IMPACT OF PARTIAL DEMAND INCREASE ON THE PERFORMANCE OF IP NETWORKS AND RE-OPTIMIZATION APPROACHES

12th GI/ITG CONFERENCE ON MEASURING, MODELLING AND
EVALUATION OF COMPUTER AND COMMUNICATION SYSTEMS
3rd POLISH-GERMAN TELETRAFFIC SYMPOSIUM
IMPACT OF PARTIAL DEMAND INCREASE ON THE PERFORMANCE
OF IP NETWORKS AND RE-OPTIMIZATION APPROACHES
Eueung Mulyana, Ulrich Killat
Department of Communication Networks, Hamburg University of Technology (TUHH)
Address: BA IIA, Denickestrasse 17, 21071 Hamburg, Germany
E-mail: {mulyana,killat}@tu-harburg.de
Abstract
An important aspect in management of IP networks is to control traffic traversing links on the
network, while optimizing performance. Using offline approaches, this means that recomputation
should be carried out on a periodical basis to adjust network configuration to the most actual traffic
situation obtained from measurements or forecasts. In this work we investigate the effect of partial
demand increase on the performance of the network and propose a simple policy scheme to decide
whether re-optimization should be performed. Two re-optimization approaches based on plain local-
search and simulated-annealing are presented. We apply our method for metric based traffic
engineering scheme to the German scientific network (G-WiN) for which a traffic matrix and several
traffic-increase patterns were randomly generated. Several computational results are provided.
Keywords
IGP routing, offline traffic engineering, metaheuristics, IP networks, re-optimization
1. INTRODUCTION
In recent years, many efforts have been invested to control and engineer IP
traffic, due to rapid traffic growth and increasing requirements of service quality.
An important aspect that triggers traffic engineering (TE) in IP networks is, that
they were originally designed for robustness and reliability - if necessary at the cost
of other performance measures. Generally, in the literature [3] TE is defined as
mapping traffic flows onto the existing physical network topology in the most
effective way to accomplish desired operational objectives. There are several
approaches for deploying TE in current IP networks e.g. by optimizing the
parameters used for routing decisions, so that a better network performance will be
obtained [4-8,10-13], or by using explicit routing in an overlay model with ATM or

Frame Relay technology. In this work we limit ourselves to the metric based traffic
engineering scheme for IP networks running an Interior Gateway Protocol (IGP)
like OSPF (Open Shortest Path First) or IS-IS (Intermediate System to Intermediate
System). In these networks, an administrative weight or metric is assigned to each
link by network administrators and routing paths are defined as shortest paths
according to these metric values. All demands between nodes in the network will
then be routed on the corresponding shortest paths. It is obvious that in this routing
scheme, the value of administrative weights plays a prominent role for controlling
traffic. The objective of this work is firstly to investigate the impact of partial (non-
linear) demand increase on the performance of IP networks. The second objective
is to develop a policy when re-optimization should take place, since it is possibly
not necessary to be performed if this partial demand increase does not result in
significant performance degradation or if traffic engineering could not give better
solutions due to e.g. network saturation, capacity limitation etc. Last but not least,
if re-optimization is admitted, it is interesting to know, whether it is possible to
obtain solutions with minimal changes compared to the original configuration, so
that in this case partial demand increase will result in only partial an mainly local
configuration changes. We develop two methods for re-optimization based on plain
local-search and simulated-annealing approach, respectively. We apply our method
to the German scientific network (G-WiN) [2] for which a traffic matrix and
several traffic-increase patterns were randomly generated. The remainder of this
paper is organized as follows. In Section 2, we present a mathematical model for
OSPF routing and introduce some notations to describe and measure the effect of
partial demand increase. A simple policy and two approaches for re-optimization
are explained in Section 3. Finally, some investigations and computational results
are presented.
2. OSPF ROUTING AND PARTIAL DEMAND INCREASE
OSPF Routing. In OSPF networks, each link is assigned a dimensionless metric
value, also called cost or weight. Demands are routed along paths, which are
selected using Dijkstra’s shortest path algorithm with respect to these link metric
values. In the case of multiple shortest paths, some vendors have implemented a
so-called ECMP rule (Equal Cost Multi-Path) [8, 9], so that the traffic flow will be
split over those paths roughly evenly. This enhances routers’ capability for
balancing the flows in the network e.g. to avoid congestion. However, some
operators might want to avoid such a situation for management or other reasons [5,
13]. In this case, one might want to disable the splitting capability of the routers or
to find a set of metric values that result in a networkwide unique shortest path
routing. For illustration, consider two network settings in Figure 1. In the first
configuration (Figure 1 (a)) each flow will be routed uniquely, fully independent of

Impact of Partial Demand Increase on the Performance of IP Networks and Re-optimization
Approaches
whether the ECMP feature is enabled or disabled. The second configuration
(Figure 1 (b)) results in several ties, so that by enabling ECMP the flow from the
node 1 to the node 6 will be split to the paths (1-2-4-6), (1-3-4-6) and (1-3-5-6)
with the composition of traffic fraction of 50%, 25% and 25% respectively. In this
work and for the following discussion we always assume that the ECMP is
enabled. The methods for obtaining metric values for unique shortest path routing
could be found e.g. in [4, 5,13].
Figure 1 Shortest path structures seen from node 1 for the case: (a) unique, and (b)not-unique
shortest path metric values
We will now formulate the problem. Given is a directed network ),( ANG = ,
where N is the set of nodes representing the network’s routers and A is the set of
arcs representing the network’s links. Each link Aji ∈),( has a capacity jic , .
Furthermore, we have a demand vu
f ,
for each pair NNvu ×∈),( , giving the
demand to be carried from source u to destination v. A real variable vu
jil ,
, is
associated with the load on link ),( ji resulting from flow demand vu
f ,
. Let
},,,,{ ,,,
1
, vu
K
vu
k
vuvu
AAAA LL= be defined as the set of shortest paths for the flow
vu
f ,
, )},(,),,{( 121
,
vnnnunA k
s
k
s
kkvu
k === −L as the set of links that belong to the
shortest path k for the flow vu
f ,
and vu
k
,
ξ as a fraction of vu
f ,
that is routed
through vu
kA ,
(calculated using the ECMP rule). The total load on the link ),( ji can
be computed as follows:
∑=
uv
vu
jiji ll ,
,, (1)
where
∑ ∑
∈
=
k Al
vu
k
l
ji
vu
ji
vu
k
l
,
,
,
,
, ξδ (2)


 =
=
otherwise0
if1
,
(i,j)ll
jiδ (3)
vu
k
vu
k f ,,
=∑ξ (4)
(b)(a)
6
11
1
1
1
1
2
21
2
3
5
5
121
3 4
5 6
2
3 4
5 6
1
2
4
6
5
3
1
2 3
4 5
1

Note that in the case of unique shortest path routing i.e. K=1 , (2) becomes
∑∈
= vu
Al
vul
ji
vu
ji fl ,
1
,
,
,
, δ . For a given traffic NNvufF vu
×∈∀= ),(),( ,
, the problem is
to find a set of metric values AjiwW ji ∈∀= ),(),( , to increase the network
performance which can be formulated as :
}{min maxρ (5)
Ajiji ∈∀≤ ),(,max, ρρ (6)
where jijiji cl ,,, =ρ is the utilization of the link ),( ji .
Figure 2 The G-WiN network taken from [13] and its demand distributions
With (5) we prefer solutions with a low maxρ , which implies that the network
is better utilized. Using the simple objective maxρ in some cases may need special
treatment. In the network shown in Figure 2 for instance, there are no possibilities
to reroute traffic traversing the level-2 links (Figure 2 middle). Thus, in those cases
it would be better to exclude all such links for computing maxρ in (6). Having the
traffic matrix and the metric values, we can compute the load distribution on the
network. Every solution has a quality measure according to (5). Although a
solution is feasible if 1, ≤jiρ or correspondingly 1max ≤ρ , the optimization is
performed with no constraints to force this condition, but we simply minimize the
objective function. Note that the formulation presented here is intended for the
heuristic solving method to be presented in Section 3.
Partial Demand Increase. Traffic in IP networks is very dynamic and tends to
increase over time. By using a simple scaling method we could easily investigate
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G-WiN Level 1
G-WiN Level 2
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G-WiN Level 1
G-WiN Level 2
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(0,5] (5,10] (10,20] (20,30] (30,50] (50,100] (100,200] (200,355]
0
5
10
15
20
25
30
Demand-Rate Distribution
NumberofDemands(%)
Rate Interval (Mbps)
Initial Distribution
10% Increase (5-10 Mbps)
(0,5] (5,10] (10,20] (20,30] (30,50] (50,100] (100,200] (200,355]
0
5
10
15
20
25
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Demand-Rate Distribution
NumberofDemands(%)
Rate Interval (Mbps)
Initial Distribution
10% Increase (5-10 Mbps)

Approaches
the effect of the traffic increase in the network, because in this case the utilization
scales linearly. But this does not necessarily reflect reality, if we assume that traffic
and its growth are stochastic quantities. It was our interest to investigate the effect
of non-linear traffic growth on network performance. Let
NNvufF vu
oo ×∈∀= ),(),( ,
be defined as the original traffic matrix, and
NNvufF vu
×∈∀∆=∆ ),(),( ,
αα as a traffic-increase matrix where α denotes the
number of non-zero elements of αF∆ i.e. the number of source destination node
pairs with increasing demand. Our new traffic matrix, denoted by
NNvufF vu
×∈∀= ),(),( ,
αα , can be written as:
αα FFF o ∆+= (7)
Note that the linear increase oFF λ= is a special case in (7) for %100=α and
oFF )1( −=∆ λα .Increasing partially the traffic matrix could change the original
traffic distribution (see Figure 2 right) and correspondingly the original network
utilization. If o
maxρ denotes the original maximum utilization caused by distribution
of the demands oF , and α
ρmax the maximum utilization caused by αF using the
same routing pattern i.e. without changing routing configuration, we define the
increase of the maximum utilization introduced by demand increase αF∆ as:
o
maxmaxmax ρρρ αα
−=∆ (8)
Furthermore α
ρdiff∆ denotes the difference between maximum and average
utilization in the network, resulting from the new demand αF , i.e. :
ααα
ρρρ −=∆ maxdiff (9)
3. POLICY AND APPROACHES FOR RE-OPTIMIZATION
Policy for Re-optimization. After recalculating network parameters with the
current configuration, a decision should be made whether the network has to be re-
optimized. One possibility is to check the value of the increase of the maximum
utilization, that is whether 1max ερα
>∆ For illustration consider Figure 3, which
shows the values of α
ρmax∆ for the 500 samples of traffic-increase matrices αF∆ for
%2=α with vu
f ,
α∆ randomly distributed in the interval [5,10] Mbps (Figure 3 left)
and ]50,5[,
∈∆ vu
fα Mbps (Figure 3 right) respectively. The investigation
environment will be explained in detail in Section 4. More than 99% of the αF∆
cause increase in maximum utilization less than 1% in the first case and lower than
5% in the second case. This means, if we set %51 =ε re-optimization should be
performed with probability less than 1% for the second case and it is absolutely not
necessary for the first case. Using the single parameter α
ρmax∆ sometimes is not
adequate, since there are cases where traffic rerouting will not yield better

situations. In those cases the network has to be expanded and new hardware
capacities should be installed, as well. A further indication could be given by the
parameter α
ρdiff∆ as given by (9) to roughly measure balance of the traffic
distribution. The higher the value of α
ρdiff∆ , the higher the probability that traffic is
distributed in an unbalanced manner. A significant increase in the value of the
parameter α
ρmax∆ max without the corresponding significant increase in the value of
the parameter α
ρdiff∆ may indicate that traffic engineering would not be sufficient
and network upgrade would probably be necessary. Putting it all together, re-
optimization to compensate the impact of demand increase αF∆ should first be
performed when :
1max ερα
>∆ and 2diff ερα
>∆ (10)
Figure 3 Increase of maxρ caused by %2F∆
Re-optimization Approaches. Re-optimization could then be applied, once
requirements (10) are satisfied. A method based on plain local-search (LS) could
be an appropriate choice since it gives exact control over the number of changes to
be performed to the original weight configuration by exploring its neighbourhood
space using all predefined move operators. For a comprehensive review of local-
search based methods (including simulated-annealing) we refer to [1]. The main
layout of the used LS algorithm is shown in Figure 4 left. The first step is to define
several move operators satisfying requirements e.g. maximum allowed number of
weight changes. Beginning with the first type of move that corresponds to the
smallest neighbourhood space, we try to find a valid solution around the original
weight configuration. The algorithm will terminate, once a valid solution is found
or there are no valid solutions found for all types of move. A validity condition
could be set in various ways depending on trade-off factors concerning network
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
Increase of the Maximum Utilization
UMaxIncrease(%)
Traffic-Increase Pattern
Mbps]10,5[,
∈∆ vu
fα
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
UMaxIncrease(%)
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
UMaxIncrease(%)
Mbps]10,5[,
∈∆ vu
fα
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
UMaxIncrease(%)
Mbps]50,5[,
∈∆ vu
fα
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
UMaxIncrease(%)
0 50 100 150 200 250 300 350 400 450 500
0
1
2
3
4
5
6
UMaxIncrease(%)
Mbps]50,5[,
∈∆ vu
fα

Approaches
performance, time limitation etc. One possibility is again to use the parameters
α
ρmax∆ and α
ρdiff∆ e.g. : a solution is said to be valid when 1max ερα
<∆ and
2diff ερα
<∆ . The second approach is based on simulated annealing (SA) that
belongs to the oldest the metaheuristics 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 the
parameter called temperature. The probability of doing such a move is decreasing
during the search. The pseudocode of the SA is displayed in Figure 4 right. In this
approach it is not possible to upper bound changes using move operators since the
search agent can move everywhere in the solution space. Partially changes could
then be achieved by integrating a changes function in the objective function and
giving an importance-factor between components in the objective [10]. The
important part of this method is to guide moves to prefer the original weight values
whenever possible.
Figure 4 Pseudocodes for plain local-search and simulated-annealing
4. ANALYSIS AND DISCUSSION
For the following results we used the German research and scientific network
G-WiN shown in Figure 2. It consists of 27 nodes (10 level-1 nodes and 17 level-2
nodes) and 76 links. Each level-1 link has a transmission capacity of either 2.5
Gbps or 10 Gbps while each level-2 link has either 6222× Mbps or 5.22× Gbps
[2]. The original traffic matrix oF is composed of 702 flows and each of them was
generated randomly in the interval [4,355] Mbps. The mean demand value is 34.6
Mbps and around 75% of the demands are below the value of 30 Mbps (Figure 2
left). For each traffic-increase investigation, 500 increase-patterns are generated
randomly with a simple rule, that only node pairs which do not share a common
level-1 node are allowed to contribute to demand increase. This is obvious, because
demand increase of node pairs sharing a common level-1 node will not affect

utilization of the links in level-1, which are our concern in this case. The values of
α used in the investigations are 2%, 5%, 10%, 25% and 50%. The metric value
was originally set inversely proportional to the link’s capacity. Setting the weights
in this way caused that 156 (around 22.2%) flows were split because of two or
more ties. The average utilization was 23.4% and the most utilized link (of 76.6%)
was the link (5,6) which carried 70 different flows. The value
%2.53maxdiff =−=∆ ρρρ was a strong indication that the network was not
configured appropriately and that traffic engineering should be performed. If we
look at the network in Figure 2, we see that traffic on level-2 links is not reroutable,
thus for optimization they were marked as unconsidered and maxρ in (5) was
substituted with cons
maxρ i.e. the maximum utilization on the level-1 network. Using a
slightly different version of the SA described in Section 3, after optimization we
obtain: %4.39cons
max =ρ for the link (7,9), %4.48max =ρ for the level-2 link (1,12)
and %1.24=ρ . Looking at these values, it is obvious that the optimization saves
significantly the network resources: %2.37cons
max =∆ρ (about 930 Mbps capacity in a
2.5 Gbps link), %3.15cons
diff =∆ρ within an acceptable increase in the average
number of hops for routing of 0.3 and the increase of 0.7% in average utilization.
With the optimized weights’ configuration, there are no split flows, since the
optimization was set to prefer unique shortest path routing e.g. by using the method
in [13].
Performance by Increase Traffic. Figure 5 shows the distributions of the values
of α
ρmax∆ and α
ρdiff∆ for all increase patterns, for different α and increase-intervals.
The values of vu
f ,
α∆ are randomly distributed in the intervals [2,5], [5,10], [10,20],
[20,30], [5,50], [5,100], [50,50] (constant) and [100,100] (constant) Mbps. Totally
we have 40 different αF∆ ’s each with 500 different patterns. Looking at the first
two graphs at the top, partial demand increase αF∆ whose elements vu
f ,
α∆ are
randomly distributed below the mean value of the original demands in worst case
will increase the maximum utilization up to 29% and the difference α
ρdiff∆ up to
33%. In other words, the probability to obtain a value of maxρ below 68.4% is quite
high, for the case of partial demand increase with %50≤α and vu
f ,
α∆ randomly
distributed below the value of 30 Mbps. For %10≤α (equivalent to 36
symmetrical pairs) the corresponding value of maxρ is around 49.4%. The last two
graphs present the distribution of α
ρmax∆ and α
ρdiff∆ using wider and overlapping
increase-intervals as well as using constant values. In general the bigger vu
f ,
α∆
and/or the value of α , the larger are the resulting values of α
ρmax∆ , α
ρdiff∆ as well
as the variance of them. And the bigger the value of these two parameters, the
higher is the probability that unbalanced traffic distribution occurs in the network
and requires re-optimization.

Approaches
Figure 5 The values of
α
ρmax∆ and
α
ρdiff∆ for all α , increase intervals and patterns ( αF∆ )
[50,50] Mbps [5, 100] Mbps
PLS SA PLS SA1ε
(%)
2ε
(%) a (%)
b (%) c (%) b (%) c (%)
a (%)
b (%) c (%) b (%) c (%)
15 25 5.6 75 3.38 39.29 25.12 25.8 48.84 3.63 25.58 24.16
15 30 4.2 57.14 3.07 61.9 24.09 23.6 54.24 3 31.36 20.63
20 25 5.6 82.14 2.52 53.57 22.63 24.4 53.28 3.2 37.7 20.25
20 30 0.6 100 1.75 100 42.98 2.6 92.31 3.29 84.62 20.57
Table 1 Re-optimization results for %10=α with different values of 1ε and 2ε
Re-optimization. Table 1 shows some computational results for different values of
1ε and 2ε , for the case of %10=α and increase intervals of [5, 100] Mbps and
[50,50] Mbps (constant). Column a indicates the number of different increase
patterns αF∆ , which trigger the re-optimization procedure, column b the number of
successful re-optimizations and column c the average number of weight changes
yielded by all successful re-optimizations. Looking at the values in the columns b
and c, almost in all cases PLS performs better than SA in terms both of the number
of successful re-optimizations and the average value of the number of necessary
weight changes. However, under identical termination condition (cf. Figure 4)
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
Increase of the UMax
UMaxIncrease(%)
Percentage of flows being increased
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
Difference UMax - UAverage
Difference(%)
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
UMaxIncrease(%)
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
Difference(%)
[50,50]
[100,100]
[5,100]
[50,50]
[5,50]
[2,5]
[5,10]
[10,20]
[20,30]
[20,30]
[2,5] [5,10]
[10,20]
[5,100]
[5,50]
[100,100]
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
UMaxIncrease(%)
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
Difference(%)
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
UMaxIncrease(%)
2% 5% 10% 25% 50%
0
10
20
30
40
50
60
Difference(%)
[50,50]
[100,100]
[5,100]
[50,50]
[5,50]
[2,5]
[5,10]
[10,20]
[20,30]
[20,30]
[2,5] [5,10]
[10,20]
[5,100]
[5,50]
[100,100]

more computation time was needed for re-optimization using PLS : SA was 50 %
to 60 % faster.
5. SUMMARY AND CONCLUSION
In this paper we have investigated the impact of partial demand increase on the
performance of IP networks. We propose a simple policy for deciding whether to
re-optimize the configuration as well as two approaches for implementing the re-
optimization. Our experiments show that depending on the policy parameters and
demand increase patterns, it is possible to perform minimal re-configuration (in
terms of weight changes) in order to keep network performance within an
acceptable range. Although we considered in this work only the metric-based
traffic engineering scheme, the same principle can be applied to other TE schemes
involving other routing mechanisms (e.g. MPLS or hybrid IGP/MPLS).
BIBLIOGRAPHY
[1] Aarts E., Lenstra J.K., Local Search in Combinatorial Optimization, John Wiley & Sons
Ltd., 1997.
[2] Adler H. M., Neues im G-WiN, 37. DFN-Betriebstagung, November 2002.
[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., Gourdin E. , Liau B. , Michel N., Determining Administrative Weigths
for Efficient Operational Single-Path Routing Management, Proceedings of 1st
PGTS,
2000.
[5] Bley A., Koch T., Integer Programming Approaches to Access and Backbone IP
Network Planning, Preprint ZIB ZR-02-41, 2002.
[6] Fortz B., Thorup M., Internet Traffic Engineering by Optimizing OSPF Weights,
Proceedings of IEEE Infocom, March 2000.
[7] Gajowniczek P., Pioro M., Szentesi A., Harmatos J., Solving an OSPF Routing Problem
with Simulated Allocation, Proceedings of 1st
PGTS, 2000.
[8] Karas P., Pioro M., Optimisation Problems Related to the Assignment of Administrative
Weights in the IP Networks’ Routing Protocols, Proceedings of 1st
PGTS, 2000.
[9] Moy J., OSPF Version 2, RFC 2328, April 1998.
[10] Mulyana E., Killat U., A Hybrid Genetic Algorithm Approach for OSPF Weight
Setting Problem, Proceedings of 2nd
PGTS, 2002.
[11] Riedl A., Optimized Routing Adaptation in IP Networks Utilizing OSPF and MPLS,
Proceedings of IEEE ICC, May 2003.
[12] Staehle D., Koehler S., Kohlhaas U., Optimization of IP Routing by Link Cost
Specification, Tech. Report, University of Wuerzburg, 2000.
[13] Thorup M., Roughan M., Avoiding Ties in Shortest Path First Routing, ___________.

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