Content uploaded by R. Boutaba
Author content
All content in this area was uploaded by R. Boutaba on Feb 28, 2014
Content may be subject to copyright.
IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013 105
SVNE: Survivable Virtual Network Embedding
Algorithms for Network Virtualization
Muntasir Raihan Rahman and Raouf Boutaba, Fellow, IEEE
Abstract—Network virtualization can offer more flexibility and
better manageability for the future Internet by allowing multiple
heterogeneous virtual networks (VN) to coexist on a shared
infrastructure provider (InP) network. A major challenge in this
respect is the VN embedding problem that deals with the efficient
mapping of virtual resources on InP network resources. Previous
research focused on heuristic algorithms for the VN embedding
problem assuming that the InP network remains operational at
all times. In this paper, we remove this assumption by formulating
the survivable virtual network embedding (SVNE) problem. We
then develop a pro-active, and a hybrid policy heuristic to solve
it, and a baseline policy heuristic to compare to. The hybrid
policy is based on a fast re-routing strategy and utilizes a pre-
reserved quota for backup on each physical link. Our evaluation
results show that our proposed heuristics for SVNE outperform
the baseline heuristic in terms of long term business profit for the
InP, acceptance ratio, bandwidth efficiency, and response time.
Index Terms—Network virtualization, virtual network embed-
ding, network survivability and resilience.
I. INTRODUCTION
THE current Internet architecture has been supporting
various distributed applications and heterogeneous net-
work technologies quite successfully. However the immense
popularity of the Internet has also turned out to be its biggest
obstacle to seamless growth and innovation. The rigidity of
the current Internet architecture has resulted in the so called
Internet Ossification problem. Due to its multi-provider nature,
adopting a new architecture or modifying the existing one
requires consensus among multiple competing stakeholders.
As a result, alterations to the current Internet are limited to
incremental patches and deployment of new network applica-
tions have become increasingly difficult and error-prone.
Network virtualization has been proposed as a diversifying
attribute of the future inter-networking paradigm that can
enable seamless integration of new features to the current
Manuscript received October 23, 2011; revised October 15, 2012. The
associate editor coordinating the review of the paper and approving it for
publication was K. Van der Merwe.
This work was supported in part by the Natural Science and Engineering
Council of Canada (NSERC) under the Smart Applications on Virtual Infras-
tructure (SAVI) Research Network, and in part by the World Class University
(WCU) Program under the Korea Science and Engineering Foundation funded
by the Ministry of Education, Science and Technology (Project No. R31-2008-
000-10100-0).
M. R. Rahman is with the Department of Computer Science, Uni-
versity of Illinois, Urbana-Champaign, IL, 61801, USA (e-mail: mrah-
man2@illinois.edu).
R. Boutaba is with the David R. Cheriton School of Computer Sci-
ence, University of Waterloo, Waterloo, ON N2L 3G1, Canada, and also
with the Division of IT Convergence Engineering, Pohang University of
Science and Technology (POSTECH), Pohang 790-784, Korea (e-mail:
rboutaba@cs.uwaterloo.ca).
Digital Object Identifier 10.1109/TNSM.2013.013013.110202
Internet resulting in rapid evolution of the Internet architecture
[1]–[3]. By allowing multiple heterogeneous network architec-
tures to cohabit on a shared physical infrastructure, network
virtualization promises better flexibility, security, manageabil-
ity and decreased power consumption for the Internet.
Players in the network virtualization model differ from those
in a traditional network environment. Here, the traditional
role of the Internet Service Provider (ISP) is divided into
two separate entities: (1) the infrastructure providers (InP)
who are responsible for deploying and maintaining physical
network resources (routers, links etc.) and (2) the service
providers (SP) who implement various network protocols on
virtual networks (VNs) for the end users by utilizing physical
resources leased from multiple infrastructure providers. This
allows multiple heterogeneous network architectures to be
deployed without the inherent inflexibilities of the existing
rigid Internet architecture. A service provider can also create
child virtual networks in a recursive manner, and lease its
child networks to other service providers, creating a hierarchy
of virtual networks.
In network virtualization models, a weighted undirected
graph GS=(NS,ES)usually represents the physical topol-
ogy, where each node in the network is a vertex vS∈NS,
with a set of attributes AvS. Each physical link between two
nodes is represented by an edge eS∈ESwith an attribute set
AeS. The virtual topology is similarly represented by another
weighted graph GV=(NV,EV)with corresponding attribute
sets. The virtual topology is also known as a logical topology.
A virtual node can be a virtual host or a virtual router. A virtual
host acts as a packet source or sink, whereas, a virtual router
forwards packets according to the routing protocols specified
for the virtual topology. A virtual link can span over multiple
physical links, i.e., it usually corresponds to a physical path.
Often a single virtual link can be mapped to multiple physical
paths in-order to satisfy some of the constraints of the virtual
link, e.g., bandwidth constraints that cannot be satisfied using
a single path.
Efficient utilization of substrate network resources is depen-
dent on effective techniques for virtual network embedding,
which maps virtual networks on physical substrate network
resources. The VN embedding problem is quite challenging,
due to finite node and link resource constraints, admission con-
trol, and the on-line nature of virtual network requests. These
properties make the VN embedding problem very difficult. In-
fact the problem remains computationally intractable even if
some conditions are relaxed. Due to multiple constraints, the
VNE problem is in general NP−hard, even in the off-line
case. On the other hand, traditional techniques for solving on-
line problems are not practical in this case, since the character-
1932-4537/13/$31.00 c
2013 IEEE
106 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
istics of the incoming VN requests are generally unpredictable
and the search space is huge when the underlying substrate
network is large.
Studies have shown that link failures occur as part of
everyday operation in today’s ISP networks [4]. Many net-
works deploy survivable IP over WDM (wave-length division
multiplexing) techniques for resource multiplexing. Here IP is
the logical layer, whereas WDM would be the physical layer.
Failures in these infrastructures can occur at either logical or
physical layer. Logical failures affect the logical layer only,
and are transparent to the physical layer. In contrast, physical
failures not only affect the physical layer, but also propagate to
the logical layer, and if the network is recursively virtualized,
any number of upper layers. We can also distinguish among
single and multiple failures. The single failure case is more
important and common, while considering multiple failures
can facilitate modeling large systems under high stress. Al-
though survivability from link failures has been thoroughly
investigated for ISP and optical networks, the same results do
not hold for network virtualization environments.
In this paper, we formulate the survivable virtual network
embedding (SVNE) problem to incorporate single substrate
link failures in VNE and propose an efficient heuristic for
solving it. Since multiple link failures is a low probability
event, we focus on single substrate link failures. In this paper,
we don’t explicitly deal with node failures. This is because
any node failure aware virtual network embedding algorithm
depends on tolerating adjacent link failures. As a result, we
need to address link failures before dealing with node failures.
Moreover, our proposed heuristic can be extended to deal with
multiple link failures, and subsequently combined with a node
migration strategy [5] to solve the single substrate node failure
problem.
Our main contributions in this paper are as follows:
1) We add survivability mechanisms to the link map-
ping phase of virtual network embedding using efficient
restoration and protection policies that can increase the
long term business profit of the InP. We formulate the
survivable virtual network embedding (SVNE) problem
and provide efficient heuristics to solve it.
2) We add service level agreement (SLA) assurance to
the embedding process by prioritizing the restoration of
failed virtual links based on customer SLA constraints
with the objective of minimizing the overall impact of
failure and maximizing the business profit of the InP.
3) We propose a hybrid policy heuristic to solve SVNE. This
solution is based on linear programming modules and
has a number of configurable parameters. For example,
the InP can control the percentage of resources dedicated
for backup recovery and the number of paths allowed
for primary and detour flows. This gives the InP greater
control over its backup resource allocation policies and
enables flexibility in determining the optimal allocation
based on current failure patterns.
4) We introduce path-flow based optimization formulations
for the different recovery and protection policies. Besides
reducing the number of constraints and variables, there
are other advantages in a path flow based formulation.
Most notably, it allows control over the characteristics
of the paths selected for embedding and protection. For
instance, we can directly control the total number of paths
and the number of hops per path for quality of service
(QoS) management purposes.
This paper extends the results presented in [6] on several
aspects. First, we include detailed mathematical optimization
formulations of the proactive policy for SVNE which were
omitted from the conference version. Second, the paper covers
the basic concepts of network virtualization, virtual network
embedding, and network survivability in more detail. Third,
we also discuss the trade-offs of penalty function and business
utility function formulation for the infrastructure provider in
the presence of failures. Finally we have more experimental
results including analysis of the effect of path selection
algorithm parameters on SVNE policies and performance for
special topologies like hub-and-spoke and mesh VN topolo-
gies. We also include a theoretical performance analysis for
the online proactive policy for solving the SVNE problem.
The rest of the paper is organized as follows. Section II
discusses related works on survivability and virtual network
embedding. Section III formalizes the network model and for-
mulates the virtual network embedding and survivable virtual
network embedding problems. In section IV, we describe our
proposed pro-active, and hybrid policy heuristics for the sur-
vivable virtual network embedding problem. Sections V, and
VI describe node embedding algorithms, and path selection
mechanisms, respectively, which we use in conjunction with
our proposed SVNE solutions for link embedding. Section
VII presents simulation results that evaluate the proposed
heuristics. Finally, we conclude in Section VIII by identifying
future research directions.
II. RELATED WORK
A. Virtual Network Embedding
Virtual Network Embedding (VNE) is the central resource
allocation problem in network virtualization. It deals with the
efficient mapping of virtual networks onto physical network
resources. More specifically, for each virtual network creation
request, the VNE is responsible for mapping virtual nodes
onto physical nodes and virtual edges onto one or more
physical paths. The VNE problem, with constraints on virtual
nodes and virtual links, can be reduced to the NP-hard
multi-way separator problem, even if the schedule of VN
requests is known beforehand [7]. Even when all the virtual
nodes are already mapped, the virtual link embedding problem
remains NP-hard. In order to reduce the hardness of the VN
embedding problem and enable efficient heuristics, existing
research has been restricting the problem space in different
dimensions, e.g., considering the off-line version of the prob-
lem [8], [9], ignoring either node or link requirements [8],
[10], [11], assuming infinite capacity of the substrate nodes
and links to obviate admission control [8]–[11], and focusing
on specific virtual topologies [8]. Recently the authors in
[12]–[14] proposed VNE heuristics that combine the node
and link embedding phases. The authors in [15] proposed a
distributed algorithm that simultaneously maps virtual nodes
and virtual links without any centralized controller. Recently,
the intra-domain algorithms to support VN embedding have
RAHMAN and BOUTABA: SVNE: SURVIVABLE VIRTUAL NETWORK EMBEDDING ALGORITHMS FOR NETWORK VIRTUALIZATION 107
been extended across multiple administrative domains [16],
[17], and geo-distributed cloud computing environments [18],
[19]. The authors in [19] propose a hierarchical approach
to solve the inter-domain embedding problem for networked
clouds over multiple administrative domains.
However, a limitation of these heuristics is that they assume
the substrate network to be operational at all times, which
is not realistic. The existing heuristics are not capable of
handling substrate node and link failures, which may lead to
poor performance and increased frustration for the SP.
VN embedding is also related to the network testbed map-
ping problem [20]. The Assign algorithm used in the Emulab
testbed [20] considers bandwidth constraints alongside con-
straints on exclusive use of nodes (i.e., different VNs cannot
share a substrate node). But sharing of substrate nodes and
links by multiple VNs is one of the core principles of network
virtualization [2], and VN embedding algorithms must support
these objectives. Emulab itself is aligning its resource mapping
policies with that of network virtualization [21].
B. Survivability
Survivable Virtual Network Embedding (SVNE) or virtual
network embedding in the presence of arbitrary node and link
failures is a research challenge that has yet to be addressed
in the network virtualization literature. Node and link failure
survivability problems have been investigated extensively for
optical and multi-protocol label switched (MPLS) networks
[22], and real time systems [23]. Two well known approaches
for handling link failures in optical networks are protection
and restoration. Protection is normally employed at the sub-
strate network level during the design phase by provisioning
backup light-paths. On the other hand restoration is done at
the virtual network level by provisioning the network with
additional capacity and is more reactive in nature. The key to
efficient restoration mechanisms is survivable mapping in the
presence of link failures. The authors in [24] mention three
existing paradigms for survivable IP-over-WDM mapping
algorithms based on (1) Integer Linear Programs (ILP), (2)
Meta-heuristics like Genetic Algorithms (GA), Ant Colony
Optimization (ACO), Tabu Search, and (3) Graph Theoretic
algorithms. The most recent approach based on graph theoretic
results called SMART [25], [26] is more efficient and scalable
than ILP and heuristic local search approaches.
SMART repeatedly picks connected subgraphs of the log-
ical topology and finds survivable mappings for them. It
then reduces the logical topology by contracting the already
mapped subgraph and continues the process. The authors
in [24] continue working in this direction by exploiting
duality between circuits and cuts due to the Max-flow min-
cut theorem in Combinatorial Optimization [27]. They pro-
pose primal and dual algorithms that extend SMART (called
CIRCUIT-SMART and CUTSET-SMART) and develop some
heuristics to speed up their algorithms. Recently the authors
in [28] extended the Max-flow min-cut theorem for multi-
layer networks. They proposed new connectivity metrics suited
for multi-layer networks and developed some heuristics for
maximizing connectivity in the logical layer.
Our work on survivable virtual network embedding (SVNE)
differs in a number of aspects, due to unique challenges
introduced by the network virtualization environment (NVE).
First, the VNE problem is on-line in nature, whereas the
survivable logical topology design problem in optical and
multi-protocol label switched (MPLS) networks [24], [28] is
off-line. Second, in NVEs, we need to ensure that all virtual
links are intact in the presence of failures. This restriction
is not present, for example, in optical networks where the
goal is to only ensure that all nodes remain connected in
the presence of failures, even if they are not connected
via a direct overlay link. Our contribution also differs from
existing work in terms of the objective formulation. Our aim
is to develop a survivable virtual network embedding solution
that simultaneously maximizes the long term revenue for the
InP, and minimizes the long term penalty incurred by the
InP due to service violations caused by failures. This dual
nature of the objective function in the presence of failures
is absent both in the existing research on optical and MPLS
networking domains and the existing VNE heuristics. Another
novel aspect of our work is that we utilize path-flow based
optimization formulations for solving the SVNE problem. The
path formulation allows control over the characteristics of the
paths selected for embedding and survivability against failures.
For instance, we can directly control the total number of paths,
number of hops per path, and impose delay constraints on
virtual links for QoS purposes. This is not possible with a link-
flow based formulation which has been used for the previous
VNE heuristics [9], [12]–[14], [29].
In optical networks, end-to-end connection requests arrive
on-line and are processed as soon as they arrive [22]. For
a VN request, we have to guarantee survivability of all the
VN links simultaneously, which makes the problem harder.
We differentiate between We a k and Strong survivability in the
context of SVNE. Weak survivability only ensures that the
virtual nodes will stay connected in the presence of failures.
Strong survivability guarantees that the original VN topology
remains intact in the presence of failures. Failures in the
underlying physical network can give rise to complex multi-
layer failures in the network virtualization environment. Any
such failure can effectively cause a cascading series of errors
in the virtual networks directly hosted on those substrate
network components, and possibly in many others that are
recursively designed. In NVE, we require strong survivability
since in the basic revenue model for NVE, the service provider
pays an amount that is proportional to the resource (cpu for
nodes, bandwidth for links) and VN topology requirements of
the virtual network request. This means that provisioning of
backup resources is essential in an NVE, since without backup
provisioning we can only ensure weak survivability.
III. SVNE PROBLEM FORMULATION AND SOLUTIONS
In this section, we provide a mathematical formulation of
the survivable virtual network embedding (SVNE) problem as
an extension of the VNE problem. We then devise efficient
heuristics to solve SVNE. Since we deal with substrate link
failures in this paper, our main focus is on the second phase of
VNE, that is the link embedding phase. For node embedding,
we use the existing heuristics proposed in the literature. As a
result our approach to on-line SVNE for each incoming VN
request is as follows:
108 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
TAB LE I
SUMMARY OF KEY NOTATIONS USED IN THE PAPER
Notation Description
GS(NS,ES)Substrate graph
GV(NV,EV)Virtual network request
RN(x)Residual cpu capacity of a substrate node
RE(s)Residual bandwidth capacity of a substrate link
α(s)(β(s)) Percentage of bandwidth reserved for primary
(backup) flows on substrate link s
PSSet of simple paths in the substrate graph
ΓN:NV←NSNode embedding function
ΓE:EV←P
SLink embedding function
Π(.)Revenue function
X(.)Penalty function
δs(p)Link-path indicator variable, δs(p)=1if link
s∈p
b(p, v)Bandwidth allocated on path pfor virtual link v
b(d, p, v)Re-routed bandwidth on detour dfor B(p, v )
•Node Embedding: Greedy [9], [29], Mixed Integer Pro-
gramming [13].
•Link Embedding: Add survivability policies to handle
arbitrary substrate link failures. [our contribution].
The existing node embedding heuristics and path selection
mechanisms used in our SVNE solutions are described in
subsequent sections. The key mathematical notations used for
the SVNE problem formulation and solutions are summarized
in Table I.
A. Substrate Network
We model the substrate network as a weighted graph
GS(NS,ES),whereNSand ESrepresent the set of substrate
nodes and links respectively. Each substrate node x∈NShas
an associated cpu capacity cpu(x)and a geographical location
loc(x). A substrate link s=(sx,s
y)∈ESbetween substrate
nodes sx,s
y∈NShas a bandwidth capacity b(s).Fromnow
on, we denote the endpoints of any substrate link sas sxand
sy.
B. Virtual Network Request
A Virtual Network (VN) request GV(NV,EV)is also
modeled as a weighted graph. VN requests are associated with
constraints and QoS requirements embodied into service level
agreements (SLA). A virtual node y∈NVhas a cpu capacity
requirement cpu(y)and geographical location requirement
loc(y). A virtual link v∈EVis characterized by a bandwidth
capacity requirement b(v)and a delay constraint d(v).d(v)is
used to preselect the set of admissible simple substrate paths1
that can be used to embed v. An example of a typical substrate
network and two virtual network topologies are shown in
figure 1. The numerical values beside the substrate nodes and
links represent cpu and bandwidth constraints of those nodes
and links respectively.
1A substrate path that repeats no substrate node.
a
H
BA
F E
DCG
90 45
5389
67
56 79
78
15
1312
1216
y z
a
b c
x
22
22
12
56 17
17
15 20 10
25
12
15
10
10
c
b
x
z
y
Substrate Network Topology
VN Request 1
VN Request 2
I
56
55
43
Fig. 1. Mapping of VN requests onto a shared substrate network.
C. Resource Usage Metrics
We assume that substrate network resources are finite. As
a result, the amount of residual substrate network resources
diminishes as new VN requests are processed. We keep track
of the residual substrate node and link capacities in order to
make sure we don’t accept a request unless there are adequate
resources to serve it. The residual capacity of a substrate node
x∈NSis defined as:
RN(x)=cpu(x)−
y∈V(x)
cpu(y),(1)
where V(x)denotes the set of virtual nodes mapped onto
x. Similarly the residual capacity of a substrate link s∈ES
is defined as:
RE(s)=b(s)−
{v:∃p∈ΓE(v),s∈p}
b(v),(2)
where, ΓE(v)defines the set of paths in the InP that are
used to embed the virtual link v(Section III-D). The residual
capacity values are updated after each new VN request has
been successfully mapped on top of the substrate network
as long as there remains adequate residual resources. The
values are also updated after a VN departs and link failure
occurrences and repairs.
In order to protect against single substrate link failures,
we dedicate a certain percentage of bandwidth resources on
each substrate link for backup purposes. For a substrate link
swith total bandwidth b(s),α(s)b(s)bandwidth is reserved
for primary flows, whereas β(s)b(s)is reserved for backup
flows, where α(s)+β(s)=1. The residual bandwidth measure
is accordingly decomposed into primary and backup residual
bandwidth measures Rα(s)and Rβ(s)respectively. As a
result, we need to keep track of these two residual bandwidth
measures separately.
D. VN Embedding
The VN Embedding process refers to the mapping of the
virtual network topology (logical topology) on top of the
substrate network topology (physical topology) subject to
certain constraints. The constraints are normally manifested
in terms of the residual resource availability of the substrate
network and the QoS parameters specified by the VN request.
RAHMAN and BOUTABA: SVNE: SURVIVABLE VIRTUAL NETWORK EMBEDDING ALGORITHMS FOR NETWORK VIRTUALIZATION 109
An example of a VN embedding can be seen on the right in
figure 1. Here the solid lines represent the substrate network
topology. The dashed (colored) lines represent the substrate
links used for embedding the corresponding virtual networks.
The virtual nodes are shown beside the substrate node they
have been mapped on. From a graph theoretic standpoint, the
VN embedding process can be divided into two stages:
1-Node Embedding Phase: Each virtual node from a VN
request is mapped to a single distinct substrate node by a
one-to-one mapping: ΓN:NV←NS, such that ΓN(x)=
ΓN(y),iffx=y∀x, y ∈NV, subject to the cpu capacity
constraints: cpu(x)≤RN(ΓN(x)) ∀x∈NV.
2-Link Embedding Phase: Each virtual link is mapped to
either an unsplittable substrate path or a splittable multi-
commodity flow based set of paths between the substrate
nodes corresponding to the endpoints of the virtual link.
Mathematically, we have a mapping: ΓE:EV←P
S,such
that ∀v=(vx,v
y)∈EV,andPSis the set of simple paths
of GS.WehaveΓE(v)⊆P(ΓN(vx),ΓN(vy)), subject to
the bandwidth capacity constraints: b(v)≤RE(p),∀p∈
ΓE(eV),whereP(z, w)denotes the set of simple substrate
paths between substrate nodes zand w,andRE(p)=
mins∈pRE(s). For any virtual link v∈EV, we specify the
set of QoS constrained substrate paths for vas P(v)={p∈
PS|delay(p)≤d(v)}.
Figure 1 shows an example of the embedding process. The
substrate and virtual nodes are labeled with letters inside the
corresponding node. We have the embedding of GVon GS
as Γ,whereΓis defined as follows: ΓN(a)=C, ΓN(b)=
H, ΓN(c)=Band ΓE(ab)={CD, DG, GH},ΓE(bc)=
{HF,FE, EB},ΓE(ac)={CA,AB}.
E. Penalty Function and Business Utility for InP
An SP negotiates a Service Level Agreement (SLA) with
the InP for uninterrupted service throughout the lifetime of
its requested VN. If the SLA contract is violated due to a
substrate resource failure, then this results in frustration on part
of the SP and subsequent penalty for the InP based on the level
of frustration of the SP. Each SP owning a VN is characterized
by a Service class which is represented by a function Sj(db),
where j∈{1,2,...,C}and Cdenotes the number of distinct
service classes and db denotes the bandwidth differential,
that is the difference between requested bandwidth and the
bandwidth granted by the InP. We can model Sj(db)as an
increasing function, however for simplicity, we assume that the
function takes the shape of a step function, that is for db < TB,
Sj(db)=0,andfort>T
B,Sj(db)=P. We call TBthe
frustration threshold for the service class j. Therefore the set
of all SPs is partitioned into equivalence classes based on their
respective service class associations. We denote the mapping
between VNs and service classes as ϕ(.),whereϕ(i)=j
means that VN iis associated with service class j.Sincewe
have reserved a percentage of bandwidth on each substrate
link for backups, it cannot be ensured that all the SPs will
retain their complete VN topology when a failure occurs. In
that case our objective will be to minimize the total penalty
incurred due to SP frustration. For each v∈EVand service
class jfor a VN, we will denote Sj(v)as the penalty incurred
due to service disruption.
F. Formulation of SVNE
We represent the input to SVNE as an |ES|+4 tuple <
GS,G
V,j,l,{α(s)}s∈ES>,whereGSand GVrepresent the
substrate and virtual networks respectively, jrepresents the
service class of the SP owning GV,l∈ESis the failed
substrate link, and β(s)=1−α(s), such that β(s)represents
the percentage of bandwidth on each substrate link sreserved
for backups. Let Π(GV)denote the revenue generated from
GV,where
Π(GV)=T(GV)[C1
v∈EV
b(v)+C2
x∈NV
cpu (x)] (3)
C1and C2are weight factors which represent the relative
importance of bandwidth and cpu to the generated revenue
respectively. T(GV)represents the lifetime of the VN char-
acterized by GV. Each service class jis associated with a
penalty function Sj(.),whereSj(v)represents the monetary
penalty incurred if the bandwidth contract of virtual link vis
violated.
Let Vdenote the set of all virtual links affected by the
failure of l. Then the expected total penalty incurred by the
InP to the corresponding SP is:
X(GV;l)=MTTR(l)
v∈V∩EV
Sj(v)db(v)
b(v)(4)
MTTR(l)is the mean time to repair for l. The differ-
ence between the bandwidth requested for v, and the ac-
tual bandwidth supplied by the InP is represented as db(v).
Let GV
1,G
V
2,G
V
3,... be the sequence of VN requests, and
l1,l
2,l
3,... be the sequence of substrate link failure events.
Then the objective of SVNE is to maximize long term business
profit expressed as:
Π∞=
∞
p=1
∞
q=1
[Π(GV
q)−X(GV
q;lp)] (5)
G. Protection and Restoration Models
For fast protection against substrate link failures, we employ
two types of restoration mechanisms in this paper, namely
link (local) restoration and path (end-to-end) restoration. In
the existing literature on survivable topology design, both of
these mechanisms fall under the category of fast restoration
mechanisms, due to their low restoration latency. The main
objective in this paper is to provide link embedding heuristics
with fast restoration.
1) Link Protection and Restoration: For protecting a sub-
strate path pcorresponding to a virtual link against single
link failures, we associate a primary path W(p)and for each
substrate link e∈p, a local backup detour Be(p).Sofor
a substrate path with ksubstrate links, there will be klink
detours for fast restoration against single link failures. From
now on, when we refer to a path pin this model, it will
consist of {W(p),B
e(p, ∀e∈p)}. It should also be mentioned
that backup detours for different substrate paths can share
bandwidth on their common substrate links. Link restoration
is also known as local restoration due to the localized fault
tolerance mechanism around each substrate link.
110 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
2) Path Protection and Restoration: In the simplest ap-
proach to path restoration, namely 1:1protection, a con-
nection pconsists of a primary working path and a link
disjoint backup path. Our approach to path restoration is
more sophisticated in that we use a survivable version of
the multi-commodity flow problem for path restoration in link
embedding [30]. A survivable flow from a substrate node uto
vconsists of a primary flow of value famong the paths from
uto v, and a distinct secondary flow of the same value fin
such a way that both flows pass through link disjoint paths.
Path restoration is also known as global restoration due to its
end-to-end fault tolerance nature.
IV. HEURISTICS FOR SVNE
In this section, we describe our proposed solutions to the
SVNE problem. Our first solution is proactive, that is, it
provisions redundant resources for possible failures in the
future. This solution is suitable for scenarios where even the
slightest delay due to failures is unacceptable. A drawback
of this approach is wastage of resources. In a failure-free
case, we will waste approximately 50% substrate network
resourses. Our second solution overcomes this limitation by
using a reactive approach, where failures are handled after we
have an actual substrate link failure. We describe these two
solutions in the next sub-sections.
A. PROACTIVE Policy Heuristic for SVNE
The PROACTIVE policy protects each virtual link using
a survivable version of the multi-commodity flow problem
[30]. For each virtual link v, we send a primary flow of
value b(v)and also a secondary flow of value b(v)among the
QoS constrained paths allowed for v. To protect against single
substrate link failures, we have to ensure that primary and
secondary flows are edge disjoint. We formulate the problem
as a mixed integer program in the following manner:
PROACTIVE MIP LE
Minimize
-Objective Function
v∈EV
Sj(v)[1 −
p∈P(v)
b2(p, v)
b(v)]+
v∈EV,p∈P(v)
[b1(p, v)+b2(p, v)]
(6)
Subject to
-Primary and Secondary Capacity Constraints
v∈EV,p∈P(v)
δs(p)b1(p, v)≤R
α(s)∀s∈ES(7)
v∈EV,p∈P(v)
δs(p)b2(p, v)≤R
β(s)∀s∈ES(8)
-Primary and Secondary Bandwidth Constraints
p∈P(v)
b1(p, v)=b(v),∀v∈EV(9)
p∈P(v)
b2(p, v)≤b(v),∀v∈EV(10)
-Disjointness Constraints
b1(p, v)≤b(v)σ1(p, v),∀v∈EV,∀p∈P(v)(11)
b2(p, v)≤b(v)σ2(p, v),∀v∈EV,∀p∈P(v)(12)
δs(p)δs(q)[σ1(p, v)+σ2(p, v)] ≤1,∀s∈ES(13)
-Variables
σ1(p, v)∈{0,1},∀v∈EV,∀p∈P(v)(14)
σ2(p, v)∈{0,1},∀v∈EV,∀p∈P(v)(15)
b1(p, v)≥0,∀v∈EV,∀p∈P(v)(16)
b2(p, v)≥0,∀v∈EV,∀p∈P(v)(17)
B. Remarks
•jdenotes the service class associated with the VN. Sub-
sequently Sj(v)denotes the penalty incurred for violating
the bandwidth reservation for a virtual link vbelonging
to a VN of service type j.
•δs(p)is a link-path indicator variable, i.e., δs(p)=1if
s∈p,0otherwise.
•b1(p, v)and b2(p, v)represent the primary and backup
flows on the simple path pfor the virtual link v.
•The objective function 6 has two parts. The first part is
for minimizing the total penalty incurred due to band-
width violations, whereas the second part is concerned
with minimizing the overall substrate network usage for
primary and secondary flows.
•Constraints 7and 8are the primary and secondary
capacity constraints, and they specify that for each sub-
strate link, the overall bandwidth used for primary and
secondary flows must be within the primary and backup
residual capacities of that substrate link respectively.
•Constraints 9and 10 are bandwidth constraints for pri-
mary and secondary flows respectively.
•Constraints 11,12 and 13 represent the disjointness con-
straints. They are expressed in terms of the two integer
variables σ1and σ2. The third constraint in this set of
constraints enforces that only one of them can take the
value 1.Ifσ1is 0, then the first constraint forces b1to
0also. However if σ1is 1, then the first constraint is
trivially satisfied. The case for σ2is similar.
C. Solution Approaches
PROACTIVE MIP LE is a mixed integer program, and
hence NP−hard to solve. The usual approach is to relax
the integer constraints and solve the relaxed Linear Program
(LP) to obtain a fast heuristic. However the integrality of the
MIP stems from the disjointness constraints 13,14,and15
which force the primary and backup flows to pass through
link disjoint paths. It should be noted that we have a dedi-
cated percentage of bandwidth resources for backups on each
substrate link through the α(s),β(s)values for each substrate
link s∈ES.Thisseparation property readily leads towards
a fast simple heuristic using two sequential LP’s as follows:
PROACTIVE LP LE P
-Objective Function
RAHMAN and BOUTABA: SVNE: SURVIVABLE VIRTUAL NETWORK EMBEDDING ALGORITHMS FOR NETWORK VIRTUALIZATION 111
Minimize
v∈EV,p∈P(v)
b1(p, v)(18)
Subject to
v∈EV,p∈P(v)
δs(p)b1(p, v)≤R
α(s)∀s∈ES(19)
p∈P(v)
b1(p, v)=b(v),∀v∈EV(20)
We define a boolean variable ϕ(s),∀s∈ESwhich keeps
track of the substrate links that have been used for sending
primary flow. These values are then used in the second LP
to avoid conflicts between primary and backup flows on the
same substrate link.
PROACTIVE LP LE B
-Objective Function
Minimize
v∈EV
Sj(v)[1 −
p∈P(v)
b2(p, v)
b(v)]+
v∈EV,p∈P(v)
b2(p, v)(21)
Subject to
v∈EV,p∈P(v)
δs(p)b2(p, v)≤(1 −ϕ(s))Rβ(s)∀s∈ES
(22)
p∈P(v)
b2(p, v)≤b(v),∀v∈EV(23)
It should be noted that we have multiplied the term (1 −
ϕ(s)) to the right hand side of the first constraint in 22. If a
substrate link shas been used for a primary flow, then ϕ(s)
will be 1, forcing the right hand side of that constraint to be
0. This ensures the disjointness of the primary and secondary
flows. We now have a polynomial time LP based heuristic
showninAlgorithm1.
Algorithm 1 LP Based Heuristic for Proactive Recovery
Policy (LPHPP)
procedure LPHPP(GS,G
V)
Solve PROACTIVE LP LE P
for all s∈ESdo
ϕ(s)=0
end for
for all v∈EVdo
for all p∈P(v)do
if b1(p, v)>0then
ϕ(s)=1
end if
end for
end for
Solve PROACTIVE LP LE B
end procedure
D. Competitive Ratio of LPHPP
We can think of LPHPP as a greedy algorithm, since it first
assigns bandwidth for primary flows and marks the substrate
links used. Marking a substrate link is equivalent to deleting
that link while assigning bandwidth to backup flows, and this
is the key property that ensures link disjointness for primary
and backup flows for each virtual link. LPHPP is also an
online algorithm, since we have to find an embedding for
each new virtual network. As a result, LPHPP will perform
worse compared to an optimal offline algorithm. We have the
following theorem specifying the worst case competitive ratio
for LPHPP.
Theorem 1 Let GS(NS,ES)be a substrate network and
<G
V
i>be a sequence of virtual networks to be embedded
on GS.LetOP T denote an optimal off-line algorithm for
the SV NE problem. Then A(LP H P P )≥(n−1)A(OP T ),
where n=|NS|is the size of the substrate network, and A(.)
is a function that returns the number of VN requests fulfilled
by a particular algorithm.
Proof
The proof is by construction in two phases. In the first
phase, we show how to convert an instance of SV NE(l)to an
instance of failure free VNE for LPHPP, where lis the failed
substrate link. Next, we show the existence of a worst case
substrate graph, and a worst case sequence of input requests
that satisfy the competitive ratio bound.
For the first phase, we can create an instance of VNE
corresponding to SV NE(l), by replacing each virtual link
request vin SV NE(l)with bandwidth requirement b(v)with
two virtual links in VNE, each with bandwidth b(v).We
can easily see that solving VNE is equivalent to solving
SV NE(l)using LPHPP.
For the second phase, consider a chain substrate network
consisting of nsubstrate nodes. Assume the first VN request
requires a virtual link (1,n)from node 1to node n,and
there are n−1subsequent single virtual link VN requests
of the form (i, i +1),fori=1,2,...,n−1, where each VN
requires a single virtual link with end-points at i,andi+1.The
greedy algorithm LPHPP accepts the first request and cannot
accept any other requests. So A(LP H P P )=1.Howeverthe
optimal solution OP T would have accepted the later n−1
VN requests, so A(OP T )=n−1. Since this is a worst-case
scenario, we have, A(LP HP P )≥(n−1)A(OP T ).
E. HYBRID Policy Heuristic for SVNE
Since, LPHPP has poor worst-case performance, we pro-
pose a hybrid policy heuristic for solving SVNE, which avoids
the complexity associated with mixed-integer programs. The
heuristic consists of three separate phases. In the first phase,
before any VN request arrives, the InP pro-actively computes
a set of possible backup detours for each substrate link using
a path selection algorithm. Therefore, for each substrate link l,
we have a set Dlof candidate backup detours. The InP is free
to utilize any path selection algorithm that suits its purposes,
e.g., k-shortest path algorithm [31], or column generation
or primal dual methods [32]. The second phase is invoked
when a VN request arrives. In this phase, the InP performs
a node embedding using existing heuristics [9], [13], [14]
112 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
and a multi-commodity flow based link embedding, that we
denote as HYBRID LP LE. Finally, in the event of a substrate
link failure, a reactive backup detour optimization solution
HYBRID LP BDO is invoked which reroutes the affected
flows along candidate backup detours selected in the first
phase. The pseudo-code for the hybrid policy is shown in
Algorithm 2.
Algorithm 2 Hybrid Policy Heuristic (HRP)
procedure HRP(GS,G
V)
for all s∈ESdo
pre-compute candidate detour set Ds.
end for
for all event arrivals do
if event type == VN arrival then
compute node embedding for GV(NV,EV).
solve HYBRID LP LE.
for all sused in HYBRID LP LE do
update Rα(s).
end for
end if
if event type == Failure arrival then
solve HYBRID LP BDO.
for all sused in HYBRID LP BDO do
update Rβ(s).
end for
end if
end for
end procedure
We now show the formulations of HYBRID LP LE and
HYBRID LP BDO.
F. Formulation of HYBRID LP LE
In this phase we use a path based multi-commodity flow
formulation to embed all the virtual links simultaneously. For
each pair (x, y)∈VS×VS, we have a set of preselected end-
to-end paths P(x, y). For a virtual link v∈EV, we denote
P(v)=P(vx,v
y)as the set of pre-selected QoS constrained
simple paths for embedding v,wherevxand vyare the end-
points of v. Since the node embedding phase precedes the
link embedding phase, we already know which virtual node
is mapped to which substrate node. For any virtual link v=
(x,y
)∈EV, we denote this as x→ΓN(x)=xand
y→ΓN(y)=y. HYBRID LP LE can be expressed as the
following linear program:
HYBRID LP LE
-Objective Function
Minimize
v∈EV
p∈P(v)
b(p, v)(24)
Subject to
-Primary Capacity Constraint
v∈EV
p∈P(v)
δs(p)b(p, v)≤R
α(s),∀s∈ES.(25)
-Primary Bandwidth Constraint
p∈P(v)
b(p, v)=b(v),∀v∈EV(26)
1) Remarks:
•δs(p)is the link-path indicator variable, that is, δs(p)=1
if s∈p,0otherwise.
•The objective function 24 corresponds to the revenue
function Πfor the VN.
•b(p, v)is the amount of bandwidth allocated on path p
for virtual link v. A strictly positive value for b(p, v)will
indicate that pis a substrate path used for v. The values of
b(p, v)are stored and later used in the subsequent phase
of the heuristic.
•Constraint 25 is the primary capacity constraint which
states that the total primary bandwidth allocated for all
virtual links must be within the primary residual capacity
of each substrate link.
•Constraint 26 is the primary bandwidth constraint which
specifies that the total bandwidth requirement of each
virtual link must be distributed among all the QoS
constrained paths allowed for that virtual link.
G. Formulation of HYBRID LP BDO
HYBRID LP BDO can be expressed as the following lin-
ear program.
HYBRID LP BDO
-Objective Function
Minimize
v∈EV
Sj(v)
p∈P(v)
δl(p)b(p, v)[1 −
d∈Pl
b(d, p, v)
b(p, v)]
(27)
Subject to
-Backup Capacity Constraint
v∈EV,p∈P(v),d∈Dl
b(p, v)δs(d)b(d, p, v)δl(p)≤R
β(s)∀s∈ES
(28)
-Recovery Constraint
d∈Dl,v∈EV,p∈P(v)
δl(p)b(p, v)δs(d)b(d, p, v)≤
d∈Dl,v∈EV,p∈P(v)
δl(p)b(p, v)
(29)
1) Remarks:
•jrepresents the service class associated with the VN.
Subsequently Sj(v)denotes the penalty incurred for
violating the bandwidth reservation for a virtual link v
belonging to a VN of service type j.
•xdenotes the ceiling of x,thatisx=1iff x>0.
So b(p, v)=1indicates that pisapathusedfor
the embedding of v. Note that the b(p, v)values are
calculated and stored in the HYBRID LP LE phase.
•For the failed substrate link l, we have the set of candidate
backup detours, Dl=P(lx,l
y)\{l}.
•b(d, p, v)denotes the amount of rerouted bandwidth on
detour d∈D
lfor b(p, v), that is for the primary path p
allocated for virtual link v.
•The objective (equation 27) refers to the penalty function
formulated in equation 4.
RAHMAN and BOUTABA: SVNE: SURVIVABLE VIRTUAL NETWORK EMBEDDING ALGORITHMS FOR NETWORK VIRTUALIZATION 113
•Constraint 28 is the backup capacity constraint which
states that the total backup flow on all the detours passing
through a substrate link must be within the backup
residual capacity of that substrate link.
•Constraint 29 is the recovery constraint and it signifies
that the total disrupted primary bandwidth must be allo-
cated along the precomputed set of detours. The objective
function ensures that the virtual links that have higher
penalty values will be given priority during the recovery.
2) Discussion: Our proposed HYBRID policy is a polyno-
mial time heuristic for SVNE, since both HYBRID LP LE
and HYBRID LP BDO are linear programs. Another impor-
tant feature of HYBRID is that it decouples primary and
backup bandwidth provisioning. As a result, we don’t need
complex disjoint constraints in our solution which would
have resulted in a hard mixed integer program. The objective
functions of HYBRID LP LE and HYBRID LP BDO jointly
solve the long term objective of SVNE as expressed in
equation 5.
V. H EURISTICS FOR NODE EMBEDDING
A. Greedy Node Embedding
The main advantage of a greedy node embedding heuristic
is that it is simple and cost efficient, in contrast to iterative
methods or meta-optimization techniques, e.g., simulated an-
nealing. The greedy algorithm maps virtual nodes to substrate
nodes with maximum residual substrate resources in order to
minimize the use of resources at bottleneck nodes and links
[9], [29]. The metric quantifying available substrate resources
is H(x)=RN(x)l∈L(x)b(l),whereL(x)is the set of links
adjacent to x,andRN(x)is the residual cpu capacity of x.
This metric leads to the greedy node embedding algorithm
in Algorithm 3, which assumes batch processing, i.e., the
InP collects VN requests at the end of a fixed time interval,
allocates them simultaneously. The algorithm can be easily
converted to a pure online algorithm.
Algorithm 3 Greedy node embedding algorithm
procedure GNE(GV=(NV,EV))
Sort VN requests according to revenue.
exit if no requests left.
Take the request with largest revenue.
Find the set of substrate nodes Sthat satisfy restrictions
and available cpu capacity.
if S={} then
exit.
end if
For each virtual node n∈GV, find the substrate node
x=argmaxxH(x).Mapnto x.
end procedure
B. D-ViNE Algorithm
In this section, we describe a node embedding heuristic
based on a mixed integer programming formulation that max-
imizes correlation between node and link embedding phases
in order to increase revenue and minimize cost [13], [14]. The
basic idea is to augment the substrate graph and simultane-
ously map the virtual nodes and links using a mixed integer
programming formulation. Since mixed integer programs are
computationally intractable, the authors used relaxation and
rounding to develop polynomial time heuristics. For details,
we refer the reader to [13], [14]. We use these existing
node embedding algorithms to implement the node embedding
phase of our SVNE solutions.
VI. PATH SELECTION MECHANISMS
The effectiveness of the proposed heuristics depend on
efficient path selection mechanisms. Especially the proposed
hybrid policy heuristic can adopt any path selection algorithm
that suits its purpose. In this section we delineate various path
selection mechanisms that can be utilized in our solutions.
A. Static Path Selection Heuristics
The k-shortest path algorithm is the simplest heuristic that
can be employed in our solutions. It is a static algorithm,
in the sense that the path set for each virtual link remains
constant throughout the duration of the virtual network. In our
experiments, we used a k-shortest path algorithm adapted for
efficient path computation in communication networks [31].
B. Dynamic Path Selection Heuristics
The first dynamic path selection approach is to use a
primal dual formulation, where we first find the dual LP
associated with the relaxed primal LP by swapping variables
and constraints. The primal dual approach leads to an iterative
algorithm which raises another issue of fast convergence. Nor-
mally theoretical convergence guarantees of iterative primal
dual algorithms do not always work well in practice. That is
why we opt for the simpler static path selection algorithms in
our experiments.
The second approach for handling dynamic path selection
is to employ a column generation approach. Here instead of
solving the LP with all the flow variables at once, only a subset
of path variables is considered at each step. After solving the
LP at each step with an active set of paths, the path set is
updated by adding improved paths and removing unused ones.
This is also an iterative algorithm, however the convergence
test is usually simpler and more practical than the primal
dual approach. But an additional issue with this approach is
updating the active path set at each step using an efficient path
selection heuristic.
VII. PERFORMANCE EVA L UA T I O N
In this section, we first describe our simulation environment,
then present evaluation results. Our evaluation is aimed at
quantifying the performance of the proposed solutions to the
SVNE problem in terms of long term business profit for the
InP by maximizing revenue earned from VNs and minimizing
the penalty incurred due to substrate link failures.
114 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
TAB LE I I
SIMULATION PARAMETERS AND PERFORMANCE METRICS
Notation Description
Parameter: αPercentage of bandwidth of a substrate link
for primary flow.
Parameter: γ=λF
λVRatio of failure and VN arrival rate.
Parameter: nVNumber of VN nodes.
Parameter: kNumber of paths allowed for link embed-
ding and detours.
Metric: πAverage business profit in the long run.
Metric: ar Average acceptance ratio in the long run.
Metric: bru Average backup resource usage percentage
in the long run.
Metric: tAverage response time to a failure.
A. Simulation Environment
We implemented a discrete event simulator for SVNE
adapted from our ViNE-Yard simulator (http://www.mosharaf.
com/ViNE-Yard.tar.gz) [13], [14]. Since network virtualization
is still not widely deployed, the characteristics of VNs and
failures are not well understood yet. Specifically there are no
analytical or experimental results on the substrate and virtual
network topology characteristics, VN arrival dynamics or link
failure dynamics in network virtualization environments. As
a result, we use synthetic network topologies, and Poisson
arrival processes for VNs and link failures in our simulations.
However our choice of substrate and virtual topologies and
VN arrival process parameters are chosen in accordance with
previous work on this problem [13], [14], [29]. We used the
GNU linear programming toolkit (glpk) to solve all the linear
programs in our formulations on an Ubuntu 12.04 virtual
machine on top of Windows 7. The hardware platform used for
the simulation experiments was an Intel(R) Core(TM) i5-2410
2.3GHz processor with 8GB RAM.
The substrate network topologies in our experiments are
randomly generated with 50 nodes using the GT-ITM tool [18]
in 25 x 25 grids. Each pair of substrate nodes is randomly con-
nected with probability 0.5. The cpu and bandwidth resources
of the substrate nodes and links are real numbers uniformly
distributed between 50 and 100. We assume that both VN
requests and substrate link failure events follow a Poisson
process with arrival rates λVand λF, respectively. The ratio
γ=λF
λVis a parameter that we vary in our simulations. We use
realistic values for MTTR(l)based on failure characteristics
of real ISP networks [33] which represent InP networks in a
NVE. The MTTR values were generated using an empirical
distribution derived in [33]. In each VN request, the number
of virtual nodes is a uniform variable between 2 and 20.
The average VN connectivity is fixed at 50%. The bandwidth
requirement of a virtual link is a uniform variable between
0 and 50, and the penalty value Sj(v)for a virtual link vis
set to a uniform random variable between 2 and 15 monetary
units. In our simulations, we set α(s)=α, ∀sbelonging to the
substrate network and vary α,where0≤α≤1. For each set
of experiments conducted, we plotted the average of 5 values
for the performance metrics. The simulation parameters and
output performance metrics are shown in Table II.
TABLE III
COMPARED ALGORITHMS
Notation Algorithm Description
SVNE-Greedy-Hybrid Greedy Node Embedding with Hybrid Pol-
icy
SVNE-DViNE-Hybrid DViNE Node Embedding with Hybrid Pol-
icy
SVNE-Greedy-Proactive Greedy Node Embedding with Proactive
Policy
SVNE-DViNE-Proactive DViNE Node Embedding with Proactive
Policy
SVNE-Greedy-Blind DViNE Node Embedding with Blind Policy
SVNE-DViNE-Blind DViNE Node Embedding with Blind Policy
B. BLIND Policy Heuristic for SVNE
The BLIND policy is the simplest scheme among all the
policies, hence the name. This policy is oblivious to any
underlying structure of the problem space and the failure
pattern. Whenever a substrate link fails, the BLIND policy
simply recomputes a new link embedding for each VN affected
by the substrate link failure. Although this policy seems
simple, it has a high recovery complexity and reconfiguration
cost, since even though the substrate link failure will only
affect a localized portion of the embedding of a VN, it still
recomputes the entire embedding.
C. Comparison Method
Comparing our heuristics with previous work is difficult
since the earlier heuristics do not consider substrate resource
failures. As a result we compare our proposed hybrid and
proactive policy solutions against the base-line blind policy.
For node embedding, we use greedy [9] and DViNE heuristics
[13], [14]. In our evaluation, we have compared six algorithms
that combine different node embedding strategies [9], [13],
[14] with our proposed survivable link embedding strategies,
as shown in Table III.
D. Evaluation Results
We use several performance metrics for evaluation purposes
in our experiments. We measure the long term average profit
earned by the InP by hosting VNs. The profit function depends
on both the revenue earned from VNs by leasing resources and
penalties incurred due to service disruption caused by substrate
link failures. The penalty depends on both the amount of
bandwidth violated due to a failure and the time it takes
to recover from a failure as expressed in equations 4 and
5. We also measure the long term average acceptance ratio,
percentage of backup bandwidth usage, and response time to
failures. We present our evaluation results by summarizing the
key observations in the following subsections.
1) Acceptance ratio and Business profit: The hybrid policy
leads to higher acceptance ratio and increased business profit
in the presence of failures. Figures 2, and 3 show the long
term business profit against the percentage αof substrate link
bandwidth for primary flows, and the ratio of failure and VN
rate γ, respectively. We notice that over the range of values
for αand γ, the hybrid policy outperforms both the blind
and proactive policies. Also the hybrid policy generates the
RAHMAN and BOUTABA: SVNE: SURVIVABLE VIRTUAL NETWORK EMBEDDING ALGORITHMS FOR NETWORK VIRTUALIZATION 115
Fig. 2. Business profit against α.Fig. 3. Business profit against γ.
Fig. 4. Acceptance ratio against α.Fig. 5. Acceptance ratio against γ.
highest profit at α= 80%, whereas the proactive and blind
policies generate lesser profit with increased values of α.As
αincreases, there is less bandwidth available for backups on
the substrate link and this hinders the performance of these
policies. This also affects the hybrid policy, but it still has
better performance due to its reactive nature. The profit and
acceptance ratio for the blind policy drops more rapidly than
for the hybrid policy with increase in γas shown in Figures 3
and 5. Although, the profit for the proactive policy increases
with γ, it is still outperformed by the hybrid policy for the
range of the simulation parameters.
It should be noted that as αincreases, the business profit
initially increases, and then starts to go down. The average
profit depends on the number of virtual networks admitted
and the number of subsequent failures. As we increase α,we
have more resources to admit new virtual networks, but less
resources for survivability. So as alpha increases, the profit
gained due to new requests is gradually lost due to failure
penalties. In our experiments, alpha = 80% was the threshold
point after which the penalty due to failures dominated the
profit from new virtual network requests.
On the other hand, as αincreases, the acceptance ratio
gradually decreases, as shown in Figure 4. In our experiments,
the acceptance ratio is calculated by considering both the
number of requests admitted to the systems, and the number of
failed virtual networks. If an accepted virtual link is embedded
on a substrate link that later fails, we consider that virtual
network as a failed request. So as αincreases, the algorithms
have less resources for tolerating failures, and this leads to
lower acceptance ratio.
2) Responsiveness to Failures: The hybrid policy has faster
reaction time to failures than its counterparts. In Figure 7,
we notice that the hybrid policy reacts faster than the blind
policy when a failure occurs. When a substrate link fails, the
blind policy recomputes the entire embedding, which is time
consuming. The hybrid policy, on the other hand, only re-
routes the flows of the affected virtual links which results in
faster response time and ultimately lower penalty for the InP.
3) Bandwidth Efficiency: The hybrid policy is bandwidth
efficient. The proactive policy pre-reserves additional band-
width for each virtual link during the instantiation phase.
In turn, the hybrid policy does not pre-reserve any backup
bandwidth during the link embedding phase. It pre-selects the
candidate paths for re-routing and allocates backup bandwidth
only when an actual failure occurs. As a result, the average
bandwidth usage increases less rapidly with γcompared to
the blind policy. This is shown in Figure 6.
4) Trade-off between Survivability and Bandwidth Effi-
ciency: In our experiments, we measure survivability through
business profit, since lower survivability leads to higher
penalty, and hence lower profit. We measured profit against
α, and backup bandwidth usage against the rate of failures.
As αincreases, we have less resources for survivability. On the
other hand, as γincreases, we have more failures compared
to virtual network arrivals. Our results indicate that with more
stringent failure scenarios (higher values of αand γ), our
proposed algorithms achieve higher business profit, and steady
increase in backup bandwidth usage, compared to baseline
heuristics.
116 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
Fig. 6. Backup resource usage against γ.Fig. 7. Response time against VN size.
E. Execution Time
For the node embedding phase, we use existing algorithms
from [14], [29]. The run-time of these algorithms have been
reported there. The number of variables and constraints in each
linear program for SVNE depends on the number of virtual
links and the number of paths for each virtual link. Although
there can be an exponential number of paths for each virtual
link, we tackle this complexity by using the k-shortest path
algorithm for path selection.
Let us analyze the time complexity of the proactive pol-
icy. The linear programs in LPHPP can be solved in time
O(k|EV|)3.5L2ln Lln ln L),wherekis the number of paths
selected for each virtual link, and Ldenotes the desired input
precision in terms of the number of bits required to specify
inputs to the linear program [34]. So the total time complexity
of LPHPP is also O(k|EV|)3.5L2ln Lln ln L).
For the hybrid policy, HYBRID LP LE can be solved
in O(k|EV|)3.5L2ln Lln ln L)time, where kis the number
of paths selected for each virtual link. On the other hand
HYBRID LP BDO takes O(k(k+1)|EV|)3.5L2ln Lln ln L)
time, where kis the number of paths selected for each virtual
link, and for each detour. So the time complexity of HRP
for each event arrival is dominated by the time complexity
of HYBRID LP BDO. It should be noted that the time
complexity of all our algorithms are independent of the size
of the substrate network.
We also measured the actual run-times for each policy.
On average, to solve SVNE, the blind policy took 32.15 ms,
whereas the proactive and hybrid policies took 5.613 ms, and
3.834 ms respectively. Note that these execution times depend
on the linear programming solver (glpk), and the hardware
platform specified in section VII-A.
F. Performance on Specific VN Topologies
Up until now we have focused on arbitrary VN request
topologies in our evaluations. However, some classes of
topologies are naturally expected to be more prevalent than
others due to their use in popular applications. For example,
hub-and-spoke topologies are commonly used to connect
distributed sites to a centralized server, e.g., in content dis-
tribution networks. Virtual Private Networks (VPN), which
are virtual networks with only bandwidth constraints, usually
adhere to standard topologies like hub-and-spoke and mesh
TAB LE I V
COMPARATIVE PERFORMANCE ON HUB-AND-SPOKE TOPOLOGIES
Business Profit Acceptance Ratio Backup Usage
SVNE-G-H 0.756 0.642 0.459
SVNE-D-H 0.813 0.717 0.395
SVNE-G-P 0.662 0.576 0.835
SVNE-D-P 0.525 0.496 0.887
SVNE-G-B 0.372 0.412 0.695
SVNE-D-B 0.441 0.324 0.760
TAB LE V
COMPARATIVE PERFORMANCE ON MESH TOPOLOGIES
Business Profit Acceptance Ratio Backup Usage
SVNE-G-H 0.743 0.675 0.489
SVNE-D-H 0.876 0.777 0.391
SVNE-G-P 0.608 0.580 0.809
SVNE-D-P 0.598 0.501 0.882
SVNE-G-B 0.333 0.417 0.699
SVNE-D-B 0.448 0.321 0.708
[35]. In this section, we compare the performance of the
proposed policies on these two special topologies.
1) Hub-and-Spoke Topologies: We have used similar simu-
lation settings for this set of experiments while ensuring hub-
and-spoke topologies in the VN requests instead of random
graphs. Table IV summarizes the results of the compared
algorithms for the five performance metrics. The results pre-
sented here are for an arrival rate of 4VNs per 100 time
units, and we present all values after standard deviations of
their successive samples become negligible. The algorithms
used for this experiment are the exact same ones without any
topology-specific modifications. As seen in Table IV, relative
performance of the compared algorithms are unchanged for
hub-and-spoke topologies. Careful readers will notice that
related observations for random graph requests also hold true
in this case.
2) Mesh Topologies: Mesh topologies can be considered to
be at the opposite end of the spectrum of specific topologies.
In this case, we again use similar experimental settings and
make sure that the VN requests form full mesh topologies.
Simulation results in steady states are summarized in Table
V for similar experimental conditions. The algorithms used
for this experiment are also without any topology-specific
RAHMAN and BOUTABA: SVNE: SURVIVABLE VIRTUAL NETWORK EMBEDDING ALGORITHMS FOR NETWORK VIRTUALIZATION 117
0
5 10 15 20 25 30
Backup Resource Usage
k
SVNE-Greedy-Hybrid
SVNE-DViNE-Hybrid
SVNE-Greedy-Proactive
SVNE-DViNE-Proactive
SVNE-Greedy-Blind
SVNE-DViNE-Blind
(a)
0
5 10 15 20 25 30
Acceptance Ratio
k
SVNE-Greedy-Hybrid
SVNE-DViNE-Hybrid
SVNE-Greedy-Proactive
SVNE-DViNE-Proactive
SVNE-Greedy-Blind
SVNE-DViNE-Blind
(b)
0
5 10 15 20 25 30
Business Profit
k
SVNE-Greedy-Hybrid
SVNE-DViNE-Hybrid
SVNE-Greedy-Proactive
SVNE-DViNE-Proactive
SVNE-Greedy-Blind
SVNE-DViNE-Blind
(c)
Fig. 8. Effect of k(number of allowed paths) on SVNE policies in terms of: (a) backup resource usage; (b) acceptance ratio; and (c) business profit.
modifications. The natural dense formation of mesh topologies
require more resources than substrates can usually provide. As
a result, the mesh topologies can lead to degraded performance
in some cases. However, relative performance of the compared
algorithms are mostly unchanged.
3) Effect of k(Number of Paths Allowed): We also evaluate
our performance metrics against k(Figures 8(c), 8(b), 8(a)),
which specifies the size of the path-sets for primary and detour
flows in our path-flow based formulations. The results indicate
the superior performance of the hybrid policy against the
baseline policies. However there is some variability among
the performance metrics for different values of k, which could
suggest that a SVNE solution that continuously updates kin
order to improve performance, might be better than a static
solution that always uses the same value for k. This might
also point towards iterative approaches using primal dual or
column generation approaches.
In this set of experiments, we vary the value of kbetween
5,10,15,20,25,and30. We observe a similar trend in
performance against k, since the hybrid policy exhibits better
performance compared to the baseline policies. For business
profit, we observe that the hybrid policy with DViNE has
highest profit for value k=5, whereas, for the other values
of k, the hybrid policy with greedy node embedding has
maximum profit. For the previous set of experiments, we did
not observe any significant variation in performance due to
the selected node embedding heuristic. This implies that the
performance metrics against kare affected by the selected
node embedding mechanism. However the acceptance ratio
against kexperiments do not exhibit any variation due to the
selected node embedding heuristic.
VIII. CONCLUSION AND FUTURE WORK
In this paper, we have addressed the important aspect
of adding survivability to network virtualization in-order to
ensure seamless operation of the virtual networks embedded
on top of an InP in the presence of failures. In this regard, we
have formulated the SVNE problem to incorporate substrate
failures in the virtual network embedding problem. We have
also proposed baseline policy solutions and an efficient hybrid
policy heuristic to solve SVNE. To the best of our knowledge
this is the first attempt to add survivability to virtual network
embedding algorithms along with support for business profit
driven optimization. Moreover, our proposed heuristics can be
extended to deal with multiple link failures, and subsequently
combined with a node migration strategy [5] to solve the single
substrate node failure problem. We have shown detailed for-
mulations of our proposed SVNE policies and derived efficient
heuristics using optimization techniques. We also performed
evaluations to demonstrate the validity and importance of our
contributions.
There are many possible research directions that can be
directly pursued from our current work. Survivability in a
multi-domain NVE could raise further challenges since it
involves both intra and inter domain link failures. It would also
be interesting to extend survivability to recursive NVE, where
the first level VNs can act as InPs to a second level of VNs.
Resource allocation, protection, and restoration issues in such
recursive environments could be investigated under cross layer
optimization or network utility maximization frameworks. Our
proposed solutions to SVNE are static in the sense that at any
given solution instance we have fixed values for the α:β
proportions and k. However the revenue of the InP might
depend on complex combinations of these parameters which
points towards dynamic solutions to SVNE using control
theory or statistical machine learning techniques.
REFERENCES
[1] T. Anderson, L. Peterson, S. Shenker, and J. Turner, “Overcoming the
Internet impasse through virtualization,” Computer, vol. 38, no. 4, pp.
34–41, 2005.
[2] N. M. M. K. Chowdhury and R. Boutaba, “A survey of network
virtualization,” Comput. Netw. , vol. 54, np. 5, pp. 862–876, 2010.
[3] N. Feamster, L. Gao, and J. Rexford, “How to lease the Internet in your
spare time,” 2007 ACM SIGCOMM CCR, pp. 61–64.
[4] G. Iannaccone, C.-N. Chuah, R. Mortier, S. Bhattacharyya, and C. Diot,
“Analysis of link failures in an IP backbone,” in Proc. 2002 ACM
SIGCOMM Workshop on Internet Measurment.
[5] Y. Wang, E. Keller, B. Biskeborn, J. van der Merwe, and J. Rexford,
“Virtual routers on the move: live router migration as a network-
management primitive,” in Proc. 2008 ACM SIGCOMM, pp. 231–242.
[6] M. R. Rahman, I. Aib, and R. Boutaba, “Survivable virtual network
embedding,” in Proc. 2010 IFIP Netw., pp. 40–52.
[7] D. Andersen, “Theoretical approaches to node assignment.”
[8] J. Lu and J. Turner, “Efficient mapping of virtual networks onto a shared
substrate,” Washington University, Tech. Rep. WUCSE-2006-35, 2006.
[9] Y. Zhu and M. Ammar, “Algorithms for assigning substrate network
resources to virtual network components,” in Proc. 2006 IEEE INFO-
COM, pp. 1–12.
[10] J. Fan and M. Ammar, “Dynamic topology configuration in service
overlay networks—a study of reconfiguration policies,” in Proc. 2006
IEEE INFOCOM, pp. 1–12.
118 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 10, NO. 2, JUNE 2013
[11] A. Capone, J. Elias, and F. Martignon, “Models and algorithms for the
design of service overlay networks,” IEEE Trans. Netw. and Service
Management, vol. 5, no. 3, pp. 143–156, 2008.
[12] J. Lischka and H. Karl, “A virtual network mapping algorithm based
on subgraph isomorphism detection,” in Proc. 2009 ACM SIGCOMM
VISA, pp. 81–88.
[13] N. Chowdhury, M. Rahman, and R. Boutaba, “Virtual network embed-
ding with coordinated node and link mapping,” in Proc. 2009 IEEE
INFOCOM, pp. 783–791.
[14] N. M. K. Chowdhury, M. R. Rahman, and R. Boutaba, “Vineyard:
virtual network embedding algorithms with coordinated node and link
mapping,” IEEE/ACM Trans. Netw., vol. 20, no. 1, pp. 206–219, 2011.
[15] I. Houidi, W. Louati, and D. Zeghlache, “A distributed virtual network
mapping algorithm,” in Proc. 2008 IEEE ICC, pp. 5634–5640.
[16] M. Chowdhury, F. Samuel, and R. Boutaba, “Polyvine: policy-based
virtual network embedding across multiple domains,” in Proc. 2010
ACM SIGCOMM VISA, pp. 49–56.
[17] I. Houidi, W. Louati, W. Ben Ameur, and D. Zeghlache, “Virtual net-
work provisioning across multiple substrate networks,” Comput. Netw. ,
vol. 55, no. 4, pp. 1011–1023, 2011.
[18] Y. Xin, I. Baldine, A. Mandal, C. Heermann, J. Chase, and
A. Yumerefendi, “Embedding virtual topologies in networked clouds,”
in Proc. 2011 International Conference on Future Internet Technologies,
pp. 26–29.
[19] A. Leivadeas, C. Papagianni, and S. Papavassiliou, “Efficient resource
mapping framework over networked clouds via iterated local search
based request partitioning,” IEEE Trans. Parallel and Distributed Sys-
tems, vol. PP, no. 99, pp. 1–1, 2012.
[20] R. Ricci, C. Alfeld, and J. Lepreau, “A solver for the network testbed
mapping problem,” Proc. 2003 ACM SIGCOMM CCR, pp. 65–81.
[21] M. Hibler, R. Ricci, L. Stoller, J. Duerig, S. Guruprasad, T. Stack,
K. Webb, and J. Lepreau, “Large-scale virtualization in the emulab
network testbed,” in Proc. 2008 USENIX ATC, pp. 113–128.
[22] W. Lau and S. Jha, “Failure-oriented path restoration algorithm for
survivable networks,” IEEE Trans. Netw. and Service Management,
vol. 1, no. 1, pp. 11–20, 2004.
[23] Q. Zheng and K. G. Shin, “Fault-tolerant real-time communication in
distributed computing systems,” IEEE Trans. Parallel and Distributed
Systems, vol. 9, no. 5, pp. 470–480, 1988.
[24] K. Thulasiraman, M. S. Javed, and G. L. Xue, “Circuits/cutsets duality
and a unified algorithmic framework for survivable logical topology de-
sign in IP-over-WDM optical networks,” Proc. 2009 IEEE INFOCOM,
pp. 1026–1034.
[25] M. Kurant and P. Thiran, “Survivable MApping Algorithm by Ring
Trimming (SMART) for large IP-over-WDM networks,” in Proc. 2004
Broadband Netw., pp. 44–53.
[26] M. Kurant and P. Thiran, “Survivable routing of mesh topologies in
IP-over-WDM networks by recursive graph contraction,” IEEE J. Sel.
Areas Commun., vol. 25, no. 5, 2007, pp. 922–933, 2007.
[27] C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization:
Algorithms and Complexity, 2nd edition. Dover Publications, 1998.
[28] K. Lee and E. Modiano, “Cross-layer survivability in wdm-based
networks,” in Proc. 2009 IEEE INFOCOM, pp. 1017–1025.
[29] M. Yu, Y. Yi, J. Rexford, and M. Chiang, “Rethinking virtual network
embedding: substrate support for path splitting and migration,” ACM
SIGCOMM CCR, vol. 28, no. 2, pp. 17–29, 2008.
[30] A. Todimala and B. Ramamurthy, “Approximation algorithms for sur-
vivable multi-commodity flow problems with applications to network
design,” in Proc. 2006 IEEE INFOCOM, pp. 1–12.
[31] D. M. Topkis, “A k shortest path algorithm for adaptive routing in
communications networks,” IEEE Trans. Commun., vol. 36, no. 7, pp.
855–859, 1988.
[32] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory,
Algorithms, and Applications. Prentice Hall, 1993.
[33] A. Markopoulou, G. Iannaccone, S. Bhattacharyya, C.-N. Chuah,
Y. Ganjali, and C. Diot, “Characterization of failures in an operational
IP backbone network,” IEEE/ACM Trans. Netw., vol. 16, no. 4, pp. 749–
762, 2008.
[34] N. Karmarkar, “A new polynomial-time algorithm for linear program-
ming,” in Proc. 1984 ACM STOC, pp. 302–311.
[35] S. Raghunath, K. K. Ramakrishnan, S. Kalyanaraman, and C. Chase,
“Measurement based characterization and provisioning of IP VPNs,” in
Proc. 2004 ACM SIGCOMM IMC, pp. 342–355.
Muntasir Raihan Rahman received his B. Sc.
degree in computer science and engineering from
Bangladesh University of Engineering and Technol-
ogy in 2006, and the M. Math. degree in com-
puter science from the University of Waterloo in
2010, and is currently pursuing the Ph.D. degree
in computer science at the University of Illinois at
Urbana-Champaign. His research interests include
distributed storage, cloud infrastructure, and dis-
tributed computing theory.
Raouf Boutaba received the M. Sc. and Ph.D.
degrees in computer science from the University
Pierre & Marie Curie, Paris, in 1990 and 1994,
respectively. He is currently a Professor of computer
science at the University of Waterloo, Canada and
a Distinguished Visiting Professor at the Pohang
University of Science and Technology (POSTECH),
Korea. His research interests include control and
management of networks and distributed systems.
He has received several best paper awards and
other recognitions such as the Premier’s Research
Excellence Award, the IEEE Hal Sobol Award in 2007, the Fred W. Ellersick
Prize in 2008, the Joe LociCero Award and the Dan Stokesbury Award in
2009. He is a fellow of the IEEE.
