2010 - Stapelberg, Krzesinski - Network Re-engineering using Successive Survivable Routing

Network Re-Engineering Using
Successive Survivable Routing
D. Stapelberg and A.E. Krzesinski
Department of Mathematical Sciences
University of Stellenbosch
7600 Stellenbosch, South Africa
Email: dstapel@gmail.com, aek1@cs.sun.ac.za.
Abstract—The Spare Capacity Assignment (SCA) problem is
a constrained non-linear optimization problem which describes
how to route backup paths and configure the network links with
the least amount of backup capacity in order to be able to deploy
equivalent failure-disjoint recovery paths.
The Successive Survivable Routing heuristic provides a com-
putationally efficient approximate solution to the SCA problem
in networks subject to arbitrary failure scenarios.
This paper applies the SSR algorithm to several network
models and describes how the SSR algorithm can be used to
substantially reduce the backup backup capacity requirements
when simple topology changes are applied to the network models.
I. INTRODUCTION
Consider an MultiProtocol Label Switching Network where
the traffic is routed over a set of working Label Switched
Paths. MPLS-based recovery [11, 12, 13, 16] is intended to
effect rapid and complete restoration of traffic affected by a
fault in an MPLS network.
Network survivability includes two complementary mecha-
nisms namely survivable network design (the centralized pre-
planning of the recovery routes and spare capacity alloca-
tion for various failure scenarios) and restoration schemes
(distributed mechanisms for fault detection, fault signalling,
connection re-routing and bandwidth re-allocation).
Many models have been proposed for the efficient calcu-
lation recovery paths and to compute the minimal amount of
spare capacity that has to be allocated to each link so that
equivalent recovery paths can be deployed: see [1, 7] and the
references therein.
The Spare Capacity Assignment (SCA) problem is a con-
strained non-linear optimization problem which describes how
to route backup paths and configure the network links with the
least amount of backup capacity in order to be able to deploy
equivalent failure-disjoint recovery paths.
The remainder of the paper is organised as follows. Sec-
tion II presents a description of the SCA problem and sum-
marises the improvements that we made to the Successive
Survivable Routing (SSR) heuristic algorithm [7] for approx-
imately solving the SCA problem. Section III describes the
characteristics of the network models that were used in this
paper. Section IV describes the results produced when the
AEK is supported by grant numbers 2054027 and 2677 from the South
African National Research Foundation, Nokia-Siemens Networks and Telkom
SA Limited.
SSR algorithm was used to route backup paths for these
network models. Section V describes how the SSR algorithm
can be used to substantially reduce the backup backup capacity
requirements when simple topology changes were applied to
the network models.
II. NETWORK RESTORATION
A. The Spare Capacity Assignment (SCA) problem
The SCA problem describes how to route backup paths
and configure the network links with the least amount of
backup capacity in order to be able to deploy equivalent
failure-disjoint recovery paths. An equivalent recovery path
provides the same QoS as its working counterpart. Two routes
are failure-disjoint if in any failure scenario, at most one
of the routes fails: the recovery routes thus offer 1-to-1
protection [16]. The SCA problem for a directed network is
given by
minQ,s φ(s) (1)
where
s = max G (2)
G = QT
MU (3)
T + Q ≤ 1 (4)
QBT
= D. (5)
The objective (1) is to minimise the total cost φ(s) of backup
capacity by selection of the backup paths Q and the backup
capacity allocation s. Constraints (2) and (3) compute the
backup capacity s and the backup provision matrix G where
M is a diagonal matrix of bandwidth allocations and U is the
path failure incidence matrix.
Constraint (4) guarantees that the backup paths Q do not use
any links which might fail simultaneously with their working
paths where T is the flow tabu matrix. Constraint (5) expresses
flow conservation where B is the node link incidence matrix
and D is the route node incidence matrix. The SCA problem
is known to be NP complete. Table I presents the notation
used in the definition of the SCA problem.
B. The Successive Survivable Routing (SSR) Heuristic
Liu et al. [7] developed the SSR heuristic which provides
a computationally efficient approximate solution to the SCA

TABLE I
THE SCA PROBLEM: NOTATION
N, L, R, K Number of nodes, links, paths, failure scenarios.
Q = {(qrℓ}R×L Backup path link incidence matrix: (qk)rℓ = 1
if the backup path qr for path r in scenario k
traverses link ℓ and 0 otherwise.
M = Diag({mr})R×R Diagonal bandwidth demand matrix: mr is the
bandwidth demand of path r.
F = {fkℓ}K×L Failure link incidence matrix: fkℓ = 1 if link ℓ
fails in scenario k and 0 otherwise.
U = {urk}R×K Flow failure incidence matrix: urk = 1 iff flow
r’s working path is affected in scenario k and 0
otherwise.
T = {trl}R×L Flow tabu-link matrix: trℓ = 1 iff link ℓ should
not be used on flow r’s backup path.
D = {drn}R×N Flow node incidence matrix.
φ = {φℓ}L×1 Backup capacity cost function: φℓ is the cost of
a unit of backup capacity on link ℓ.
G = {gℓk}L×K Backup provision matrix: gℓk is the backup
capacity required on link ℓ for failure scenario k.
B = {bℓk}L×K Giveback capacity matrix: bℓk is the giveback
capacity released from link ℓ for failure sce-
nario k.
s = {sℓ}L×1 Vector of link backup capacity: sℓ is the backup
capacity required on link ℓ for any failure sce-
nario.
problem in networks subject to arbitrary failure scenarios.
The SSR heuristic addresses failure independent (state inde-
pendent) path restoration where each working path has one
failure-disjoint recovery counterpart. The SSR heuristic can be
extended to (1) state dependent (failure dependent) restoration
which uses different recovery paths to protect against different
failures, and (2) capacity giveback where the bandwidth that
was reserved for a failed route is returned to the surviving
links of the route. A description of an improved and extended
version of the SSR heuristic can be found in [5].
III. NETWORK MODELS
A. Reference network models
The eight network models presented in [7] will be referred
to as the reference network models. These models were used to
verify our implementation of the SSR algorithm. In addition,
the reference models were used to evaluate the performance
of capacity giveback and state-dependent SSR. Table II lists
the parameters of the reference network models where d is the
average node-degree.
B. Realistic network models
Several network topologies were obtained from the Rock-
etfuel project [14] and other sources of real network data.
These models will be referred to as realistic network models.
The AT&T North American network model, the EBONE
network model, the Tiscali network model, and the Australian
TABLE II
REFERENCE NETWORKS: PARAMETERS
SSR1 SSR2 SSR3 SSR4 SSR5 SSR6 SSR7 SSR8
N 10 12 13 17 18 23 26 50
L 22 25 23 31 27 33 30 82
d 4.40 4.17 3.54 3.65 3.00 2.87 2.31 3.28
TABLE III
REALISTIC NETWORKS: PARAMETERS
EBONE AT&T MCI Tiscali Telstra
N 26 31 43 48 50
L 48 65 65 101 79
d 3.69 4.19 4.19 4.21 3.16
Telstra network model were created using data from [14]. The
MCI North American network model was created using data
from [8].
As in [6] we examine POP-level (point of presence level)
topologies. Each of the realistic models was modified in two
ways. First, the POP-level representation was simplified in
cases where multiple POPs located in the same metropolitan
area were aggregated into a single node. Second, the network
topologies are subject to a minimum node-degree of two: this
is to facilitate those network recovery algorithms which require
link disjointness. Table III lists the parameters of the realistic
network models. Details concerning these models can be found
in [15].
C. The BRITE network topology generator
Several synthetic network models were generated using the
BRITE topology generation tool [4, 10]. These models are
intended to accurately reflect many aspects of the Internet.
Table IV list the parameters that must be supplied when
generating a BRITE router level topology.
The HS and LS parameters are relevant in topologies that
use heavy-tailed node-placement where the nodes are grouped
into squares of size LS on a plane of size HS. In contrast,
random node placement locates nodes at random on a plane
of size HS.
The Waxman model [17] generates a random network where
the probability P(i, j) of connecting node i to node j is given
by
P(i, j) = αe−x/(βL)
where α > 0, β ≤ 1, x is the Euclidean distance from node i
to node j and L is the maximum distance between any two
nodes.
The Barabási-Albert [2] model generates a scale-free net-
work. These networks display a power law in the frequency
distribution of the node-degrees which may arise due to (1)
incremental growth: networks are formed by the continual
TABLE IV
BRITE NETWORK GENERATION: PARAMETERS
HS and LS The size of one side of the plane, and of one side of
a high-level square
N The number of nodes in the network
model Waxman or Barabási-Albert
α Waxman parameter for node interconnect probability
β Waxman parameter for node interconnect probability
node placement random or heavy-tailed
m the number of links per new node (node-degree)
growth type all or incremental
BWDist constant, uniform, exponential or heavy-tailed
MaxBW, MinBW the maximum and minimum bandwidth values

TABLE V
BRITE NETWORKS: PARAMETERS
N10W N10B N20W N20B N30W N30B
N 10 10 20 20 30 30
L 34 30 40 55 60 119
d 6.80 6.00 4.00 5.50 4.00 7.93
addition of new nodes, and (2) preferential connectivity: new
nodes connect to existing nodes that are highly connected,
which form hubs.
The probability P(i, j) of connecting node i to node j in
the Barabási model is given by
P(i, j) = dj/
k∈V
dk
where dj is the out-degree of node j and V is the set of nodes
that have previously joined the network.
The number m of links per new node determines the
minimum number of connections that a new node makes when
it connects to the network. The number N of nodes determines
the size of the synthetic network model. City populations have
been observed to follow a power law [18]. We use a Pareto
distribution to create a set of city populations so that the link
bandwidth and distribution parameters in Table IV need not be
specified. Table V lists the parameters of the Waxman (N10W,
N20W and N30W) and the Barabási (N10B, N20B and N30B)
models.
IV. SSR RESULTS FOR LINK FAILURE SCENARIOS
A. SSR results for the reference network models
We first apply the SSR algorithm to the reference network
models.
Let B denote the total capacity of all the links in the
network. The SSR algorithm computes an approximate value
for the least amount sℓ of spare capacity on each link ℓ that is
needed to configure equivalent recovery paths. Let S denote
the total backup (spare) capacity. The ratio S/B expressed as
a percentage denotes the effectiveness of the backup paths.
The following variants of the SSR algorithm were evaluated:
(1) SSR, (2) SSR with capacity giveback, (3) state-dependent
SSR, and (4) state-dependent SSR with capacity giveback.
Table VI presents the network backup capacity requirements as
computed by the four variants of the SSR algorithm. The table
shows that enhanced (SD+GB) SSR yields on average a 12%
reduction in the backup capacity requirement as compared to
standard SSR. No results are presented for the state-dependent
simulations of SSR8. The size of the network and number
TABLE VI
REFERENCE NETWORKS: BACKUP CAPACITY REQUIREMENTS
% SSR 43.7 54.5 47.5 44.1 61.0 68.6 66.4 53.5
% GB 42.3 53.8 47.5 43.8 58.3 66.8 59.9 47.6
% SD 36.6 46.4 39.5 35.7 58.3 65.4 65.4 -
% SD+GB 36.6 45.5 38.9 35.7 55.4 63.6 62.0 -
TABLE VII
REALISTIC NETWORKS: BACKUP CAPACITY REQUIREMENTS
AT&T MCI EBONE Tiscali Telstra
% SSR 67.2 77.6 86.8 94.7 133.0
% GB 65.0 76.8 86.0 89.1 129.8
% SD - - 77.7 90.9 -
% SD+GB 57.8 67.7 76.8 - 121.7
of states to be maintained in the simulation is too large to
compute the results in a reasonable amount of time.
The network SSR7 which shows the most giveback im-
provement has the lowest average node-degree of all the
reference networks. Networks with a low node-degree have
limited path diversity. In this case the working paths share
many common links so that in any failure scenario, if capacity
giveback is used so that the failed routes return their bandwidth
to the surviving links, then this bandwidth can be better utilised
by the surviving routes.
B. SSR results for realistic network models
We next apply the SSR algorithm to the realistic network
models. Table VII presents the network backup capacity
requirements as computed by the four variants of the SSR
algorithm. Note that if one SSR replication cannot be com-
pleted after 5000 minutes, the simulation is aborted. In the
cases where at least one SSR replication could be completed,
we use the one result obtained. If there is no result for the
given network and SSR algorithm combinations, the table will
have a dashed entry to indicate no result.
Table VII shows that enhanced (SD+GB) SSR yields on
average a 12% reduction in the backup capacity requirement
as compared to standard SSR.
C. SSR results for BRITE synthetic networks
We next apply the SSR algorithm to the BRITE network
models. Table VIII presents the network backup capacity
requirements as computed by the four variants of the SSR
algorithm. The table shows that enhanced (SD+GB) SSR
yields on average a 30% reduction in the backup capacity
requirement as compared to standard SSR.
V. USING SSR IN NETWORK RE-ENGINEERING
In the remainder of this paper we will focus on the SSR6
reference network model and the EBONE, AT&T and MCI
realistic models and the N10B and N20B models. The SSR6
and the N20B models were chosen since they had the largest
backup capacity requirement of the reference and the BRITE
models respectively. The EBONE network model was chosen
TABLE VIII
BRITE NETWORKS: BACKUP CAPACITY REQUIREMENTS
N10W N10B N20W N20B N30W N30B
% SSR 51.8 56.7 54.2 62.4 52.0 52.4
% GB 46.4 56.7 52.5 62.4 50.6 52.4
% SD 32.1 33.3 44.6 49.4 41.7 34.7
% SD+GB 32.1 33.3 42.9 49.1 38.8 34.7

TABLE IX
REFERENCE NETWORKS: BACKUP CAPACITY REQUIREMENTS SORTED
d 2.31 2.87 3.00 3.28 3.54 3.65 4.17 4.40
% SSR 66.4 68.6 61.0 53.5 47.5 44.1 54.5 43.7
because, although it has the third largest backup capacity
requirement of the realistic models, it has a relatively small
number of nodes and links which made the analysis of this
network easier. The AT&T and MCI networks were chosen
for the same reason: they have a relatively small number of
nodes and links.
The question arises as to what are the major factors that
determine the effectiveness of the recovery paths.
1) Table IX shows that in the case of the reference net-
works, the backup requirements generally decrease with
increasing average node-degree.
2) Table X shows that in the case of the three realistic
models (admittedly a small sample) the backup capacity
requirement is not solely determined by the average
node-degree.
3) As far as the BRITE models are concerned, the backup
capacity requirements for the random network models
(Waxman) are independent of the average node-degree;
the backup capacity requirements for the scale-free
network models (Barabási) decrease with increasing
average node-degree.
The SSR results presented above require further investi-
gation regarding the network parameters and their resulting
backup capacity requirements. It is of concern that the in-
herent properties of the realistic network models have such a
significant impact on the performance of the SSR algorithm.
Table X presents the backup capacity requirements, the
average node-degree, the standard deviation (SD) of the node-
degree and the maximum node-degree (MD) for the six net-
works. The EBONE and MCI networks have large maximum
node-degrees and have large backup requirements. However,
the N20B network has an even larger maximum node-degree,
yet its backup capacity requirement is the second lowest.
The evidence is mixed, but it suggests that both the average
node-degree and the maximum node-degree have an effect on
the backup capacity requirement.
A. EBONE Re-Engineering
The EBONE network model contains two hubs: nodes 8
and 9 have 8 and 7 incident links respectively. Eight out of
the 26 nodes have the minimum required node-degree of 2.
TABLE X
NODE-DEGREE DEVIATION
SSR6 EBONE AT&T MCI N20B N10B
% SSR 68.7 86.8 67.2 77.6 62.4 52.7
d 2.87 3.69 4.19 4.37 5.5 6
SD 0.8 1.7 2.3 3.2 3.5 1.6
MD 5 8 9 15 13 8
TABLE XI
HUBBED EBONE NETWORK: PROPERTIES AND RESULTS
Original Hubbed ∆
% SSR 86.8 45.8 -41.1
d 3.69 3.69 0.00
SD 1.71 1.35 -0.37
MD 8 8 0
The EBONE network model was modified to yield a more
preferentially connected (hubbed) network as in [9]. The mod-
ified network has the same number of nodes and links, but 8
links were moved to obtain a more preferentially connected
(hubbed) network. Nodes 22 and 24 were chosen as additional
hubs to which the links were relocated. After these changes, all
the nodes have a node-degree of 3 or more. Details concerning
the link changes can be found in [15].
The SSR algorithm was run on the hubbed EBONE network
model. Table XI compares the results for the original EBONE
network and the hubbed EBONE network. The relocation of 8
links leads to a 41% reduction in the required backup capacity.
The node-degree standard deviation is reduced by 0.37. The
maximum node-degree is unchanged.
B. SSR6 Re-Engineering
The same approach was applied to the SSR6 network model.
The SSR6 model contains 3 hubs: nodes 6, 11 and 16. The
modified network has the same number of nodes and links. Six
links were moved. Details concerning the link changes can be
found in [15].
The SSR algorithm was run on the hubbed SSR6 network
model. Table XII compares the results for the original SSR6
network and the hubbed SSR6 network. The relocation of 6
links leads to a reduction of only 10% in the required backup
capacity. The node-degree standard deviation increased by
0.39. The maximum node-degree increased by 1. Note that
in the original SSR6 model only 7 of the 23 nodes have the
minimum required node-degree of 2. Due to the restriction
of maintaining the same number of links in the hubbed SSR6
network, the modified network has 12 nodes with the minimum
required node-degree of 2.
We now augment the hubbed modification by increasing the
minimum node-degree for all nodes to 3. This was done by
moving 3 links and adding 2 new links. Details concerning
the link changes can be found in [15].
The SSR algorithm was run on the augmented SSR6 net-
work model. Table XIII compares the results for the original
SSR6 network and the augmented SSR6 network. The aug-
mented network model yields a 32% reduction in the required
TABLE XII
HUBBED SSR6 NETWORK: PROPERTIES AND RESULTS
Original Hubbed ∆
% SSR 68.6 58.6 -9.9
d 2.87 2.87 0.00
SD 0.75 1.14 0.39
MD 5 6 1

TABLE XIII
AUGMENTED SSR6 NETWORK: PROPERTIES AND RESULTS
Original Augmented ∆
% SSR 68.6 36.6 -32.0
d 2.87 3.04 0.17
SD 0.75 0.21 -0.54
MD 5 4 -1
backup capacity as opposed to the 10% improvement in our
first attempt at re-engineering the SSR6 network.
C. MCI Re-Engineering
We now apply the minimum node-degree recommendation
of 3 to the MCI network model. The MCI model has 3
hubs: nodes 6, 9 and 16 have 15, 14 and 10 incident links
respectively. Nine links were moved: all the nodes now have
a minimum node-degree of 3. Details concerning the link
changes can be found in [15].
The SSR algorithm was run on the hubbed MCI network
model. Table XIV presents the results of the original MCI
network and the augmented MCI network model. The changes
delivered a 27% reduction in the backup capacity requirement.
The original network hubs were not significantly modified,
with one link being added to hub node 9. The node-degrees
of hub nodes 6 and 10 were not changed. The largest improve-
ment in the performance of the SSR algorithm is obtained by
increasing the minimum node-degree from 2 to 3.
D. AT&T Re-Engineering
We finally apply the minimum node-degree of 3 to the
AT&T network model. The AT&T model has 2 hubs: nodes 14
and 15 have 9 and 8 incident links respectively. Twelve links
were moved. All nodes now have a node-degree of 3; nodes 14
and 15 now have 15 and 14 incident links respectively. Details
concerning the link changes can be found in [15].
The SSR algorithm was run on the augmented AT&T
network model. Table XV compares the results for the orig-
inal AT&T network and the augmented AT&T network. The
changes resulted in a 16% reduction in the required backup
capacity.
E. BRITE Re-engineering
The N20B network has 20 nodes of which only 3 have the
minimum required node-degree of 2. We therefore perform
similar modifications to the BRITE N10B and N20B models.
Tables XVI and XVII present the results for the augmented
N10B and N20B models respectively.
TABLE XIV
AUGMENTED MCI NETWORK: PROPERTIES AND RESULTS
% SSR 77.6 50.4 -27.2
d 4.73 4.73 0.00
SD 3.23 2.85 -0.38
MD 14 15 1
TABLE XV
AUGMENTED AT&T NETWORK: PROPERTIES AND RESULTS
% SSR 67.2 50.8 -16.4
d 4.19 4.19 0.00
SD 2.28 2.75 0.47
MD 8 15 7
F. Summary
Table XVIII summarises the improvement in SSR backup
capacity requirements for the six networks under investigation.
The improvements obtained by network re-engineering in most
cases substantially exceed the SSR SD+GB results for im-
provement in required backup capacity. In the case of the two
BRITE synthetic network models, the improvements obtained
by network re-engineering in falls short of the improvements
obtained from SSR SD+GB.
The improvements can be explained in terms of how SSR
operates. The backup path is selected using the OSPF algo-
rithm, with the incremental backup capacity being the link
cost. If each node has a minimum node-degree of 2, then the
routing options are limited. If each node has a minimum node-
degree of 3, more options are available for the routing in the
network to minimize the backup capacity cost. Working and
backup paths are link-disjoint. This means that the selection
of links on 2-connected nodes are restricted to the remaining
link on the node. A 3-connected node, even after one of the
links is disabled, can select between the two remaining links.
VI. CONCLUSIONS
This paper applies the Survivable Routing (SSR) heuristic as
a basis for a link disjoint failure recovery scheme. The SSR
algorithm was initially tested [7] on a set of reference net-
works. We developed several realistic network models based
on data contained in [14]. The SSR heuristic does not perform
as well on these realistic network models. We investigated the
properties of the realistic network models, and discovered that
we could gain a significant reduction in the backup capacity
requirement by enforcing a minimum node-degree of 3 for all
nodes in the network models under investigation.
TABLE XVI
AUGMENTED N10BNETWORK: PROPERTIES AND RESULTS
Original Hubbed ∆
% SSR 56.7 43.3 -13.3
d 6.00 6.00 0.00
SD 1.63 1.63 0.00
MD 2 2 0
TABLE XVII
AUGMENTED N20BNETWORK: PROPERTIES AND RESULTS
Original Hubbed ∆
% SSR 62.4 65.03 2.68
d 5.50 5.50 0.00
SD 3.49 3.75 0.26
MD 13 16 3

TABLE XVIII
BACKUP CAPACITY REDUCTION: AUGMENTATION VS. SD + GB
∆ SSR6 EBONE AT&T MCI N10B N20B
AUG % SSR -32.0 -41.1 -16.4 -27.2 -13.3 2.70
SD+GB % SSR -7.3 -13.0 -14.0 -12.8 -23.4 -13.3
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Dieter Stapelberg obtained the MSc degree in Computer Science from the
University of Stellenbosch, South Africa.
Anthony Krzesinski is a Professor of Computer Science at the University
of Stellenbosch, South Africa.

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