Routing Optimization in IP/MPLS Networks under Per-Class Over-Provisioning Constraints

Routing Optimization in IP/MPLS Networks under Per-Class
Over-Provisioning Constraints
Eueung Mulyana, Ulrich Killat
Department of Communication Networks, Hamburg University of Technology (TUHH)
Address : BA IIA, Denickestrasse 17, 21071 Hamburg
Phone: +49-40-42878-2925, fax : +49-40-42878-2941
Email: mulyana killat @tuhh.de
Abstract
MPLS (Multi-Protocol Label Switching) and DiffServ (Differentiated Services) provide means to implement various QoS types
in IP networks. While MPLS enhances the classical IP networks by supporting efficient connection control through explicit
label-switched paths (LSPs), DiffServ allows differentiated QoS parameters commitments to be supported on the same IP back-
bone for different classes of service. In this paper, we address an offline multi-class traffic engineering problem in IP/MPLS
networks, where each class of traffic for a certain source destination pair is routed through a unique LSP, subject to per-class
over-provisioning constraints. We introduce a heuristic, which indirectly solves the problem by iteratively optimizing IGP (Inte-
rior Gateway Protocol) link metrics for both the aggregate and the particular class of demands. Several computational results for
the case of two and three traffic classes are provided.
keywords : routing, traffic engineering, IP/MPLS networks, differentiated services (DiffServ)
1 Introduction
The increase of competition between Internet Service Providers (ISPs) together with the heightened importance of IP to business
operations has led to an increased demand and consequent supply of IP services with tighter Service Level Agreements (SLAs) for
IP performance [8]. To support those SLAs commitments, IP networks have to be engineered and enhanced, since they originally
supported and mainly were designed for best-effort traffic. To cope with limitations of the classical IP networks, several advanced
technologies have been developed. MPLS (Multi-Protocol Label Switching)[18] among other things, provides a basic means to
efficiently engineer IP traffic, while DiffServ (Differentiated Services) [6] gives the possibility to differentiate treatments for IP
packets with respect to their class of service. Traffic engineering (TE) is generally concerned with the performance optimization
of operational networks [2, 3, 22]. In classical IP networks running an IGP (Interior Gateway Protocol), TE can be deployed by
optimizing the parameters used for routing decision [4, 5, 7, 9, 11, 15, 19]. These parameters (also known as weights or metrics)
are administratively assigned to each link in the network and used by routers to compute shortest paths to each destination for
routing of the demands. In this regard, the main benefit of MPLS is the ability to use paths other than shortest paths selected by
the IGP to achieve a more balanced network utilization. Such a path is called an explicit-route label-switched path (ER-LSP).
Recent work such as [4, 12, 16, 17] presents hybrid TE approaches where several MPLS capable nodes are installed in a classical
IP domain to bring this MPLS benefit in that network. In the context of multi-class DiffServ/MPLS networks, TE could be
implemented both on per-aggregate as well as per-class basis [13, 14]. Here we use the term aggregate to point to the total
demands between two nodes for all traffic classes. Using demands’ aggregate, on the one hand TE may result in globally optimal
performance, but on the other hand it may lead to several class specific constraints (e.g. over-provisioning constraints) not being
satisfied. Over-Provisioning (OP) is a usual and easy way to provide a certain QoS level in backbone networks. For some cases
as addressed in [8], OP based on traffic aggregate can be more expensive than that based on each traffic class, for instance if the
portion of important traffic in a backbone is much less than that of normal best-effort traffic. In this paper we propose as our main
contribution an offline TE approach for the problem of per-class unsplittable routing in IP/MPLS networks to specifically address
such per-class over-provisioning traffic constraints. As management complexity may be increased by installing a large number
of ER-LSPs, we adapt a hybrid routing strategy, where packets can be routed using both hop-by-hop (vanilla) LSPs based on
IGP link metrics and ER-LSPs, which are established only to achieve better performance or to obtain a feasible routing solution
if one or more constraints are violated. The remainder of this paper is organized as follows. The following section introduces
some notations and mathematically describes the problem of unsplittable per-class TE problem using both vanilla and ER-LSPs.
In Section 3 we discuss the heuristic which will be used for solving the problem. In Section 4 we present some results for the
case of two and three traffic classes.

(c)(a) (b)
3
5 6
Vanilla
LSP
1 2
5
5
3
2
1 2
2
LSP
ER−
21
65
43
1
2
4
6
5
3
4
Figure 1: Routing in an IP/MPLS network using both
vanilla and ER-LSPs
3
13
9
14
11
8
10
6
5
74
2
1
12
Figure 2: An example ISP network net14 (14 nodes, 22
bidirectional-links)
2 Problem Description
Per-class Unsplittable MPLS Routing (Using Vanilla and ER-LSPs). In MPLS networks, demands can be routed using
either hop-by-hop (vanilla) or explicit route (ER-) LSPs. A vanilla LSP is actually part of a tree, which is built by a certain
protocol (e.g. vanilla Label Distribution Protocol LDP) using existing IP forwarding tables [20]. On one hand it provides a very
fast and simple forwarding mechanism but on the other hand it only generates the same routes as normal IP data paths. In contrast
by using ER-LSPs, routes other than shortest paths can be selected, since the control message to establish such an LSP is source
routed. This introduces routing flexibility, which is very important from operator point of view, e.g. to implement policy-based or
QoS-based routing for certain classes of traffic in the network. In this paper we consider per-class unsplittable MPLS routing i.e.:
(1) demand for a certain source, destination and class of traffic can not be split and has to be carried by one LSP (either vanilla
or ER-LSP); and (2) demands with different traffic classes for the same source and destination are routed by LSPs, which do not
necessarily have to follow the same route. This is illustrated in Figure 1. Figure (a) shows the metric value used by IGP for each
link on the network, (b) the shortest path tree constructed by IGP seen from node ½, and (c) two (vanilla and ER-) LSPs used for
routing from node ½ to node . The vanilla LSP follows the same route as the IP data path ´½ ¿ µ, while the ER-LSP could
be set differently e.g. through the node sequence ´½ ¾ µ. In the context of per-class unsplittable MPLS routing, each
LSP for the same source and destination node will carry a different class of traffic e.g. in Figure 1(c) vanilla LSP could be used
for best-effort traffic, while ER-LSP for premium traffic or vice versa. Since vanilla LSPs are built using IP forwarding tables,
which are determined by shortest path computation with respect to IGP link metrics, routing optimization can be performed in
the same way as for pure IGP networks i.e. by directly optimizing link metrics. More flexibility for traffic engineering is offered
by ER-LSPs: a path can completely be specified by the source. In spite of this, it is commonly argued that networks relying
intensively on ER-LSPs lack scalability and correspondingly that the number of ER-LSPs installed is proportionally related to
management complexity. Therefore, it is reasonable to deploy ER-LSPs in sparse manner, concentrating on cases where vanilla
LSPs can not satisfy requirements or performance objectives. For the following discussions we use the term ”LSP” and ”ER-
LSP” interchangeably, while the term ”vanilla LSP” will always be stated explicitly. For optimizing paths for vanilla LSPs we
will search for IGP metrics that result in unique shortest path routing pattern [5, 7, 21]. Now we will formulate the problem in
mathematical notation. A directed network ´Æ µ is given, where Æ is the set of nodes representing the network’s routers
and is the set of arcs representing the network’s links. Each link ´ µ ¾ has a capacity . The set of all supported traffic
classes is denoted by ¢ and is indexed by . A demand Ù Ú
for traffic class , gives the demand to be carried from source Ù
to destination Ú, Ù Ú ¾ Æ. A set of LSPs for traffic class is denoted by ¥ and indexed by . An LSP´ µ consists
of a loop-free node sequence ´ Ø µ where , Ø denote the head and tail nodes, respectively. A real variable ÐÙ Ú
´ µ is
associated with the load on link ´ µ resulting from flow demand Ù Ú
along shortest path routing (vanilla LSP), and ÐLSP´ µ
resulting from the flow in LSP´ µ. Let Ù Ú
be defined as a set of links that belong to the shortest path for the flow Ù Ú
(always the same for all ). For a given set of traffic classes and the corresponding traffic matrix ´ Ù Ú
µ Ù Ú ¾ Æ,
knowing the set of metrics Ï ´Û µ ´ µ ¾ and the set of LSPs ¥
Ë ¥ , the total load on the link ´ µ can be
computed as follows:
Ð Ð ´
ÙÚ
ÐÙ Ú
´ µ · ÐLSP( )
µ (1)
where
ÐÙ Ú
´ µ
Ù Ú
if ´ µ ¾ Ù Ú
and ´Ù Úµ ´ Ø µ
¼ otherwise
(2)

ÐLSP( )
Ù Ú
if ´Ù Úµ ´ Ø µ and ´ µ belongs to the LSP´ µ
¼ otherwise
(3)
The capacity on a link has to be sufficiently available for all demands that are routed through that link i.e. the following constraints
have to be satisfied.
max Ñ Ü
´ µ¾
Ð ½ (4)
min Ñ Ò
´ µ¾
£
Ð
ÇÈ
, ¾ ¢ (5)
(4) is the utilization upper-bound constraint for aggregate traffic while (5) is the minimum OP constraint for traffic class . Note
that ÇÈ
denotes the the given minimum OP factor for traffic class and £ È ½
× ½ Ð×
the residual link capacity
available for traffic class , assuming that the set ¢ is ordered from high to low priority traffic (i.e. ½ more important than
¾ ¡¡¡). Thus, the problem of per-class unsplittable MPLS routing using vanilla and ER-LSPs is to find the set of metric values
Ï and the set of LSP ¥, such that network resources are used efficiently while satisfying the constraints. Due to the management
complexity reasons by applying ER-LSPs, this problem can therefore be seen as a multi-objective optimization problem: (1) to
optimize network resources e.g. by minimizing Ñ Ü; and (2) to minimize management complexity i.e. in terms of ¥ . As it
will be addressed in the next section, we solve the problem indirectly using a metric-based TE approach, where (4) and (5) are
implemented as soft constraints i.e. during the search process they can be violated. At the end of the optimization, it will then be
checked whether the solution is valid and satisfies both constraints.
A Heuristic for Installing LSPs
¥ ; fail false;
optimize network( ) ÊÌ;
if( min
ÇÈ ) then break;
for each ¾¢ do
optimize network( ) ÊÌ ;
compare(ÊÌ ÊÌ );
update ¥;
if( min
ÇÈ ) then break;
if( min
ÇÈ) then fail true; break;
end for
Simulated Annealing
Ü£ ÜÓ; Ü ÜÓ; Ì ÌÓ;
while (not stopCriterion) do
while (not equilibriumAt(T)) do
Ü¼ move(Ü);
evaluate(Ü¼);
Ô computeProbability(Ì Ü¼ Ü);
if(accept(Ü¼ Ô)) Ü Ü¼;
if(Ü¼ better than Ü£) Ü£ Ü¼;
end while
Ì update(Ì);
end while
Figure 3: A heuristic for installing LSPs and a general simulated annealing framework
3 A Solving Strategy
Figure 3 (left) shows the heuristic used for solving the problem. It makes use of a traffic engineering procedure based on simulated
annealing (Figure 3 right), that returns a set of metric values (a weight-system) Ï and the corresponding routing patterns for the
given demands, each time it is called by the heuristic. The TE procedure as shortly explained in [15] will search for a weight-
system that results in unique shortest path routing. In the first step, the network will be optimized using the demand aggregateÈ . The resulting weight-system ÏÓ
´ÛÓ
µ ´ µ ¾ is used as IGP metrics for establishing vanilla LSPs.
Afterwards, it will be checked whether the constraints (4) and (5) are already satisfied. If it is the case, no further steps are
necessary. Otherwise several ER-LSPs have to be installed and the heuristic calls the metric-based TE procedure in each iteration
using the traffic matrix for the corresponding traffic class. The resulting routing pattern (ÊÌ ) is compared with that resulting
from ÏÓ
(ÊÌ). Routing entries in ÊÌ , which do not match those in ÊÌ will be installed as ER-LSPs. As will be discussed later
in this section, the metric-based TE procedure tries to indirectly minimize the number of ER-LSPs to be installed by searching
for weight-systems that do not differ very much with the reference set ÏÓ
. This heuristic is for most cases sufficient, though
there is surely no guarantee that a small number of weight changes can always yield a small number of different routing paths.
A Simulated Annealing (SA) Approach for Metric-Based TE. Simulated Annealing (SA) belongs to the oldest metaheuris-
tics and is one of the first algorithms which had an explicit strategy to avoid local optima by allowing moves towards less
performing solutions with a certain probability, which is a function of a parameter called temperature. The probability of doing
such a move is decreasing during the search. Here we focus on a general SA framework as displayed in Figure 3 (right) and refer
to [1] for a comprehensive review of local-search based methods (including SA). In each iteration step a move operator is called
to pick a neighbour Ü¼ around the current (search) agent Ü. After evaluating Ü¼ and computing the acceptance probability Ô, it
will be checked whether Ü¼ is accepted and the best agent Ü£ is necessary to be updated. The temperature is decreased each time
the equilibrium for the current temperature is reached. The search process is terminated if the system is frozen i.e. all stopping
criteria are satisfied. In our implementation, the SA is joint with a plain local-search (PLS) approach by forcing the probability
to have the value of zero, if at least one of the following conditions is satisfied: (1) the neighbourhood around Ü£ is not yet

completely explored; or (2) Ü£ is improved. This hybridization aims among other things, at speeding-up convergence at small
number of iterations, by concentrating the search around Ü£ first, before exploring other neighbourhood regions. Let ÈÄË be
defined as a boolean variable which expresses whether a condition for performing PLS is satisfied ( ÈÄË ½) or not ( ÈÄË ¼),
the acceptance probability for the case of minimization can thus be expressed by:
Ô
½ if ´Ü¼µ ´Üµ
ÜÔ´ ´Ü¼µ ´Üµ
Ì
µ if ´Ü¼µ ´Üµ and ÈÄË ¼
¼ otherwise
(6)
where denotes the objective function, and Ì the parameter temperature, respectively. As mentioned earlier, the metric-based
TE procedure tries indirectly to minimize the number of ER-LSPs to be installed by searching for weight-systems that do not
differ very much with the reference set ÏÓ
. An easy way to achieve these partial changes is by integrating a function measuring
weight changes in the optimization objective:
min ½ ¡ max ·
×¾
Ý× (7)
Ý×
½ if Û× ÛÓ
×
¼ else
(8)
The last term in (7) measures similarities between the reference weight-system ÛÓ
½ ÛÓ
¾ ¡¡¡ ÛÓ
× ¡¡¡ ÛÓ
and the current
weight-system Û½ Û¾ ¡¡¡ Û× ¡¡¡ Û . (7) is the optimization objective to prefer solutions with a low maximum utilization,
which implies that the network is better utilized and a small number of weight changes. A constant ½ is used to trade between
these two components. In this approach, in spite of guidance performed by the objective function, search agent Ü can still move
everywhere in the solution space. Thus, sometimes it is necessary to additionally guide moves to prefer the original weight values
whenever possible.
4 Results and Analysis
For the following discussion we use the networks as shown in Figure 1 (net6) and Figure 2 (net14). Network net6 consists of 6
nodes and 14 directed links (each of 100 units capacity), while network net14 consists of 14 nodes and 44 directed links (each of
2.5 Gbps capacity), respectively. For net6 two traffic matrices (¢ premium´ ½µ best-effort´ ¾µ ) and for net14 three
traffic matrices (¢ premium´ ½µ assured´ ¾µ best-effort´ ¿µ ) are randomly generated. Demands for best-effort
traffic were produced using the hot-spot model as introduced in [9], while those for premium and assured traffic were just taken
randomly from several predefined demand values. The resulting mean demand values for each traffic class are: ´ ¼ µ
units for net6; and ´ ¿ µ Mbps for net14, respectively. The constant ½ in (7) was set to ½¼¼¼ in order to prioritize
solutions, which result in better values of Ñ Ü.
50 100 150 200 250 300 350 400 450 500
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
SA Convergence (Aggregate Demands)
ObjectiveValues
Iteration Number
Objective
values of
current−agent
Objective
values of
best−agent
Temperature
Figure 4: The convergence characteristic of the
hybrid SA applied to aggregate demands
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
5
10
15
20
25
OP Factor (Aggregate)
OPFactor
Link Number
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
5
10
15
20
25
OP Factor (Aggregate)
OPFactor
Link Number
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
2
4
6
8
10
12
14
OP Factor (class 1)
OPFactor
Link Number
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
5
10
15
20
25
OP Factor (class 1)
OPFactor
Link Number
(a−i)
(a−ii)
(b−i)
(b−ii)
minimum
OP constraint
Figure 5: OP factor for both aggregate and premium traffic for
the case without ER-LSPs (a) and with several ER-LSPs (b)

Convergence. Figure 4 shows the convergence characteristic of the hybrid SA applied to net14 using traffic aggregate .
The parameters were set as follows. The search terminates if the maximum number iterations of 500 or the maximum number
iterations without improvements of 300 is exceeded. The equilibrium for temperature T is reached if the number of iterations
without improvements at that temperature exceeds the value of 30. ÈÄË is set to have the value of 1 if the current number of
iterations without improvements is less than the value of 25. The Figure shows that from the start and at a small number of
iterations, the algorithm performs plain local-search since improvements always exist at least every 25 iterations. Once the value
is exceeded, the algorithm performs the normal SA till the next event for PLS is triggered i.e. a new value for best agent is found.
Looking at the SA parts in the Figure, the impact of temperature values on the moves is very obvious. High temperatures imply
high acceptance probabilities for moving towards less performing solutions, while at low temperatures only moderate moves are
allowed.
OP Factor and Link Utilization. The common rule-of-thumb for capacity provisioning is to have a minimum OP factor larger
than ¾ ¼ or correspondingly a maximum utilization below ¼ ¼±. For dealing with network failure situations or unexpected
traffic demands, several network providers might want to have larger OP factors. For the following experiments, we always set
the value of ÇÈ
for other than best-effort traffic larger than ¾ ¼. Figure 5 shows OP factor for net6 after optimization by using:
(a) the traffic aggregate , where all demands regardless their classes are routed using vanilla LSPs; and (b) each traffic matrix
, where several demands are routed using ER-LSPs. The minimum OP factor for premium traffic was set to ¿ ¼. This can not
be achieved without ER-LSPs, since optimization using traffic aggregate results in ½
min ¾ ¿. Thus, further steps as shown
in Figure 3 (left) are necessary. Applying optimization using ½ results in ½
min ¿ ¼¿ which now satifies the requirement.
This is achieved: (1) by installing a symmetrical LSP for the premium traffic; and (2) at the cost of a small decrease in the
minimum OP factor for aggregate traffic from ½ ¾ (without the LSP) to ½ ½ (with the LSP). The corresponding graphs for net14
are shown in Figure 6. After the first step we have the maximum utilization for aggregate traffic of ± and the minimum
OP factor values of ´¿ ¼¼ ¿ ¿ ½ ¼ µ for the premium, assured and best-effort traffic, respectively (Figure 6 a). By setting the
minimum OP constraints to ´ ¼ ¼ ½ ¼µ we need again to re-route some of the traffic using ER-LSPs. After optimization using
½ and ¾, Ñ Ü decreases to ¿ ± and the minimum OP factor values of ´ ¼ ¼½ ½ ¼ µ can be achieved by installing
13 symmetrical LSPs for premium and 4 symmetrical LSPs for assured traffic. Figure 6 (b-ii) and (b-iii) show the resulting OP
factor for each link for ¾ ½ ¾ . Although the minimum OP constraints are already satisfied, the optimization can be applied
for ¿ to investigate whether a better solution is available. In our case, after optimization ¿
min is improved from ½ ¼ to ½ ½
while Ñ Ü decreases to ¾ ¾ ±. This happens at the cost of additional 9 symmetrical LSPs that have to be installed for ¿.
The resulting link utilizations are shown in Figure 6(b-i).
5 Summary and Outlook
In this paper we have considered the problem of offline routing control in multi-class IP/MPLS networks using both vanilla and
ER-LSPs, while simultaneously taking OP constraints for each traffic class into account. We proposed a simple heuristic which
iteratively calls a metric-based TE procedure, that indirectly minimizes the number of ER-LSPs to be installed by searching for
weight-systems that do not differ very much with the reference set of weights, which is used for establishing vanilla LSPs. Our
experiments show that starting from an optimized weight-system for traffic aggregate, we can improve OP factors for each traffic
classes by establishing several ER-LSPs for the corresponding traffic, although this happens at the cost of increasing management
complexity. Finally, since the work presented in this paper is entirely based on heuristic frameworks, several issues remain open
e.g. the question how good are the results from our approach compared to (possible) optimal solutions. With respect to network
resources a comparison can be made with the results from a so-called general routing problem [9]. But it seems non-trivial to
make a comparison with respect to the number of ER-LSPs to be installed. We are currently working on these issues.
References
[1] Aarts E., Lenstra J.K., ”Local Search in Combinatorial Optimization”, John Wiley & Sons Ltd., 1997.
[2] Awduche D., ”MPLS and Traffic Engineering in IP Networks”, IEEE Communications Magazine, Vol. 37, No. 12, pp. 42-47, December 1999.
[3] Awduche D., Chiu A., Elwalid A., Widjaja I., Xiao X., ”Overview and Principles of Internet Traffic Engineering”, RFC 3272, May 2002.
[4] Ben-Ameur W., Michel N., Liau B., Geffard J., Gourdin E., ”Routing Strategies for IP-Networks”, Telektronikk Magazine, 2/3, pp. 145-158, 2001.
[5] Ben-Ameur W., Gourdin E., Liau B., Michel N., ”Determining Administrative Weights for Efficient Operational Single-Path Routing Management”, Proceedings
of 1st Polish-German Teletraffic Symposium PGTS, pp.169-176, September 2000.
[6] Blake S. et al., ”An Architecture for Differentiated Services”, RFC 2475, December 1998.
[7] Bley A., Koch T., ”Integer Programming Approaches to Access and Backbone IP Network Planning”, preprint ZIB ZR-02-41, 2002.
[8] Filsfils C., Evans J., ”Engineering a Multiservice IP Backbone to Support Tight SLAs”, International Journal of Computer and Telecommunications Networking,
40/1, pp. 131-148, 2002.
[9] Fortz B., Thorup M., ”Internet Traffic Engineering by Optimizing OSPF Weights”, Proceedings of IEEE Infocom, pp. 519-528, March 2000.
[10] Gouveia L., Patricio P., de Sousa A.F., Valadas R., ”MPLS over WDM Network Design with Packet Level QoS Constraints based on ILP Models”, Proceedings
of IEEE Infocom, April 2003.
[11] Karas P., Pioro M., ”Optimisation Problems Related to the Assignment of Administrative Weights in the IP Networks’ Routing Protocols”, Proceedings of 1st
Polish-German Teletraffic Symposium PGTS, pp. 185-192, September 2000.
[12] Koehler S., Binzenhoefer A., ”MPLS Traffic Engineering in OSPF Networks - A Combined Approach” Proceedings of 18th International Teletraffic Congress
ITC, pp. 21-30, September 2003.
[13] Le Faucher F., Lai W., ”Requirements for Support of Differentiated Services-aware MPLS Traffic Engineering”, RFC 3564, July 2003.
[14] Le Faucher F.(ed) et al., ”Multi-Protocol Label Switching (MPLS) Support of Differentiated Services”, RFC 3270, May 2002.

0 10 20 30 40
0
20
40
60
80
100
Utilization(%)
Link Utilization
class 1
class 2
class 3
0 10 20 30 40
0
20
40
60
80
100
Utilization(%)
Link Utilization
class 1
class 2
class 3
0 10 20 30 40
0
5
10
15
20
OP Factor (class 1)
OPFactor
0 10 20 30 40
0
5
10
15
20
OP Factor (class 1)
OPFactor
0 10 20 30 40
0
5
10
15
20
25
30
OP Factor (class 2)
OPFactor
Link Number
0 10 20 30 40
0
5
10
15
20
25
30
OP Factor (class 2)
OPFactor
Link Number
(a−i)
(a−ii)
(a−iii)
(b−i)
(b−ii)
(b−iii)
min. OP constraint
Figure 6: Link utilization and OP factor without ER-LSPs (a) and with several ER-LSPs (b) for the case of
3 traffic classes, applied to net14.
[15] Mulyana E., Killat U., ”Impact of Partial Demand Increase on the Performance of IP Networks and Re-optimization Approaches”, Proceedings of the 3rd
Polish-German Teletraffic Symposium PGTS, pp. 275-284, September 2004.
[16] Mulyana E., Killat U., ”Optimization of IP Networks in Various Hybrid IGP/MPLS Routing Schemes”, Proceedings of the 3rd Polish-German Teletraffic
Symposium PGTS, pp. 295-304, September 2004.
[17] Riedl A., ”Optimized Routing Adaptation in IP Networks Utilizing OSPF and MPLS”, Proceedings of IEEE ICC, Vol. 3, pp. 1754-1758, May 2003.
[18] Rosen E., Viswanathan A., Callon R., ”Multiprotocol Label Switching Architecture”, RFC 3031, January 2001.
[19] Staehle D., Koehler S., Kohlhaas U., ”Optimization of IP Routing by Link Cost Specification” , Technical Report, University of Wuerzburg, 2000.
[20] Smith P.A., Jamoussi B., ”MPLS Tutorial and Operational Experiences”, NANOG 17 Meeting, October 1999.
[21] Thorup M., Roughan M., ”Avoiding Ties in Shortest Path First Routing”, [online].
[22] Xiao X., Hannan A., Bailey B., Ni LM., ”Traffic Engineering with MPLS in the Internet”, IEEE Network Magazine, pp. 28-33, March 2000.

Routing Optimization in IP/MPLS Networks under Per-Class Over-Provisioning Constraints

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