Verification of MPLS traffic engineering techniques
ABSTRACT Multiprotocol label switching (MPLS) provides a framework for doing more flexible traffic engineering via its explicit routing capability. In this paper, MPLS routing models with two different objectives that utilise MPLS explicit routing are presented and discussed. The objectives are to minimise the network cost and maximise the minimum residual link capacity. The model that maximises the minimum residual link capacity is found to perform substantially better, in terms of network throughput and packet loss. The performance is verified by using the wellknown ns2 simulator under different network loads. The MPLS techniques described in this paper can substantially improve network throughput and user perception of quality in comparison to traditional intradomain routing methods.
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ABSTRACT: In light of the global focus on greenhouse gas emissions, energy consumption of communication networks has become an important research area. Networks are major energy consumers and are generally dimensioned for peak loads. For extended periods, resources consume power, but are lightly or unused. This research investigates the concept of dynamic topologies, i.e. networks that adapt their topology according to traffic volume. The key aim of this study is to investigate power reductions that can be achieved by dynamic topologies. It proposes a network transformation and introduces mathematical programming models that results in energy optimal topologies for given traffic loads. This paper focuses on the optimisation problems and investigates gains in static environments. Numerical results are presented for example networks using a large set of traffic matrices. For the test networks, dynamic topologies reduce the average network power consumption, depending on the network load, by approximately 12–52%.Computer Networks. 01/2011; 55:22712288.  SourceAvailable from: Alfonso GazoCervero
Conference Paper: RSVPTE Extensions to Provide Guarantee of Service to MPLS.
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ABSTRACT: Independent Quality of Service (QoS) models need to be set up in IP and ATM integration and they are difficult to coordinate. This gap is bridged when MultiProtocol Label Switching (MPLS) is used for this purpose. We propose Guarantee of Service (GoS) to improve performance of privileged flows in congested MPLS networks. We first discuss the GoS requirements for the use in conjunction with MPLS. Then we propose a minimum set of extensions to RSVPTE that allow signaling of GoS information across the MPLS domain.NETWORKING 2007. Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet, 6th International IFIPTC6 Networking Conference, Atlanta, GA, USA, May 1418, 2007, Proceedings; 01/2007  SourceAvailable from: J.L. GonzálezSánchez[Show abstract] [Hide abstract]
ABSTRACT: Independent Quality of Service (QoS) models need to be set up in IP and ATM integration and they are difficult to coordinate. This gap is bridged when MultiProtocol Label Switching (MPLS) is used for IPATM integration purposes. Guarantee of Service (GoS) allows MPLS to improve performance of privileged data flows in congested domains. We first discuss the GoS requirements for the utilization in conjunction with MPLS. Then we propose a minimum set of extensions to RSVPTE that allow signaling of GoS information across the MPLS domain.09/2007: pages 149154;
Page 1
Verification of MPLS Traffic Engineering
Techniques
Robert Suryasaputra*, Alexander A. Kist* and Richard J. Harrist
*Centre for Advanced Technology in Telecommunications (CATT)
School of Electrical and Computer Engineering, RMIT University, GPO Box 2476V VIC 3001, Australia
Email: robert@catt.rmit.edu.au, kist@ieee.org
tlnstitute of Information Sciences and Technology
Massey University, Private Bag 11 222 Palmerston North, New Zealand
Email: R.Harris@massey.ac.nz
Abstract MultiProtocol Label Switching (MPLS) provides a
framework for doing more flexible traffic engineering via its
explicit routing capability. In this paper, MPLS routing models
with two different objectives that utilise MPLS explicit routing
are presented and discussed. The objectives are to minimise the
network cost and maximise the minimum residual link capacity.
The model that maximises the minimum residual link capacity
is found to perform substantially better, in terms of network
throughput and packet loss. The performance is verified by using
the wellknown ns2 simulator under different network loads.
The MPLS techniques described in this paper can substantially
improve network throughput and user perception of quality in
comparison to traditional intradomain routing methods.
I. INTRODUCTION
Recent years have seen a tremendous growth in Internet
traffic. This ongoing growth increases the need for Internet
Service Providers (ISPs) to operate and manage their networks
efficiently to avoid congestion on their customers' traffic flows.
Throwing an abundant amount of bandwidth into the network
to address customers' demand for bandwidth is neither a
sensible nor an efficient solution to improving network per
formance. ISPs, typically control one or more Autonomous
Systems (AS). To avoid the high cost of network assets,
another solution is required which emphasises the need for
maximum operational efficiency.
Congestion typically occurs when network resources are
insufficient or inadequate to accommodate the offered load
or when traffic streams are inefficiently mapped onto network
resources. Traffic Engineering (TE) addresses the latter, which
causes some subsets of the network to become overutilised
while others remain underutilised [1]. A major goal of In
ternet Traffic Engineering is to facilitate efficient and reliable
network operations while simultaneously optimising network
resource utilisation and traffic performance.
Interior Gateway Protocols (IGP), such as Open Shortest
Path First (OSPF) [2] or Intermediate SystemIntermediate
System (ISIS) [3], are typically used to route IP traffic inside
an AS. Currently, these IGP protocols have very little traffic
and resource control capabilities. These protocols operate
according to a shortest path paradigm by using a suitable
distance metric on the links (without taking load and network
resources into consideration). To overcome this problem, an
overlay model is proposed in [4]. The overlay model creates
virtual links between every node in the network. However, this
solution does not scale well in large networks. To overcome the
scalability problem with the overlay model, weight setting has
been proposed [5] [6]. The idea is to find a set of "good" link
weights, assuming a known traffic demand matrix, to balance
the link loads. Unfortunately, finding a good set of weights
can take a very long time if particular search methodologies
are employed. On the other hand, a Linear Programming
formulation can be solved to attain a set of weights much
more rapidly, with an optimality tradeoff [7].
Multiprotocol Label Switching (MPLS) [8] has been de
veloped to address the traffic engineering problem from a
different angle. The idea is to affix a short fixed length label
to packets when packets enter an MPLS domain. Packets with
the same MPLS label indicate that they belong to the same
Forward Equivalence Class (FEC). Packets in the same FEC
will receive the same forwarding treatment. In this work, the
FEC granularity is made based on the destination. Hence,
packets with the same label will be forwarded along the same
path to their destination. This process is accomplished by a
Label Distribution Protocol [9]. This label is used to rapidly
guide the packet through a predefined tunnel, which is known
as a Label Switched Path (LSP).
MPLS offers many advantages, namely traffic shaping and
policing, classbased routing, traffic monitoring, and most
importantly, a framework for traffic engineering [8] [10].
The MPLS forwarding process causes less load on network
routers compared to the method of IP forwarding, because IP
forwarding is based on longest prefix matching for the next
hop lookup process.
With an increasing number of networks supporting MPLS
features, it has become mandatory to use this technology to
perform traffic engineering. It is also shown in [5] that MPLS
can be used to carry out optimal routing, wherein the objective
is to keep the link utilisation for all links below a certain
target value. The most important feature of MPLS in the
context of this paper is its ability to perform TE using the
explicit routing capability. Given an MPLS enabled domain,
a network operator can control how traffic flows are routed
in their network. In this paper, it is assumed that an Origin
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Page 2
Destination pair (ODPair) is associated with a single traffic
flow.
Given a traffic demand matrix and a network topology, the
question to be addressed is: which path should be chosen
for each individual ODPair to comply with the performance
objective? Two mathematical formulations are developed and
discussed in this paper to address this problem. Part of the
problem has already been discussed in [11]. However, this
work did not specifically target MPLS technology. Further
more, this paper presents simulation results to verify the
methods. As shown later, MPLS has enabled the application
of the result directly, rather than having to rely on older
technology, such as shortest path routing. As an example,
in [12] [131, the LSPs are established based on IGP metrics
(MPLS over OSPF).
The principal contributions made in this paper can be
summarised as follows: Firstly, the Mixed Integer Linear Pro
gramming (MILP) fonnulation for the LSP allocation problem
is outlined and two different objective functions are proposed
and evaluated. The solutions from these models are then used
to determine the maximum link utilisation in the network.
Secondly, the MILP models for MPLS are verified using the
well known ns2 simulator [14] and the statistics of packet
loss in the network are presented.
The rest of the paper is structured as follows: Section II
outlines different formulations for the optimisation problem
with the various different objective measures. Section HI
describes the setup for carrying out the experimental work.
Section IV describes the results obtained from the calculation
and the simulation and also gives some detailed discussion of
the results. Finally, section V summarises the paper.
II. PROBLEM FORMULATION
This section introduces two MPLS routing allocation prob
lem formulations, namely a single path multicommodity flow
problem (MinCost) in section I1A and the maximum residual
capacity singlepath problem (MaxResidual) in section HB.
The classical multicommodity flow problem (MCF prob
lem) as described in [15] or [16] addresses the problem of
how to send a specified amount of commodity from a source
to a destination such that the total cost is minimised. In
this problem, a graph, which is a collection of nodes and
links, is specified and the links have an associated cost. The
amount of the commodity can be associated with the size of
the traffic flow in the routing problem. The link cost can be
associated with an form of routing metric or it may relate
directly to real dollar costs. The classical MCF formulation
can be represented by a linkflow formulation or by a path
flow formulation. In this paper, the pathflow formulation is
used for easier understanding and representation  it also has
certain advantages over the linkflow formulation which have
been considered in other contexts.
Although the traditional MCF pathflow solution can be
used for network resource allocation, the formulation typically
requires some adjustment via additional constraints. In partic
ular, the MCF solution does not consider that the flow for
an ODPair should be limited to a single path. The general
formulation allows an ODPair flow to be split into two or
more separate routes to fill the cheaper route first. In the
context of this paper, an ODPair needs to be routed on one
and only one path from the source to the destination. Hence,
additional constraints are required to prevent splitting of the
ODPair flows.
The network is modelled as a unidirectional graph. A
path is defined as a series of links that connects the origin
and the destination node of the associated ODPair. In our
analysis, these paths are calculated for each ODPair using
the kshortest path algorithm due to Yen [17]. The following
notation is used in the formulation:
A isequalto1if link i is used inpath jof ODPair k
and 0 otherwise.
dk is the traffic demand for ODPair k.
ui is the capacity of link i.
f
on path j for ODPair k.
ck is the sum of link metrics or link costs along path j.
xk is a binary decision variable which takes the value 1 if
path j is used to carry flow in ODPair k and 0 otherwise.
is a decision variable which denotes the amount of flow
A. SinglePath Multi Commodity Flow Problem (MinCost)
(1)
Minimise
E Eckfk
k
j
subject to
E6k.k < u,<Vi
j
k
5xkfk =dk,Vk
xk = 1,Vk
i
(2)
(3)
(4)
x E (0, 1)
fjk>0,VjVk
The above formulation is a single path multicommodity
flow problem version. Whilst the objective is to minimise the
total cost to transfer the commodity from the source node to
the destination node eq. (1), the total amount of commodity
flowing on a particular link cannot exceed the link capacity eq.
(2). These constraints are also known as bundle constraints.
Equation (3) specifies that the total flow carried on all available
paths for a particular ODPair must be equal to the traffic
demand for that pair. Equation (4) enforces the requirement
that only one path is permitted to be used to carry the demand
from the source to the destination. The formulation is also
presented in [11].
However,'multiplying two unknown variables in equation
(3) results in nonlinear constraints. The constraints need to
be written differently to form linear constraints. Since only
one path can carry the whole ODPair flow, there exists one
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Page 3
and only one of f s which must be nonzero. Furthermore,
the value of this nonzero f
equation (3) can be rewritten as follows:
Zxkdk = dk,Vk
must be equal to dk. Hence,
Dividing both sides by dk yields the same constraint as
equation (4). Hence, equations (3) can be discarded because
they are redundant. Substituting fxk
lem for simplicity gives the reduced formulation as follows:
MinimiseEEckxjdk
k
subject to
S E Sa
kj
= xkdk in the above prob
j
'kdk<U2aVi
E5x
=1,Vk
3
E (0, 1),VjVk
B. Maximum Residual SinglePath Problem (MaxResidual)
To minimise the delay and packet loss while sending packets
from the source to the destination, it is necessary that the
traffic be spread such that none of the links are congested.
In this formulation, the objective is to avoid a bottleneck in
the network. In other words, the objective is to maximise the
minimum residual link capacity. The residual link capacity of
link i,Ri,is defined as the difference between the link capacity
and the total of the traffic carried on that link. A common R
is defined as miniR,for every link.
Maximise R
(5)
subject to
ESE6Xkdk+R < ui,Vi
k
Exk=IVk
(6)
(7)
R>0
xkE(0,1),VjVk
In the initial feasible solution, some links might have no
residual capacity at all (Ri= 0 for some links, hence R=0).
In order to perform practical calculations of the required
variables in this project, a wellknown standard package for
solving Linear Programming problems, known as CPLEX has
been used. Through the branch and bound process in CPLEX,
a better solution can be attained by moving flows away from
these links to "push up" the values of Ri (equation (5))
resulting in a better objective value. Equation (6) denotes the
total flows on the link and the minimum residual capacity must
be less than the link capacity. The single path flow allocation
is enforced by introducing equation (7).
Fig. 1.
Simulated topology
C. Models Application in MPLS
When the above formulations are solved using an LP solver
(such as [181), the outputs will be a series of decision variables
x.r
ODPair k will be routed on path j, whose value xk sS
equal to one. In MPLS, this can be easily implemented by
setting up an explicit route.
Upon receiving a request for an explicit route in MPLS,
the Label Edge Router (LER) will send out a message to its
neighbour to pin down the path to be used to reach the desired
destination. This neighbour then propagates the request down
the path to the destination. When the request is successful, the
LER creates a label associated with this path to the destination.
III. EXPERIMENTAL SETUP
Figure 1 depicts the network topology used in this study. It
consists of 8 routers. Each of these routers is connected to a
single workstation that acts as a traffic generator and a traffic
sink. 10 Mbps and 100Mbps links are used to connect between
the routers. 300 Mbps links are used to connect between the
workstation and the router. 10 Mbps and 100 Mbps links are
assigned OSPF weights of 1 and 10, respectively. Assuming a
traffic demand exists between every pair of workstations, there
will be a total of 56 possible traffic flows. The size of these
traffic flows has been generated randomly for this experiment.
Throughout this study, 3887 different traffic matrices have
been used; each will be referred to as an instance. These in
stances are then categorised into 41 different groups according
to their load level. These groups will be referred to as group
10 to group 51. Figure 2 depicts the number of instances that
belong to the same group. Whilst most ofthe groups have more
than 80 associated instances, there are a few groups that only
have a few instances associated with them. This difference
will affect the range of the confidence intervals obtained  as
discussed in section IV.
Figure 2 also shows the average the total demand for each
individual group. An increasing total demand from 26.5 Mbps
(group 10) to 120 Mbps (group 51) is intended to simulate the
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Page 4
I
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aTota instances I
60
I
10
t5
20
25
30
Grop
3540
45
so
SS
d
Fig. 2.
Grouping profiles
network under different load conditions, from lightly loaded
up to a saturated condition. Instances that belong to groups 10
to 25 are considered to be light loads. Those in groups 26 to
40 and groups 41 to 51 are considered as moderate and heavy
loads, respectively.
In this study, OSPF will be used to provide benchmark
performance, because it is widely used in practice. Nowadays,
OSPF link metrics are often used for establishing LSPs in
MPLS; the MPLS Traffic Engineering feature is rarely utilised.
In addition, the performance of the two MILP schemes
described earlier will be compared. The link utilisation in
the OSPF case is calculated by assuming an even splitting
whenever equal cost paths to the destination exist. This is
commonly achieved by employing Equal Cost Multi Path
(ECMP) in a router's forwarding plane to balance the load.
Ns2 with the MPLS extension module [141 was used as
the simulator in this study. Since such routing is only done
in the core networks (i.e. among the 8 routers, see Figure 1),
only these 8 routers need to be included in the MPLS domain.
Explicit routes exist within these 8 nodes in MPLS domain.
ODPairs are modelled as constant bit rate (CBR) sources.
This has been done for simplicity reasons. The CBR rate
is governed by the size of the individual traffic flows and
the packet size. The packet size is chosen to be 500 bytes.
The packet interarrival time is uniformly randomised to avoid
synchronisation among traffic sources. The CBR sources are
activated at the start of the simulation and CBR datagrams are
carried by UDP packets. On the receiving end, a loss monitor
is set up to collect statistics on the number of packets that are
received or lost.
The ns2 simulation is run for 20 seconds. The first one
second is regarded as the simulation warmup period and
measurements during this period are discarded. At the end
of the simulation, the statistics of packet lost and received for
each individual ODPair are collected and analysed.
IV. RESULTS AND DISCUSSIONS
This section presents the calculation results after evaluating
the MILP models using the simulator. The results that have
I
I
I
10
1520
25
30
35
40
45
0.o
hkbta
Fig. 3.
Maximum Link Utilisation in the 8 node test network
been obtained are discussed in Section IVA. The model
solutions are also used as the inputs for the ns2 simulation.
The simulation results are discussed in Section IVB.
A. Models Comparison
The solution of the MILP formulation, which is a set
of paths used to cany flows for each of the ODPairs, is
used to detennine the amount of traffic on every link in
the network. Given that the link capacities are known, the
utilisation can be calculated directly. The parameter of interest
in this comparison is the maximum link utilisation. It is used
to determine the severity of a congestion bottleneck in the
network.
Figure 3 depicts the maximum link utilisation when three
different routing schemes are used with the different load
groups. The 95% confidence intervals for the results are shown
as error bars in the graphs. In the lightly loaded region,
the OSPF performance and the MPLS MinCost are exactly
the same. This can be explained as follows: OSPF is a
routing protocol that routes the traffic without considering
link capacities, instead it uses the "distance" metric known
as an OSPF weight on the links. A path to a given destination
that has the lowest sum of OSPF weights will be chosen.
The MPLS MinCost model will do exactly the same; it will
route the traffic on the path with the lowest cost. The bundle
constraints in this particular situation have not "kicked in" yet
because none of the links is fully utilised yet. As a result,
OSPF and MPLS MinCost routing both yield maximum link
utilisations varying from 40% to 95%. As expected, the MPLS
MaxResidual has the lowest utilisation as it spreads the load
throughout the network (30% to 65% utilisation).
Figure 3 also shows the results when the load is increased.
With the increased load, OSPF routing yields a proportional
increase in the maximum link utilisation (correlate this with
Figure 2). In cases where the the network is moderately
loaded, the bundle constraints in MPLS MinCost formulation
start to take effect. They restrict the amount of traffic on a
link to be less than the link's capacity. The overflow traffic
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Page 5
o4
J
3
2
f
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Fig. 4.
Average Loss figure in 8 node test network
will be routed on different paths with available capacity.
The maximum link utilisation is "kept" at 100% for MPLS
MinCost. The flat line in the MPLS MinCost curve in Figure 3
shows that the maximum link utilisation does not change even
when the load is increased to 40% (moderate network loads).
The MPLS MaxResidual still performs better than OSPF and
MPLS MinCost.
However,
as
load
increases
MaxResidual advantage slowly diminishes. Its maximum link
utilisation approaches that of MPLS MinCost. In the highly
loaded region, the network is completely saturated. There is
no more capacity to accommodate the additional traffic. To
deal with the infeasibility problem in MPLS formulations,
virtual capacities are made by scaling up the real capacity
by a specified factor. In this case, both MPLS models give a
similar performance (see Figure 3).
For this problem size, the calculation time for the MPLS
MinCost formulation is less than one second using CPLEX.
This processing time can be considered negligible. Solving
the MPLS MaxResidual formulation takes longer. The optimal
solution to within 20% of optimality can be obtained in less
than 5 seconds, on average, by using CPLEX. The optimality
is calculated assuming no integrality constraints. In some
of the heavily loaded cases, the solution search has to be
terminated after 40 seconds has elapsed, since it is rare that
any improvements can be made after 40 seconds. Surprisingly,
the calculated link utilisation still falls into the trend line given
by the suboptimal solutions.
The difference in the runtime is attributed to the nature
of the problems. The decision variables in MPLS MinCost
are all binaries. This yields a pure integer programming
problem. However, the MPLS MaxResidual formulation has
an additional decision variable, R, which takes a continuous
value. Hence, the problem becomes a mixed integer linear
problem.
the
further,
the MPLS
B. Simulation Results
The simulation is carried out to show the performance
improvement of MPLS explicit routing based on the MILP
Fig. 5.
Maximum Loss figure in 8 node test network
models in comparison to OSPF routing. The parameter of
interest is the number of packets that are lost. For every
instance, the number of packets lost per ODPair is monitored.
The average of these figures is then grouped, averaged and
plotted. Another measure is the maximum ODPair loss, which
is obtained by taking maximum ODPair loss figure from a
simulation instance. The average of these maxima are then
grouped, averaged and plotted. These results are summarised
in Figure 4 and 5. The 95% confidence intervals are given as
error bars in these graphs.
Figure 4 shows that OSPF routing starts to exhibit packet
loss when the network is moderately loaded (group 25). MPLS
MinCost model slightly extends the nonloss region up to
group 31. However, the most noticeable improvement is shown
by MPLS MaxResidual having no loss until group 39. With
MPLS MaxResidual, the network can support about 45% more
traffic without experiencing packet loss compared with OSPF.
When the network is heavily loaded up to its saturation point,
the advantages of the MILP models slowly diminish (both
MPLS curves curves start to approach the OSPF curve).
In tenrs of the maximum packet loss statistics as shown in
Figure 5, in group 39, MPLS MaxResidual still can perform
without experiencing packet loss, whilst OSPF and MPLS
MinCost exhibit 30% and 14% loss, respectively. Although
the average loss for MPLS MaxResidual is just slightly better
than MPLS MinCost, the MPLS MaxResidual gives much
better results in terms of the maximum ODPair loss figure.
In MPLS MaxResidual, most of the ODPairs have similar
losses because most of the links are saturated. None of them
experience more loss than the others. The 95% confidence
intervals in MPLS MaxResidual are tighter than those of
MPLS MinCost.
It can be concluded that when the network is moderately
loaded, having a model that attempts to free up bottlenecks
in the network can be very beneficial. This is verified in
terms of the average OD loss and maximum OD loss figures.
MPLS MaxResidual performs substantially better compared
to MPLS MinCost and OSPF.
It is advised to "allocate"
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Page 6
residual capacity to protect against congestion due to traffic
measurement uncertainty and bursty traffic. However, when
the network is heavily loaded, the experiment shows that
the advantage of MPLS MaxResidual slowly diminishes. To
gether with an increasing computation time when solving
the MPLS MaxResidual formulation, MPLS MinCost may
outweigh MPLS MaxResidual.
In the heavily loaded region, the loss figures do not exactly
fall into the trend. A small number of instances in these groups
contributes to the deviation. A smaller number of instances
also results in wider confidence intervals. Most of the groups
have 80 instances each, however the last few groups only have
less than 30. Maximum time restrictions for solving the MPLS
MaxResidual formulation, which yield suboptimal solutions,
may also contribute to the deviation.
Having the available capacity to reroute traffic is particularly
important in all traffic engineering methods. In a situation,
where there is no capacity available to reroute the traffic, a dif
ferent congestion management scheme needs to be employed.
Congestion control mechanisms that automatically adjust the
sending rate depending on the network load is required.
C. Optimisation on an Operational Network
It is important during the subsequent optimisations that
only few LSPs need to be reconfigured and reestablished. A
complete LSP reshuffling is generally not acceptable, because
of the introduced disturbance to customers' flows. The MPLS
optimisation process can be influenced to take this factor into
consideration.
The MILP fonnulations in this paper can be extended as
follows: The first alternative is to restrict the elements in the
path list. The path list for the ODPair, whose LSP that are
not permitted to be reconfigured, should contain only one
path. This path must correspond to the path that is currently
taken by the LSP. A second alternative approach is to pre
set the decision variable x1
uses path j. Path j corresponds to the path that should not be
changed.
V. CONCLUSION
This paper has outlined two MILP models for the LSP
allocation problem in an MPLS domain. These models make
use of the explicit routing capability in MPLS. The output
of these models has been compared against the default OSPF
routing. The calculation and simulation results for many test
scenarios has been presented to verify the formulations. It is
beneficial to maximise the minimum residual capacity in the
network in order to spread the load which, in turn, balances
the link utilisations and reduces the packet loss. The MPLS
MaxResidual outperforms OSPF and MPLS MinCost when the
network is lightly and moderately loaded. With high loads, it
loses its advantage; MPLS MinCost may be a more attractive
solution given its faster calculation time. Furthermore, these
two MILP models can be extended to allow the optiniisation
of operational networks without having to reconfigure many
existing LSPs.
to one, ensuring that ODPair k
It is argued that ILP or MILP formulation cannot be solved
in mediumsized networks in a reasonable timeframe. It will be
interesting to investigate these limits when the MILP fonnula
tion cannot be solved. A "multistaged model" of mixed pure
LP / ILP / MILP formulations could be developed to address
the problem of maximnsing residual capacity with different
network sizes. Future work also includes the formulation of
extensions that allow intermediate nodes to aggregate LSPs
with the same destination.
ACKNOWLEDGEMENT
The authors wish to acknowledge the generous financial
support of the Australian Telecommunication Cooperative
Research Centre (ATCRC) in this project. The ongoing support
of the staffs and students working at the CATT Centre is also
gratefully acknowledged.
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