failure r2
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Algorithm 1: NSMVNM algorithm Input: 1. Substrate network GS ( N S , E S , C L , C N ) ; 2. A MVN request GV ( NV , EV , CN , CL , CD , CDV ) .
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cost. A detailed description of the NSMVNM algorithm is shown in Figure 3, where the notation Dmax denotes the maximum transmission delay of the substrate paths for all of MVN links.
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Output: Mapping solution M 1: Initialize the lists UMN S , and UMNV NV . 2: Sort the substrate nodes in descending order according to eq. (1) and store in UMNS. 3: Find the root node of GV denoted as v.
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4: for each ns UMN S , do 5: calculate and record Cost(vėns) according to eq. (2). 6: end for 7: Mapped v onto ns with minimum Cost(v ė ns), update M, UMNV UMNV v and UMN S UMN S ns
Regional failure r1 (b) Substrate Network
Fig. 2 Example of MVN mapping under regional failure(s)
E. Resource sharing
8: for each vL UMNV , do
Since in this work we assume that only one regional failure occurs at any one time, the resource reserved on the substrate nodes and substrate links can be shared among the different failure scenarios. Here we reuse the strategy in our previous work [10] to allocate the backup resource to eliminate redundant resource.
9:
for each nk UMN S , do
calculate and record Cost(vLėnk) according to eq. (3). end for Mapped vL onto nk with minimum Cost(vLėnk), update M UMNV UMNV vL and UMN S UMN S nk , find a candidate path p connecting nk and ns, then stored in Mp. 13: end for 14: Adjusting the paths in Mp ensure that the delays of all paths in Mp all are fall into [Dmax-CDV, Dmax]. 15: Update M according to Mp. 16: return M
10: 11: 12:
III. ALGORITHM DESIGN For achieving survivable MVN mapping in a reasonable time, we propose efficient heuristics to solve this NP-hard problem in this work. Our main idea is starting with an ³original´ mapping without consideration of any regional failure. And then find the backup resource for each regional failure. More specific, our algorithm consists of three parts below: a). Achieve ³original´ mapping with non-survivable MVN mapping algorithm. b). Achieve survivable MVN mapping with non-survivable MVN mapping algorithm for each regional failure by fixing the substrate network. c). Eliminate redundant resource and mappings for all mappings above with the strategy of resource sharing in section II and greedy min-cost set cover algorithm.
Fig. 3 Pseudo code of the NSMVNM algorithm
We define Con(ns) as the connectivity of substrate node ns which is equal to the number of adjacent nodes of ns. Adj(ns) is the set of adjacent nodes of ns. Accordingly we can calculate Con(ns) by using following equation.
Con(ns ) | Adj (ns ) |
(1)
While mapping the root node of the MVN request we must calculate the possible mapping cost for each available substrate node, such that we can find the substrate node with minimum cost to be the mapped node of root node. In this work, we use the following equation to calculate the possible mapping cost Cost(vL ėnk) .
A. Non-Survivable MVN Mapping Algorithm While considering the non-survivable MVN mapping we need to take into consideration the constraints on transmission delay and delay variation while mapping. In this paper, we design the non-survivable MVN mapping (NSMVNM) algorithm considering the specific topology and constraints of the MVN request. Since the MVN request has a tree like topology with a source node at the root and destination nodes at the leaves of the tree, the root node has maximum connectivity among all MVN nodes. We first map the root node onto the substrate network and then map the leaf nodes according to the mapping of the root node. While mapping each leaf node, it also maps each MVN link to a path (a set of substrate links) in substrate network. The objective is to minimize the total cost including computing cost and bandwidth
Cost (v o ns )
( p(ns ) (MC Con(ns )))* H (v)
(2)
Where MC is the Con(ni) which ni has maximum connectivity among all substrate nodes. Similar to the mapping of root node, we also need to calculate the possible mapping cost for each available substrate node while mapping the leaf nodes, such that we can find the substrate node with minimum cost to be the mapped node of leaf node. The cost for a leaf node mapping onto a substrate node can be calculated by follow equation.
Cost (vL o nk )
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CNnk CPnk
(3)
Globecom 2014 Workshop - Cloud Computing Systems, Networks, and Applications
have:
Where CNnk means the node resource cost and CPnk means the bandwidth cost denoted as follow:
CNnk
CPnk
min{c(M )/ | U (M ) |}, M M S
p(nk )* H (vL )
(4)
where U(M) is the subset of regional failures that can be recovered by the mapping M. Figure 6 explains the relation between MS and R, in SOUM*-M. Figure (6) supposes there are two regional failures r1 and r2 and assumes that M0 is the no-failure mapping solution (i.e., resource allocations), and M1 and M2 are the mappings for regional failures r1 and r2, respectively. Since, r2 does not affect M0; M0 can still be used to recover from regional failure r2. Similarly, since r1 does not affect M1, hence M1 can be used to recover from r1. By the same argument we can deduce that M2 can recover from both r1 and r2. Assuming that M2 has a lower cost than M 0 M1 , then we should choose mapping M2 as our solution to recover from r1and r2, and M0 and M1 are redundant and not required any more. Then M2 should be added to M* and r1and r2 should be removed from R.
¦ p(e)*xev
eP
Where P is the substrate path connecting ns (the substrate node hosting the root node) and nk, ev is the MVN link connecting vL and v (the root node of MVN request).
B. Survivable MVN Mapping Algorithm For achieving survivable MVN mapping with NSMVNM algorithm, we will reuse part of SOUM* algorithm [10] to design our survivable MVN mapping algorithm. Similar to SOUM*, we decompose the SMVNM problem into |R| separate NSMVNM problems. For each regional failure ri, we fix the substrate network GS= GS-G(ri) and then achieve the mapping by using algorithm NSMVNM. Note that r0 means no failure ( G(r 0) ). The algorithm based on SOUM* proposed here for survivable MVN mapping is named SOUM*-M. In SOUM*-M M S {M 0 , M1 , M 2 ,..., M | R| } defines the mapping
r1
set corresponding to failure set R {r 0, r1, r 2,..., r | R |} , and
M0
c( M i ) is the cost of mapping M i M S .
M1
r2
M2
Fig. 6 example of Greedy min-cost set cover algorithm
Algorithm 2: SOUM*-M algorithm Input: 1. Substrate network GS ( N S , E S , C L , C N ) ; 2. A MVN request GV ( NV , EV , CN , CL , CD , CDV ) ;
C. Improved NSMVNM Algorithm The number of leaf nodes of a MVN request is usually greater than 1, thus the order of the leaf nodes in UMNV in algorithm NSMVNM may affect the final mapping result. Furthermore, the regional failure R is given before mapping. If we can make the mapping procedure aware the failures, we can achieve better mapping solutions. Based on the reasons above, we introduce two strategies to improve the NSMVNM algorithm proposed in Figure 3.
3. A list of regional failures R. Output: The min-cost mapping set M* to recover from any specified regional failures. 1: Initialize the cost c( M i ) of all mappings in M S to zero. 2: for each ri R , do 3: Update GS=GS-G(ri) . 4: Call NSMVNM algorithm to get the mapping solution Mi. 5: Calculate c( M i ) according to Mi.
(1) Sort on all leaf nodes.
6: end for 7: Call Greedy min-cost set cover algorithm and get min-cost mapping set M*.
For achieving a better mapping result, we sort the leaf nodes of MVN request in decreasing order of resource requirements (DR(vL)). This resource requirement is not only decided by the leaf node self, but also dependent on the MVN link (ev) connecting it to the root node. We define DR(vL) as follows.
Fig. 4 Pseudo code of the SOUM*-M algorithm
Algorithm 3: Greedy min-cost set cover algorithm Input: 1. All mapping solutions M S ;
DR(vL )
2. The list of regional failures R. Output: The min-cost mapping set M* to recover from any specified regional failures. 1: Initialize the set M * . 2: while R z , do 3: Pick up mapping M which selected by equation (4). 4: Add M to M*, and remove all failures that M recovers from R. 5: end while 6: Return min-cost mapping set M*.
H (vL ) O * xe
v
(5)
Where O is the ratio of unit bandwidth cost to the unit node resource cost. ,QWXLWLYHO\ PDSSLQJ ³larger´ resource-hungry MVN nodes first can give these MVN nodes higher priorities to reserve resources with lower cost and in turn, reduce the total overall cost. (2) Failure-Awareness in NSMVNM. In order to make NSMVNM aware of the failures while mapping the MVN request, we introduce the ³virtual´ unit cost of substrate resource. We define p *(ns ) and p *(es ) to represent ³virtual´ cost of per unit resource of substrate node ns and substrate link es, respectively. p *(ns ) and p *(es ) can be calculated as follows.
Fig. 5 Pseudo code of the Greedy min-cost set cover algorithm
Note that Greedy min-cost set cover algorithm is used in SOUM*-M algorithm to eliminate redundant resource and mappings. The details for greedy min-cost set cover algorithm are shown in Figure 5. In the Greedy min-cost set cover algorithm we
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Globecom 2014 Workshop - Cloud Computing Systems, Networks, and Applications
p *(ns )
p(ns ) D * AF (ns )
(6)
p *(es )
p(es ) D * AF (es )
(7)
(1) Cost: It is the total cost of reserving substrate network resources for mapping the MVN request to tolerate any regional failure of substrate network. It is the sum of computing cost on all substrate nodes and bandwidth cost on all substrate links resource consumption for provisioning a MVN request considering survivability.
Where Į is the factor we can change to control the mapping procedure, AF(ns) is the number of regional failures that affect substrate node ns. The main idea is to select the substrate nodes and links not only have low cost, but also are less likely to be affected by the various given regional failures. While mapping with NSMVNM algorithm, we introduce the strategy of sorting on all leaf nodes by using equation (5) and use the ³virtual´ cost calculated by equations (6) and (7) instead of p(ns ) and p(es ) . We call the algorithm SOUM*-M with these two strategies as SOUM*-MF.
(2) Average Number of Migrations: We define the average number of migrations as follows: AM ¦ r amr / | R | , where amr is the sum of the number of MVN nodes and MVN links that need to be migrated to new substrate node and substrate links under failure r under unconstrained resource. Note that, the operation of migrating would produce additional cost. (3) Unrecoverable Ratio: This is the ratio of the number of unrecoverable failure scenarios to the total number of failure scenarios when the substrate network has limited constrained capacity.
IV. SIMULATION AND RESULTS A. Simulation Environment We use the real network namely USANET (seen as Fig.7) as the substrate network in our simulation. In this substrate network, the computing resource capacity at substrate nodes and bandwidth resource capacity on the substrate links are all equal to 1000 under unconstrained capacity scenario and follow a uniform distribution from 50 to 150 when the capacity is constrained. We also assume that the per unit node resource cost and the per unit link bandwidth cost are all equal to 1 unit, respectively. The transmission delay of each substrate link is equal to 1. In our simulations the number of nodes in a MVN request varies from 4 to 12 in steps of 2 to simulate various MVN request scenarios. The resource requirement of each MVN node is uniformly generated from 10 to 30 units. The resource requested by each MVN link follows a uniform distribution from 10 to 50. We assume that the constraint on transmission delay of each MVN link is less than 6, and the delay variation of any two MVN links must not exceed 2 in our simulation. For each regional failure we randomly choose various numbers of adjacent nodes to fail. In our simulation experiments, we define 8 failure regions in the substrate network. For each region, we randomly select three adjacent nodes to fail.
C. Simulation Results and Analysis In our simulation experiments, we have compared the performances of our algorithms SOUM*-M and SOUM*-MF with the algorithm SOUM*. Where SOUM* is the separate optimization with unconstrained mapping and redundancy elimination algorithm proposed in [10], and SOUM*-MF is the improved SOUM*-M algorithm proposed in this work. Figure 8 shows the comparison of total mapping cost obtained by two approaches proposed in this work and approach SOUM*, where the MVN node number varies from 4 to 12 and increment is 2. From the figure we see that the total mapping cost of SOUM*-M and SOUM*-MF are much lower than SOUM*. This is because SOUM*-M and SOUM*-MF introduce some pre-optimizations (such as sorting of substrate nodes) on substrate network or MVN request before mapping which lead to better mapping solutions. We also note that SOUM*-MF performs better than SOUM*-M. This is because SOUM*-MF performs pre-optimizations (i.e., sorting on MVN nodes and failure-awareness) on the MVN request. 2000
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Cost
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1000
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Fig.7 Substrate network used in our simulation
B. Performance Metrics The MVN mapping cost, average number of migrations and unrecoverable ratio are three key issues of algorithm for SMVNM problem. Thus we use the following three metrics to evaluate the performance of the algorithms compared in our work. The first two are applicable when the amount of computing and bandwidth resources available in substrate network is sufficient to recover from any failure, while the last is applicable when the resources are constrained or limited.
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Fig. 8 Total mapping cost achieved with various sizes of MVN requests
Figure 9 compares the average number of migrations in the three algorithms SOUM*, SOUM*-M and SOUM*-MF, where the MVN node number varies from 4 to 12 and increment is 2. From figure 9 we can see that our algorithms SOUM*-M and SOUM*-MF achieve less average number of migrations than
Globecom 2014 Workshop - Cloud Computing Systems, Networks, and Applications
non-survivable MVN mapping problem. And then we extend the NSMVNM to SOUM*-M for achieving the survivable MVN mapping. We also introduce the strategy of sorting on MVN nodes and the factor Į into NSMVNM to optimize our mappings which makes our algorithm SOUM*-MF failure-aware. Simulation results show that our algorithm performs better in terms of mapping cost, average number of migrations and unrecoverable ratio compared to the existing SOUM* approach.
SOUM*. That means SOUM*-M and SOUM*-MF can recover from any single regional failure with less migration cost than SOUM*. This is because fixed parameter Į in SOUM*-MF can guide the mapping avoiding the failure regions.
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ACKNOWLEDGEMENT
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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), the Fundamental Research Funds for the Central Universities (ZYGX2013J002, ZYGX2012J004), Guangdong Science and Technology Project (2012B090400031, 2012B090500003, 2012B091000163, and 2012556031), and National Development and Reform Commission Project. The research of Dr. Vishal Anand is supported in part by the Provost Fellowship and Scholarly Incentive Grant at the College at Brockport, SUNY.
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Fig. 9 Average number of migrations achieved with various sizes of MVN requests
Figure 10 compares the unrecoverable ratio of three compared algorithms under substrate network. As shown in Figure 10, in this set of simulations the resource capacity of the substrate network is constrained. We can see that our algorithms SOUM*-M and SOUM*-MF lead to better unrecoverable ratio than SOUM*. This is due to the optimization strategy introduced into SOUM*-M and SOUM*-MF lead to not only lower mapping cost but also less migrations, as shown in figures 8 and 9. On the one hand, lower mapping cost means higher probability of success mapping under the substrate network with limited resource capacity. On the other hand less migrations means that the mapping solution under no failure scenario can cover more failure regions, so that increases the probability of recovering from any regional failure. 1.0
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REFERENCES
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Fig. 10 Unrecoverable ratio with various sizes of MVN requests
V.
CONCLUSION
In this research, we study the problem optimal provisioning for multicast oriented virtual network (MVN) request in cloud-based data centers considering survivability for recovering from any single regional failure of substrate network. Furthermore, we first design an efficient algorithm, NSMVNM, to solve the
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