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Proceedings ArticleDOI

Performance evaluation of pre-computation algorithms for inter-domain QoS routing

08 May 2011-pp 327-332
TL;DR: Different algorithms for QoS routing based on pre-computation based on heuristic solutions are investigated, finding the ID-MEFPA heuristic is the most appropriate with the lowest computation complexity and a success rate very close to the exact algorithm.
Abstract: Inter-domain QoS routing is a very challenging problem area. This problem combines the complexity of QoS routing, with the limitations of inter-domain routing, such as domain heterogeneity and information confidentiality. The pre-computation offers a very promising solution for addressing this problem. Although the pre-computation scheme has been investigated in several previous studies for a single routing domain, applying pre-computation on an inter-domain level is not straightforward and necessitates deeper investigation. In this work, we study different algorithms for QoS routing based on pre-computation. First, we investigate an exact algorithm. This algorithm provides an optimal solution for the QoS routing problem. However, its application in large scale networks is not always practical. Second, heuristic solutions are also investigated in this work. Particularly, a detailed study of the ID-MEFPA and the ID-PPPA heuristics is provided. Analytical studies and extensive simulations confirm that the exact algorithm achieves the best success rate, but has a very high computational complexity. The ID-MEFPA heuristic has a lower complexity and provides a success rate always close to the exact algorithm. When inter-domain connectivity is high, the ID-PPPA heuristic is the most appropriate with the lowest computation complexity and a success rate very close to the exact algorithm.

Summary (2 min read)

Introduction

  • The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
  • The authors study different algorithms for QoS routing based on pre-computation.
  • The ID-MEFPA heuristic has a lower complexity and provides a success rate always close to the exact algorithm.
  • These applications require more and more extensive and varied quality of service (QoS) guarantees.

II. THE INTER-DOMAIN QOS ROUTING PROBLEM

  • Inter-domain QoS routing, also known as inter-domain multi-constraint routing, consists of computing a path subject to multiple QoS constraints between a source and a destination node of a multi-domain network.
  • As the operators can be in competition, information about the internal topology or the available resources in the network is confidential.
  • Many extensions for BGP are proposed to support QoS routing [7]-[8].
  • When handling QoS requests with delay constraints, the first phase may precompute feasible paths for a wide range of possible delay constraints, while the second phase just needs to select a suitable path from the pre-computed set, i.e., one that satisfies the particular delay constraints of the request.
  • Work in [2] proposes a precomputation based algorithm to solve the ID-MCP problem.

III. PRE-COMPUTATION ALGORITHMS FOR INTER-DOMAIN QOS ROUTING

  • The authors investigate different pre-computation algorithms for inter-domain QoS routing.
  • Precisely, the authors detail the operations performed by the exact pre-computation algorithm pID-MCP [2]-[3], their algorithm ID-PPPA proposed in [1], and their novel pre-computation algorithm, named ID-MEFPA.
  • Note that these pre-computation algorithms rely on a distributed architecture, such as the PCE architecture.
  • These algorithms consist of two phases: an offline phase and an online phase.
  • In the second phase, the algorithms attempt to compute an end-to-end path by combining the paths pre-computed in each domain.

A. The offline phase

  • This phase is executed in each domain separately.
  • A low complexity of this phase enables to cope with a dynamic change in the network state information since it allows domains to rapidly pre-compute new valid paths.
  • Therefore, ID-PPPA executes the Dijkstra algorithm m times per border node.
  • This complexity is very high comparing with that of their proposed algorithms ID-MEFPA and ID-PPPA.

B. The online phase

  • This phase is triggered upon the reception of a QoS request.
  • When receiving a QoS request, the service provider computes the best domain sequence that links the source and the destination domain according to the cooperation policy [9].
  • Note that, without loss of generality, the authors rely on backward computation according to the PCE architecture.
  • When receiving a VSPH, an intermediate domain combines the paths in the VSPH with the internally pre-computed paths.
  • Hence, the complexity of combining the pre-computed paths with the received paths at the level of the entry border node n1 is in O(αkBk+1).

IV. SIMULATION AND ANALYSIS

  • The authors evaluate the performance of the precomputation algorithms ID-PPPA, pID-MCP, and their novel algorithm ID-MEFPA.
  • The LatticeFM(25,3) and LatticeSL(25,3) topologies allow us to evaluate the effect of inter-domain connectivity on their algorithms.
  • Figures 2, 3 and 4 illustrate the variation of the success rate according to the strictness of the QoS constraints in the LatticeSL(25,3), LatticeFM (25,3) and SYM-CORE topologies, respectively.
  • Comparing these three figures illustrates the effect of inter-domain connectivity on the path quality for each algorithm.
  • In LatticeSL(25,3) and SYM-CORE topologies the quality of paths computed by ID-MEFPA is slightly better than that of ID-PPPA.

V. CONCLUSION

  • The authors have investigated and evaluated performance of several pre-computation algorithms for interdomain QoS routing.
  • These algorithms rely on a distributed architecture, such as the PCE architecture, which allows domain confidentiality to be preserved.
  • The pID-MCP is an exact algorithm and has the best success rate.
  • The complexity of this algorithm in its offline phase is very high.
  • Besides, the complexity of the online phase of ID-PPPA and ID-MEFPA is lower than that of pID-MCP.

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Performance Evaluation of Pre-computation Algorithms
for Inter-Domain QoS Routing
Ahmed Frikha, Samer Lahoud
To cite this version:
Ahmed Frikha, Samer Lahoud. Performance Evaluation of Pre-computation Algorithms for Inter-
Domain QoS Routing. International Conference on Telecommunications (ICT), May 2011, Ayia Napa,
Cyprus. pp.327 - 332, �10.1109/CTS.2011.5898944�. �hal-00642317�

Performance Evaluation of Pre-computation
Algorithms for Inter-Domain Qo S Routing
Ahmed Frikha and Samer Lahoud
University of Rennes 1, IRISA, 35042 Rennes Cedex, France
Email:{afrikha,slahoud}@irisa.fr
Abstract—Inter-domain QoS routing is a very challenging
problem area. This problem combines the complexity of QoS
routing, with the limitations of inter-domain routing, such as
domain heterogeneity and information confidentiality. The pre-
computation offers a very promising solution for addressing
this problem. Although the pre-computation scheme has been
investigated in several previous studies for a single routing
domain, applying pre-computation on an inter-domain level is
not straightforward and necessitates deeper investigation. In this
work, we study different algorithms for QoS routing based on
pre-computation. First, we investigate an exact algorithm. This
algorithm provides an optimal solution for the QoS routing
problem. However, its app lication in large scale networks is not
always practical. Second, heuristic solutions are also investigated
in this work. Particularly, a detailed stud y of the ID-MEFPA
and the ID-PPPA heuristics is provided. Analytical studies and
extensive simulations confirm that the exact algorithm achieves
the best success rate, but has a very high computational com-
plexity. The ID-MEFPA heuristic has a lower complexity and
provides a success rate always close to the exact algorithm. When
inter-domain connectivity i s high, the ID-PPPA heuristic is the
most appropriate with the l owest computation complexity and a
success rate very close to the exact algorithm.
I. INTRODUCTION
Diverse new applications such as multimedia data transfer,
telephony, and video broadcast are becoming more com mon
over wide area networks. These applications require m ore
and more extensive and varied quality of service (QoS)
guaran tees. Providing QoS in terms of p ropagation time, loss
rate, bandwidth or jitter to these a pplications over a multi-
domain network is a very challenging problem area. Most
research on QoS routing has focused on routing within a
single domain. Ad dressing this problem in an inter-domain
context is also strategic as it is required to ensure the end-
to-end QoS guarantees. In this case the problem becomes
more c omplex because of the domain h e te rogeneity and infor-
mation confidentiality. Conten t providers, network providers
or transport network operators, man age different domains or
autonomous systems and implement heterogeneous policies
that consolidate their economic in te rests and confidentiality
clauses. Hence, ensuring end-to-en d QoS guarantees is a very
hard task. Besides, selectin g a route that meets the r e source
needs of such applications is more difficult in an inter-
domain level because of the number of nodes involved in the
computation. Conseque ntly, the route selection requir e s more
978-1-4577-0024-8/11/
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26.00
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2011 IEE E
computational time and the response time become longer.
There are two alternatives for path computation. The first is
the on-demand computation which consists in the computation
of a path which satisfies the c onstraints upon the reception
of the QoS request. The second variant is based on pre-
computation. Pre-computation consists in computing a set of
suitable pa ths a priori for a pre-determined set of possible
constraints. These constraints illustrate different classes o f
service of application requirements. Then, w hen a QoS request
arrives it attempts to rapidly provide a feasible solution.
This alternative provides a rapid response time for the path
provisioning.
In this paper, we f ocus on the pre-computation sche me for
inter-domain QoS routing. Different QoS routing algorithms
based on pre-computation are studied in this paper. First, the
inter-domain pre-computation algorithm pID-MCP [2]-[3] is
investigated in this paper. pID-MCP is an exact a lgorithm.
This algorithm was reported to be the most efficient in term
of success rate since it can find a feasible path for each QoS
request, whenever such path exists. However, the computa-
tional complexity of this algorithm is very high . This limits its
application is large scale networks. Second, heuristic solutions,
such as the ID- PPPA [1] algorithm, are also investigated in this
work. In o ur previous work [1], we showed th at ID-PPPA is a
very fast algorithm and has a high success rate. This algorithm
is suitable for high sp eed networks. The MEFPA a lgorithm
[4] was reported to be th e most efficient intra-domain pre-
computation algorithm. In this p aper, we extend MEFPA for
an inter-domain routing level; we name it ID-MEFPA. O ur
studies confirm that pID-MCP has the best success rate, but
has a very high comp utational complexity compared to the
heuristic algorithms. ID-MEFPA has a lower computational
complexity and has a success rate very close to that of pID-
MCP. ID-MEFPA always outperforms ID-PPPA. However,
when inter-domain connectivity is high, ID-PPPA presents
the most appropriate solution with the lowest computational
complexity and a success ra te very c lose to the exact algorithm
pID-MCP.
The rest of the paper is organized as follows. In section 2,
a detailed description of the inter-domain QoS routing prob-
lem is pre sented. Section 3 presents several pre-computation
algorithm s and gives a detailed analysis of their complexities.
Simulation results are presented in detail in section 4. Finally,
conclusions are given in section 5.

II. THE INTER-DOMAIN QOS ROUTING PROBLEM
Inter-domain QoS r outing, also known as inter-dom ain
multi-con stra int routing, consists of computing a path subject
to multiple QoS constraints between a source and a destination
node of a multi-domain network. Computing such a path
requires knowledge of the topology of each d omain in the
network, as well as the QoS metrics on network links. As
the operators can be in competition, in formation about the
internal topology or the available re sources in the network
is confidential. This com plicates the computation especially
when using a centralized method.
Let us introduce the requisite notation to formally define the
problem. Let G(N, E, D) denote a network of D domains,
N is the set of nodes and E the set of links. Let m be
the number of QoS constraints. Note that, in our study, we
consider only additive m etrics, such as cost and d e la y, withou t
loss of generality. In fact, multip lica tive metrics, such as loss
rate, can be translated into additive metrics using the logarithm
function; and bottleneck m etrics, such as bandwidth, can be
resolved by omitting a ll links which violate the constraints
and then computing the path on the residual graph. An m-
dimensional weight vector is associated with ea c h link e E.
This vector consists of m non-negative QoS weights w
i
(e),
i = 1..m. Let p be a path in the graph G(N, E, D) and w
i
(p)
be the weight o f p corresponding to the metric i. As metrics
are additive, w
i
(p) is given by the sum of the i
th
weights of
the component links o f path p: w
i
(p) =
P
e
j
p
(w
i
(e
j
)). Let
W
(p) = (w
1
(p), w
2
(p), ..., w
m
(p)) denote the weigh t vector
of the path p.
Definition 1
Given a source node s and a destina tion node d and a set of
constraints given by the c onstraint vector
C
= (c
1
, c
2
, .., c
m
),
the Inter-Domain Multi-Constraint Path (ID-M CP) compu-
tation prob le m consists of finding a path p which satisfies
w
i
(p) c
i
, i 1..m. Such a path p is c alled a feasible path.
The ID-M CP prob le m is NP-hard [5 ] and ma y have zero,
one, or multiple solutions. A feasible path p is called non-
dominated if the re does not exist a path p
which satisfies:
(1) w
i
(p
) w
i
(p), i 1..m and (2) j 1..m for which
w
j
(p
) w
j
(p). To speed up the computation, dominated
paths can be discarded from the computation search space
of the QoS routing a lgorithms without affecting their perf or-
mance, accor ding to [6].
Currently, the inter-domain routin g protocol is BGP. This
protocol cannot solve the I D -MCP pr oblem sinc e it does not
take into account QoS constraints. Many extensions for BGP
are proposed to suppo rt QoS routing [7]-[8]. However, the
QoS c apabilities of these propositions remain limited. Solving
the ID- MCP problem using a centralized method is a very
complex prob le m, for the aforementioned reaso ns. Therefo re,
the research community has recently been exploring the use
of distributed a rchitectures to solve this problem, such as the
PCE (Path Computation Eleme nt) architecture [9]. Distributing
the computation over domains preser ves c onfidentiality ac ross
domains and solves the scaling problem. To our kn owledge,
few works have been proposed to solve the ID-MCP pr ob-
lem using distributed methods. ID-MCP [10] is a distributed
algorithm which extends the exact algorithm SAMCRA [6]
to an inter-domain level to solve the ID-MCP problem. The
drawback of this algorithm is its high complexity. Also,
work in [11] proposes a promising distributed solution with
crankb a ck mechanisms for inter-domain rou ting. However this
solution cannot take into account more than one QoS me tric.
Besides, these solutions are based on an on-demand computa-
tion scheme which presents some serious limitations with the
emerging applications in the Internet. As explained, the ID-
MCP problem is NP-hard, consequently, the performance of
the on-demand routing alg orithms in terms of response time
are severely affected.
In this work, we focus on the pr e-computation scheme to
solve the ID-MCP problem while speeding up the r esponse
time. The pre-computation proc eeds in two phases: It p repares
in advance a set paths satisfying predetermined QoS r equests
in a first ph a se. Then, at the rec eption a of QoS request,
it seeks to rapidly provide a feasible path among the pre-
computed paths. Ideally, the second pha se ne eds only to select
one of the pre-computed solutions. However, some additional
computations may be performed. For instance, when handling
QoS re quests with delay constraints, the first ph ase may pre-
compute feasible paths for a wide range of possible delay
constraints, while the secon d phase just needs to select a
suitable path from the pre-co mputed set, i.e., one that satisfies
the particular delay constraints of the request. The execution
time of the second phase has an imm e diate impact on network
performance; hence, it is highly desirable to keep its compu -
tational complexity as low as possible. In the above example,
the less time is consumed in finding the proper path, the less
time is spent in establishing the new request.
Up to now, most research on inter-domain QoS routing
are based on an on-demand computation scheme, but rarely
on a pre-computation scheme. Work in [2] proposes a pre-
computation based algorithm to solve the ID-MCP problem.
This algorith m, named pID-MCP, relies on a distributed ar-
chitecture. However, its response time remains high, and its
applicability is not practical because of the high complexity
of its pre-computation phase.
III. PRE-COMPUTATION ALGORITHMS FOR INTER-DOMAIN
QOS ROUTING
In this section, we investigate different pre-computation al-
gorithms for inter-domain QoS routing. Precisely, we detail the
operations performed by the exact pre-computation algorithm
pID-MCP [2]-[3], our algorithm ID-PPPA proposed in [1], and
our novel pre-computation a lgorithm, named ID-MEFPA. Note
that these pre-computation algorithms rely o n a distributed
architecture , such as the PCE ar c hitecture. These alg orithms
consist of two phases: an offline phase and an online phase.
In the offline phase, the algorithms pre-compute a set of QoS

paths in each domain separately and satisfying a set of p re-
determined QoS requests. In the second phase, the algorithms
attempt to compute an end-to-end path by combining the paths
pre-computed in each domain.
A. The offline phase
This phase is executed in each domain separately. Each
algorithm pre-computes a set of paths from each border node
of the considered domain toward the other nodes in the
domain as well as the entry bor der nodes of the neighb or
domains. These paths will be used later at the onlin e phase
to compute an end-to-end pa th. Note that after an eventual
change in the network state, the pre-computed pa ths may be
not valid. Therefore, executing th e offline phase periodically
or using a ne twork state-depen dent threshold is required in
each domain. A low complexity of this phase en a bles to
cope with a d ynamic change in the network state information
since it allows domains to rapidly pre-compute new valid
paths. T herefore, in the following we investigate the operations
performed by each algorithm during this phase, and compare
their offline comp lexity.
For now, let us introduce the requisite notation. Let D
k
be
the considered domain, B the number of border nodes of D
k
,
n
1
a border node of D
k
, n
2
a node of D
k
or an entry border
node of a neighbor d omain, and m the number of the QoS
metrics. Operations performed by each algorithm during this
phase are detailed in the following.
1) The ID-PP PA algorithm: ID-PPPA pre-computes m
shortest paths between each pair of nod es (n
1
, n
2
). Each
shortest path minimizes a single QoS metric and is called
primary path. Hen ce, from each border n ode of D
k
, ID-PPPA
computes m shortest path trees. Each sho rtest path tree, also
called a primary path tree, is computed using the D ijkstra a l-
gorithm and considering a single w eight component w
i
, where
i 1..m. Therefore, ID-PPPA executes the Dijkstra algorithm
m times per border node. For one border node, ID-PPPA is in
O(m(N log(N ) + E)). Co nsequently, the complexity of th e
offline phase of ID-PPPA is in O(Bm(N log(N ) + E)).
2) The ID-MEFPA algorith m : ID-MEFPA is our novel pro-
posed algorithm. It is based on the MEFPA pro posal [4]. ID-
MEFPA computes multiple shortest paths between each pair of
nodes (n
1
, n
2
). Each shortest path minimizes a different linear
weighting given by g
a
(e) =
P
m
i=1
a
i
w
i
(e) where w
i
(e) is the
i
th
weight of link e and
a
= (a
1
, a
2
, .., a
m
) is a c oefficient
vector. Therefore, ID-MEFPA exectutes at each entry border
node n
1
the Dijkstra algor ithm and considering the linear
weighting g
a
. An ideal algorithm would use a con tinuous
variation of
a
in order to cover all the coefficient values.
However, a practical a lgorithm cannot continuously vary
a
,
therefore ID-MEFPA uses V vectors
a
unifor mly distributed
in S
m
, w here S = {
0
(b1)
,
1
(b1)
, ..,
b1
(b1)
}; b is a parameter
of the algorithm.
The complexity of ID-MEFPA depends on the parame te r b
and the number of constraints m. For one border node, ID-
MEFPA is in O (V (N log(N) + E)) corresponding to V times
the complexity of a Dijkstra algorithm, where V = C
m1
b+m2
.
The global com plexity is in O(BV (N log(N ) + E)).
3) The pID-MCP a lgorithm: pID-MCP is an exact pre-
computation algorithm; it finds a feasible path, whenever such
a path exists. It p re-computes all feasible pa ths between each
pair of nodes (n
1
, n
2
) by executing the SAMCRA alg orithm at
each entry border node n
1
of D
k
. T his computation takes into
account a set of C
v
predetermined class of service expressed
by a set of constraint vectors.
The drawback of this algorithm is its high computational
complexity. In fact, the co mplexity of executing pID-MCP
in each domain corresponds to the complexity of executing
SAMCRA at each border node of the domain for each class of
service. He nce, the complexity of pID-MCP in its offline phase
is in O(BC
v
(K
max
N log(K
max
N) + K
3
max
mE)), where
K
max
= min(exp(N 2)!,
Q
m
i=1
c
i
max
j
c
j
) [12]. T his complexity
is very high comparing with that of our proposed algorithms
ID-MEFPA and ID-PPPA.
B. The online phase
1) Concepts: This phase is triggere d upon the reception of
a QoS request. T he algorithms attempt to compute an end-
to-end path by combining the pre-computed paths in each
domain. Wh en receiving a QoS request, the service provider
computes the best domain sequence that links the source and
the destination domain accord ing to th e cooperation policy
[9]. The end-to-end path computation starts at the destina tion
domain toward the source domain following the selected
domain sequen c e. Note that, without loss of g enerality, we rely
on backward computa tion according to the PCE architectu re.
First, the destination domain selects the pr e-computed paths
that lead to the up -stream domain following to the selected
domain sequence. Then, these paths will be sent to the up-
stream do main using a novel compact structur e named VSPH
(Virtua l Shortest Path Hierarch y
1
). This structure contains only
the end nodes o f the paths (th e destination node and the entry
border nodes of the up-stream domain) as well as the weight
vector of each path. This structure allows the confide ntiality
of the domains to be preserved. When receiving a VSPH, an
intermediate domain combines the paths in the VSPH with
the internally pre-computed paths. Then, it selects the feasible
paths by comparison with the constraint vector, computes a
new VSPH an d sends it to the up-stream domain. Finally, the
computation is stopped whe n a feasible path linking the source
and destination is found, or when no feasib le path is found.
In this case, the QoS re quest is rejected.
2) Complexity: Let Seq = {D
1
, D
2
, .., D
r
} denote th e
selected domain sequence, where D
1
is the destination domain
and D
r
the source domain. Let α be the upper bound on the
number of pre-computed paths between node n
1
and node
n
2
in an intermediate domain D
k
, k = 2..r 1. Note tha t
α m for ID-PPPA, α V for ID-MEFPA a nd all feasible
paths for pID-MCP. Let B
k
denote the number of border nodes
1
The hierarchy is a structure which enables the storage of multiple paths
between any two nodes [13].

between domains D
k1
and D
k
, k = 2..r 1. At the level
of domain D
k
, there are at most α
k1
paths in the VSPH
from the destination d to the node n
1
and at most αB
k+1
pre-
computed paths to reach the upstream domain D
k+1
from n
1
.
Hence, the complexity of combining the pre-computed paths
with the received paths at the level of the entry border nod e n
1
is in O(α
k
B
k+1
). Considering all entry border nodes between
D
k
and D
k1
, the global complexity of this ph ase is given by
O(α
k
B
k+1
B
k
).
We note that the complexity of the online phase depends on
the number of pre-computed paths α: The lower the number of
pre-computed paths is, the lower is the number of combination
operations. Therefore, the complexity of the ID-PPPA and ID-
MEFPA algorith ms in the online phase is lower than that of
pID-MCP.
IV. SIMULATION AND ANALYSIS
In this section, we evaluate the performance of the pre-
computation algorithms ID-PPPA, pID-MCP, an d our novel
algorithm ID- MEFPA. We consider the following topologies:
LatticeFM(N, D) is a chain of D identical domains.
Each domain is a grid made up of N nodes and E =
2
N(
N 1) undirected links. This top ology repre sents
the worst-case for the complexity of the algorith ms. Pre-
cisely, each node o f an intermediate domain is connected
to each node in the next and in the previous domain of
the chain.
LatticeSL(N, D) is similar to the LatticeFM topology.
The only difference between these two topologies is the
inter-domain connectivity. In L a ttice SL , only the bottom-
right no de of eac h domain is connected to the top-left
node of the next-domain.
SYM-CORE is an inter-area topology. This topology
consists of five interconnected areas and is taken from
the work [14].
In the simulations, we select a number of node N equal
to 25 n odes and a number of domains D equal to 3. Th e
LatticeFM(25,3) and LatticeSL( 25,3) topologies allow us to
evaluate the effect of inter-dom a in connectivity on our algo-
rithms. In fact, in the LatticeFM (25,3) topology, the number
of links that connect two d omains is equal to 625, while in
the LatticeSL (25,3) topology this number is equal to 1. The
SYM-CORE topology is a realistic topology and represents an
intermediate case of inter-domain connectivity degree.
We associate with each link th ree additive weights g e nerated
indepen dently following a uniform distribution [10 , 1023].
The QoS constraints are also randomly generated in the
constraint generation space Z shown in figure 1. This space is
deduced by computing p
1
, p
2
, and p
3
the three shortest paths
which minimize the first, the second, and the third metric,
respectively. The problem is not NP-Ha rd outside Z, i.e.
either infeasible or trivial. As shown in fig ure 1, we select
ten zones Z
i
, i = 1..10 from this space and we browse th em
from the strictest constraint z one Z
1
to the loosest constraint
zone Z
10
. Then, we assess the performance of the algorithms
accordin g to these zones.
Fig. 1. Constraint generation zones for m = 3
In the following, we evaluate the pre-computation algo-
rithms according to two performan ce criteria. First, the Suc-
cess Rate (SR) given by the percenta ge of the requests for
which a feasible path is foun d. Second, the Cost (C) given
by the value of the path length function c(p) = 100
max
i1..m
(
w
i
(p)
c
i
) for the best path computed. The cost (C)
is considered only for the request f or which all the algorithms
find a f easible path. This performance criteria indicates the
quality of the computed path since it gives a measure of the
distance betwee n the path weights and the constraints.
Figures 2, 3 and 4 illustrate the variation of the success
rate according to the strictness of the QoS constraints in the
LatticeSL(25, 3), LatticeFM (25,3) and SYM-CORE topolo-
gies, respectively. The number of constraints m is equal
to 3. The figur e s show that the succe ss rate mea sured on
the LatticeFM (25,3) topology increases faster than the one
measured on the SYM-CORE and LatticeSL(25,3) topologies
when the constraints are increasingly loose. As the number
of border nodes depends on the inter-domain connectivity, the
number of pre-computed paths by each algorithm increases
when inter-doma in connectivity is high. Thus, the number
of feasible paths communicated among domains increases.
Therefore, the pr obability to find an inter-domain path which
satisfies the QoS c onstraints is higher when inter-domain
connectivity is high . This is why the success rate of the
ID-MEFPA and ID-PPPA algorithms is equ a l to the succe ss
rate of the exact algorithm pID-MCP in the LatticeFM(25,3)
topology. We r emark that in the LatticeSL(25,3) and SYM-
CORE topologies, the success rate of ID-PPPA is lower than
that of ID-MEFPA a nd p ID-MCP. In fact, the number of paths
pre-computed by ID- MEFPA and pID-MCP is higher than that
of ID-PPPA. An important result deduced fr om these figures is
that in all the used topologies the success rate of our proposed
algorithm ID-MEFPA is equals or slightly lower than that of
the exact algorithm. This is can be considered as a promising
result since the computational comlexity of ID-MEFPA is very
low comparing with that of pID -MCP.
Now we focus on the quality of the computed path by each
algorithm . Figures 5, 6 and 7 illustrate the variation of the

Citations
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Proceedings ArticleDOI
14 Mar 2016
TL;DR: This work suggests a novel direction for SDN innovation across domains, based on logically centralized control and programmable IXP fabrics, and introduces algorithms that inter-domain routing brokers can use to embed paths, subject to bandwidth and latency constraints.
Abstract: Modern Internet applications, from HD video-conferencing to health monitoring and remote control of power-plants, pose stringent demands on network latency, bandwidth and availability. An approach to support such applications and provide inter-domain guarantees, enabling new avenues for innovation, is using centralized inter-domain routing brokers. These entities centralize routing control for mission-critical traffic across domains, working in parallel to BGP. In this work, we propose using IXPs as natural points for stitching inter-domain paths under the control of inter-domain routing brokers. To evaluate the potential of this approach, we first map the global substrate of inter-IXP pathlets that IXP members could offer, based on measurements for 229 IXPs worldwide. We show that using IXPs as stitching points has two useful properties. Up to 91% of the total IPv4 address space can be served by such inter-domain routing brokers when working in concert with just a handful of large IXPs and their associated ISP members. Second, path diversity on the inter-IXP graph increases by up to 29 times, as compared to current BGP valley-free routing. To exploit the rich path diversity, we introduce algorithms that inter-domain routing brokers can use to embed paths, subject to bandwidth and latency constraints. We show that our algorithms scale to the sizes of the measured graphs and can serve diverse simulated path request mixes. Our work highlights a novel direction for SDN innovation across domains, based on logically centralized control and programmable IXP fabrics.

49 citations

Journal ArticleDOI
TL;DR: This paper derives the formulas for calculating the success rates of three hybrid algorithms by making use of a Markov chain, and investigates the relationships between the success rate curves of RandomWalk, Local (1+1) EA (evolutionary algorithm) and that of three hybrids based on different ways of combining the two heuristics for solving two satisfiability (SAT) problem instances.
Abstract: In recent years, combining different individual heuristics to construct hybrid algorithms seems to be a promising way for designing more powerful algorithms. We are interested in when a certain termination criterion is met, whether the success (referring to finding a globally optimal solution) rate of a hybrid algorithm can be better than that of the individual algorithms on which the hybrid algorithm is based or not. In this paper, we concentrate on rigorously analyzing the success rate of hybrid algorithms. This makes a step into theoretical understanding of hybrid algorithms, which lags far behind empirical investigations. We derive the formulas for calculating the success rates of three hybrid algorithms by making use of a Markov chain. These three hybrid algorithms are based on different ways of combining two individual heuristics. As an application of these formulas, we then investigate the relationships between the success rate curves of RandomWalk, Local (1+1) EA (evolutionary algorithm) and that of three hybrid algorithms based on different ways of combining the two heuristics for solving two satisfiability (SAT) problem instances. The computational success rate curves are validated by experimental ones. Meanwhile, we discuss the relationship between success rate and time complexity.

2 citations

Journal ArticleDOI
TL;DR: HID-MCP is a hybrid algorithm that combines the advantages of pre-computation and on-demand computation to obtain end-to-end QoS paths and relies on the PCE architecture to overcome the limitations related to inter-domain routing such as domain autonomy and confidentiality.
Abstract: Inter-domain quality of service (QoS) routing is a challenging problem for today's Internet. This problem requires the computation of paths that cross multiple domains and meet different QoS constraints. In addition, the used computation methods must meet the constraints of confidentiality and autonomy imposed by the domains of different operators. Path computation element (PCE)-based architecture offers a promising solution for inter-domain QoS routing. It ensures the computation of end-to-end QoS paths while preserving the confidentiality and the autonomy of the domains. In this paper, we propose a novel hybrid end-to-end QoS path computation algorithm, named HID-MCP, for PCE-based networks. HID-MCP is a hybrid algorithm that combines the advantages of pre-computation and on-demand computation to obtain end-to-end QoS paths. Moreover, it integrates a crankback mechanism for improving path computation results in a single domain or in multiple domains based on the PCE architecture. Detailed analyses are provided to assess the performance of our algorithm in terms of success rate and computational complexity. The simulation results show that our algorithm has an acceptance rate of the requests very close to the optimal solution; precisely, the difference is lower than 1 % in a realistic network. Moreover, HID-MCP has a low computational complexity. Besides, our solution relies on the PCE architecture to overcome the limitations related to inter-domain routing such as domain autonomy and confidentiality.

2 citations

Proceedings ArticleDOI
08 Jun 2015
TL;DR: A multi-tiers route design method, which provides more enhanced load balancing by selecting QoS specific multiple routes for each node pair, coordinating with the routes for other node pairs, has complementary relationship with the KSP based algorithms themselves.
Abstract: In the Wavelength Division Multiplexing (WDM) based optical circuit switching network, it takes longer time to set up the intermediate optical cross-connecting devices on the route. Thus, pre-computed routing approaches are desirable to instantly set up the connection. Most of their research works are based on the K Shortest Path (KSP) algorithm or it's variants considering route disjointness, because of load balancing effect in network, its simplicity, and quick response caused by heuristic approach. However, it essentially remains some issues to be solved, especially on the capability for various QoS support and fairer load balancing. In particular, the set of K shortest paths independently selected between any two nodes is insufficient for entire network load balancing. Specifically, sequential selection of the K routes for each source-destination (S-D) pair causes the unfairness and unbalance in network load among all S-D pairs. In the paper, to tackle the above problems, we propose multi-tiers route design method, which provides more enhanced load balancing by selecting QoS specific multiple routes for each node pair, coordinating with the routes for other node pairs. The proposed method is not the improvement of the KSP algorithm and it's variants themselves, but the framework to find a limited number (K') of adequate paths from the K (K' ≤ K) routes pre-computed by KSP based algorithms for each S-D pair and each QoS level, taking spatial relationship between routes into account. Thus, the proposed method has complementary relationship with the KSP based algorithms themselves.
References
More filters
Journal ArticleDOI
TL;DR: This paper first examines the basic problem of QoS routing, namely, finding a path that satisfies multiple constraints, and its implications on routing metric selection, and presents three path computation algorithms for source routing and for hop-by-hop routing.
Abstract: Several new architectures have been developed for supporting multimedia applications such as digital video and audio. However, quality-of-service (QoS) routing is an important element that is still missing from these architectures. In this paper, we consider a number of issues in QoS routing. We first examine the basic problem of QoS routing, namely, finding a path that satisfies multiple constraints, and its implications on routing metric selection, and then present three path computation algorithms for source routing and for hop-by-hop routing.

1,769 citations


"Performance evaluation of pre-compu..." refers background in this paper

  • ...The ID-MCP problem is NP-hard [5] and may have zero, one, or multiple solutions....

    [...]

  • ...As explained, the IDMCP problem is NP-hard, consequently, the performance of the on-demand routing algorithms in terms of response time are severely affected....

    [...]

Journal ArticleDOI
TL;DR: This article discusses how graph-based models can be used to represent the topology of large networks, particularly aspects of locality and hierarchy present in the Internet.
Abstract: The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph-based models can be used to represent the topology of large networks, particularly aspects of locality and hierarchy present in the Internet. Two implementations that generate networks whose topology resembles that of typical internetworks are described, together with publicly available source code.

968 citations


"Performance evaluation of pre-compu..." refers background in this paper

  • ...This topology consists of five interconnected areas and is taken from the work [14]....

    [...]

01 Aug 2006
TL;DR: This document describes a set of building blocks for the PCE architecture from which solutions may be constructed and specifies the architecture for a Path Computation Element (PCE)-based model to address this problem space.
Abstract: Constraint-based path computation is a fundamental building block for traffic engineering systems such as Multiprotocol Label Switching (MPLS) and Generalized Multiprotocol Label Switching (GMPLS) networks. Path computation in large, multi-domain, multi-region, or multi-layer networks is complex and may require special computational components and cooperation between the different network domains. This document specifies the architecture for a Path Computation Element (PCE)-based model to address this problem space. This document does not attempt to provide a detailed description of all the architectural components, but rather it describes a set of building blocks for the PCE architecture from which solutions may be constructed. This memo provides information for the Internet community.

889 citations


"Performance evaluation of pre-compu..." refers methods in this paper

  • ...When receiving a QoS request, the service provider computes the best domain sequence that links the source and the destination domain according to the cooperation policy [ 9 ]....

    [...]

  • ...Therefore, the research community has recently been exploring the use of distributed architectures to solve this problem, such as the PCE (Path Computation Element) architecture [ 9 ]....

    [...]

Journal ArticleDOI
TL;DR: It is shown that these four concepts, namely 1) nonlinear definition of the path length; 2) a /spl kappa/-shortest path approach; 3) nondominance; and 4) look-ahead, are fundamental building blocks of a multiconstrained routing algorithm.
Abstract: The underlying concepts of an exact QoS routing algorithm are explained. We show that these four concepts, namely 1) nonlinear definition of the path length; 2) a /spl kappa/-shortest path approach; 3) nondominance; and 4) look-ahead, are fundamental building blocks of a multiconstrained routing algorithm. The main reasons to consider exact multiconstrained routing algorithms are as follows. First, the NP-complete behavior seems only to occur in specially constructed graphs, which are unlikely to occur in realistic communication networks. Second, there exist exact algorithms that are equally complex as heuristics in algorithmic structure and in running time on topologies that do not induce NP-complete behavior. Third, by simply restricting the number /spl kappa/ of paths explored during the path computation, the computational complexity can be decreased at the expense of possibly loosing exactness. The presented four concepts are incorporated in SAMCRA, a self-adaptive multiple constraints routing algorithm.

278 citations


"Performance evaluation of pre-compu..." refers methods in this paper

  • ...In fact, the complexity of executing pID-MCP in each domain corresponds to the complexity of executing SAMCRA at each border node of the domain for each class of service....

    [...]

  • ...ID-MCP [10] is a distributed algorithm which extends the exact algorithm SAMCRA [6] to an inter-domain level to solve the ID-MCP problem....

    [...]

  • ...It pre-computes all feasible paths between each pair of nodes (n1, n2) by executing the SAMCRA algorithm at each entry border node n1 of Dk....

    [...]

  • ...To speed up the computation, dominated paths can be discarded from the computation search space of the QoS routing algorithms without affecting their performance, according to [6]....

    [...]

Journal ArticleDOI
TL;DR: This work studied `hop-by-hop destination based only' (HbHDBO) QoS routing that ignores the source and previous path history (as in current IP routing) and demonstrates that an exact QoS algorithm assures the avoidance of routing loops in this HbHD BO setting.

166 citations

Frequently Asked Questions (1)
Q1. What are the contributions in "Performance evaluation of pre-computation algorithms for inter-domain qos routing" ?

In this work, the authors study different algorithms for QoS routing based on pre-computation. First, the authors investigate an exact algorithm. This algorithm provides an optimal solution for the QoS routing problem. Second, heuristic solutions are also investigated in this work. Particularly, a detailed study of the ID-MEFPA and the ID-PPPA heuristics is provided. The ID-MEFPA heuristic has a lower complexity and provides a success rate always close to the exact algorithm.