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Cost-optimal VPN based VoIP network design *
Dániel Orincsay, Balázs Gábor Józsa, Levente Tamási
Ericsson Research Hungary, Traffic Analysis and Network Performance Laboratory,
Budapest University of Technology and Economics, Dept. of Telecommunications and Media Informatics
E-mail: {Daniel.Orincsay, Balazs.Jozsa, Levente.Tamasi}@eth.ericsson.se
Abstract
This paper addresses the design of cost-optimal VoIP networks. In our model the whole VoIP network is divided
into two logical components: the access network and the transport network. The access network consists of the
VoIP end-points that connect to the transport network through an edge router. Since more edge routers can be
available for a given VoIP node, one task of the design is to assign an edge router for every VoIP node. The edge
routers serve as gateways for the assigned VoIP nodes towards the transport network. The gateways have to be
connected in such way that security and availability could be assured for the VoIP traffic. One obvious approach
to realize this is to define a VPN. Supposing large volume of VoIP traffic the cost of the VPN can be significant.
Thus the other task of VoIP network design is to specify the transport VPN in the most economical way. These
two tasks of VoIP network design can be solved separately using existing methods. Nevertheless, the VoIP region specification influences the cost of the final solution to a great extent. Therefore, in this paper we propose a
novel solution, in which the edge router assignment takes the objective function of VPN specification into consideration. Moreover, a numerical analysis is provided with the help of simulations.
Keywords: VoIP, VPN, cost-optimal, network design
1
Introduction
Nowadays, the all-IP concept is favored by the infocommunication industry, intending to conduct all different types of traffic over the Internet protocol dominant in the networking area. As part of all-IP an increasing number of companies in the telephony area
commit themselves to using the voice over IP (VoIP)
technology. Assuming a large VoIP network having a
huge amount of customers it is necessary to take QoS
as well as economical goals into account during the
design phase.
In our model the VoIP network consists of two logical
components: the access network, and the transport
network. The access network includes the VoIP nodes,
namely, the customer end-points intending to use the
VoIP service. The transport network serves for carrying the aggregated VoIP traffic between the various
access areas. Its main parts are the edge routers, the
transit routers, and the physical links between them.
A VoIP node can reach more than one edge router fulfilling the QoS requirements (e.g., limited maximal
delay) of the phone call service. Therefore, it is necessary to select one of them that will serve as gateway
towards the transport network. The VoIP nodes assigned to the same edge router form a so-called VoIP
region.
*
Generally, it is more economical to apply a virtual private network (VPN) instead of deploying a brandnew physical network to realize the transport network
for a VoIP service (see e.g., [1], [2]). Thus we follow
this approach in this study.
The cost of the VPN depends on the capacity of corresponding devices, such as routers and links. The
area of cost-optimal VPN design has been widely
studied in the literature, where beside the topology the
set of traffic demands and the cost functions of devices were supposed as input parameter. However,
during VoIP network design the traffic distribution
between the VPN nodes cannot be considered as a fix
input, since it largely depends on the specification of
VoIP regions.
In summary, two main tasks can be differentiated in
the case of VoIP network design: (1) VoIP region
specification, i.e., the assignment of each VoIP node
to exactly one VPN edge router, and (2) the design of
the transport network covering the selected VPN
nodes. These two tasks can be solved independently
by applying existing methods, which means that the
objective of VPN transport network design is disregarded during the VoIP region specification. However, it can be more efficient to take also cost and
quality factors concerning the transport network to be
composed into consideration already in the first task.
This issue is addressed in this paper by making sev-
This work was supported by the Ministry of Education, Hungary, under the reference No. IKTA-0092/2002. http://w3.ttt.bme.hu/ikta-2002
eral propositions to solve the VoIP region specification task of the VoIP network design problem. In order to solve the VPN transport network design after
specifying the VoIP regions a core network design algorithm (CND) is used, which proved to be efficient
in the field of cost-optimal VPN design [3]. The numerical investigation of proposed methods is based on
the result of CND—performed after each region
specification method—that gives the final cost of the
VoIP network.
The rest of the paper is organized as follows. The next
section describes the used network, traffic, and cost
models. It also includes the formulation of the VoIP
network design problem. In Section 3 novel approaches are introduced aiming at solving the VoIP
region specification. Then Section 4 presents numerical results obtained from the performed simulations.
Finally, the conclusions are drawn.
2
Problem statement
This section introduces the interpretation of VoIP network design problem considered in the paper. First,
the applied network, traffic, and cost models are discussed. Then the formulation of the problem follows.
Finally, the optimization objective is presented.
2.1
Network model
The VoIP network is modeled by a graph in the following way. Each customer end-point that uses the
VoIP service is called VoIP node. The set of VoIP
nodes is denoted by W. The possible edge routers of
the VPN transport network to be composed are called
VPN nodes. The set of VPN nodes is denoted by V.
Further, we are given so-called VoIP edges connecting
the VoIP-VoIP and VoIP-VPN node-pairs. Each VoIP
edge f has a delay attribute delayf assigned representing its maximal one-way latency. Based on these edge
delay values the delay value dwv can be determined for
each VoIP node w∈W and VPN node v∈V pair, representing the minimal guaranteed latency between them.
If a VPN node v is not available for VoIP node w,
value of dwv is considered as ∞. In the current interpretation the QoS requirement—that the route between the VoIP node and the corresponding VPN
gateway has to fulfill—refers to the maximal access
network latency dmax.
Physical connections between the VPN nodes are
called VPN edges, and their set is denoted by E. The
use of VPN nodes as well as VPN edges is optional,
generally only a subset of them is included in the final
solution of design. The bandwidth of VPN nodes and
edges is limited, their particular capacity values are
determined during the design using the corresponding
cost functions (see Section 2.3).
2.2
Traffic model
Although a VoIP node may refer to one particular customer owning a VoIP phone, it generally represents a
private branch exchange (PBX) including a VoIP media gateway. Due to the large number of VoIP nodes
the generally applied approach of the pipe model [4]
(also known as trunk model)—that means the sourcedestination pair based handling of traffic—is inefficient. Therefore, the hose model [5] is followed,
which defines only the sum incoming and outgoing
traffic of a node. Considering that telephony calls are
handled, the incoming traffic and outgoing traffic are
equal referring to the symmetric hose model. Thus,
the traffic of VoIP node w is modeled by a bandwidth
demand value trw that shows the amount of capacity
needed to satisfy the calls generated (and received) by
the VoIP users in the given node. This value can be
derived from the number and calling behaviors of different VoIP users. However, this issue is related to the
area of traffic modeling, and it is out of the scope of
the paper.
Although the hose model based design results in such
networks that can accommodate extreme traffic distributions as well, the high amount of spare capacity
and consequently extra price make it unacceptable in
cost-sensitive situations. Therefore, in the case of the
VPN transport network the pipe model is estimated in
the following way. First, the hose traffic values of
VoIP nodes in the same region are summed representing the total hose traffic of the corresponding
VPN edge node. Considering that these traffic values
represent large number of users and the number of
VPN nodes is relatively low, the pipe model can be
approximated well in the following way. The summed
traffic of a particular VPN node is distributed among
the other VPN nodes in direct proportion to their total
hose traffic.
2.3
Cost model
In order to model the cost/capacity dependencies of
devices realistically stepwise cost functions are used.
Although this approach makes the design problem
mathematically complex, it can fulfill the high accuracy requirements arising in real situations. Moreover,
in our model each VPN node v and VPN edge e has
individual cost function costv and coste, respectively,
which enables to take special cost modifying factors
as well as policy reasons into account.
2.4
Problem formulation
The VoIP network design problem has the following
input parameters: (1) the set of VoIP nodes W, (2) the
set of possible VPN nodes V, (3) the set of possible
VPN edges E, and (4) the set of delay values dwv for
all VoIP node w∈W and VPN node v∈V pairs (derived from the structure of VoIP nodes and edges).
As the output of the region specification, each VoIP
node is assigned to exactly one VPN node, which determines a set of VPN nodes that are mandatory elements of the VPN transport network to be formed.
Further, as the result of the design process, the VPN
transport network is specified including the exact capacity values of all devices. The paths to be established corresponding to the aggregated VoIP traffic
demands are also given by the applied design method.
2.5


minimize ∑ coste (load e ) + ∑ costv (load v ), (1)
v∈V
 e∈E

where load refers to the actual capacity need on a certain device, and cost(load) indicates the corresponding price of this device.
Methods
This section proposes several methods that are capable of solving the VoIP region specification problem.
Since it is related to the so-called set-covering problem widely studied in the literature [6], [7], term
‘covering’ is used throughout the descriptions of various algorithms referring to the situation when a VPN
node is selected as gateway for a VoIP node.
3.1
Greedy covering algorithm (GC)
This section presents greedy algorithms that are based
on a well-known greedy solution of the set covering
problem (see e.g., [8]). As the first step such VoIP
nodes are searched for that reach only one VPN node
fulfilling the delay requirements. This defines a set of
VPN nodes that is a mandatory part of the solution.
Consequently, we consider covered all VoIP nodes
that can be covered by these VPN nodes. The second
step is an iteration in which further VPN nodes are
selected one by one based on a certain utility value.
When selecting a particular VPN node the corresponding (still uncovered) VoIP nodes get covered.
The iteration stops if the selected VPN nodes cover
all VoIP nodes. In the following, two utility value
variants are presented.
3.1.1
3.1.2
VPN node cost based GC (GC-C)
The utility value used by this variant is the number of
still uncovered VoIP nodes that the given VPN node
could cover divided by the cost of the first capacity
step of its cost function. The idea behind this complex
utility value is to take also the establishment costs of
the VPN nodes into account during the iteration.
Objectives
Aiming at minimizing the overall establishment cost
of the VoIP network, which basically depends on the
cost of the VPN transport network, the objective of
the whole design process is to:
3
ered by the given VPN node. Thus this approach aims
at minimizing the number of selected VPN nodes,
however, it does not take any cost factors into consideration.
VPN node number based GC (GC-N)
In this variant the utility value corresponds to the
number of still uncovered VoIP nodes that can be cov-
3.2
Evolutionary covering algorithm
(EC)
A common property of the above presented greedy
covering algorithms is that they assign a VPN node
for each VoIP node only once, which means that they
do not vary the existing assignments. This approach is
called construction method, i.e., the algorithm stops
when the first feasible solution is found. This provides fast region specification, however, its drawback
is that there is no possibility for sophisticated optimization.
This section proposes such algorithms that are based
on the well-known paradigm of evolutionary algorithms (also called genetic algorithm) [9], which enables to select among more feasible solutions using
complex entity cost calculation (see Sections 3.2.13.2.3). The representation of the VoIP region specification problem applied in the evolutionary algorithm
is the following. Each gene of an entity corresponds
to a VoIP node, and its value refers to the VPN node
the VoIP node is assigned to. During the mutation one
gene of an entity is changed randomly, which means
that the given VoIP node is re-assigned to another
VPN node. During the crossover of two entities, the
child inherits its genes from one of its parents with
equal probability. The selection of entities that do not
survive is done by killing the oldest entity from k randomly selected entities, and killing the worst one
(based on the used entity cost calculation) from another k randomly selected entities. In order to create
an appropriate initial population the GC-C was applied in the following way. A feasible solution is
sought by GC-C, excluding exactly one VPN node
from the solution. The excluded VPN node is altered,
thus more different feasible coverings consisting of
VPN nodes having low establishment cost values
form the initial population. The algorithm stops if the
cheapest solution—considering the actual cost calculation—did not change during the last n steps.
The applied entity cost calculation method has a large
influence on the quality of solution. Thus more approaches are investigated in the study, as it can be
seen in the following sections.
3.2.1
Cost approximation based EC (EC-C)
The main idea behind the cost approximation based
method (EC-C) is that we try to foresee the final cost
of the VPN transport network to be designed. It routes
the set of the aggregated VoIP traffic demands several
times, based on different random orders. Dijkstra’s
shortest path algorithm is applied for this purpose in
which such edge weight function is considered that
prefers devices having low cost per unit traffic. Finally, the price of the cheapest configuration is considered as the cost of entity.
3.2.2 Distance weighted traffic based EC
(EC-D)
When applying the distance weighted traffic based
method (EC-D), the product of the bandwidth requirement and the length of the possible shortest path
(in terms of hop-count) is calculated for each aggregated VoIP traffic demand. Then the cost of entity is
specified as the sum of these products regarding the
whole network.
3.2.3 Two-level cost metric based variants
(EC-C2, EC-D2)
We examine also the two-level variants of the above
cost metrics in the following way. The number of selected VPN edge routers serves as primary metric.
Then the cost approximation or the distance weighted
traffic methods scaled by an importance factor s are
regarded as second metric.
4
Results
In order to investigate the performance of the proposed algorithms we carried out simulations using
artificial problem instances. First, the automated
method of problem instance generation is described,
then the performed simulation scenarios are presented
including the analysis of the numerical results.
4.1
Problem instance generation
During the simulations we aimed at creating such
problem instances that represent well the real situations. However, we note that in case of other types of
problem instances the results of algorithms may differ. The first task is to generate the topology of network including VoIP nodes and edges as well as possible VPN nodes and edges. For this purpose we applied a random VoIP graph generator method that is
based on the Barabási-Albert model [10], [11]. This
approach is based on the power laws of Internet topology [12], [13], and nowadays it is frequently used
to model wide area communication networks. Various
size topologies were examined, however, we present
results for networks having 500 VoIP nodes, and 50
Fig. 1
Example network topology
possible VPN nodes. The delay value of VoIP edges
were specified randomly using such distribution that
generates values proportionally to the lengths of
edges, i.e., the distances between their end-points.
The traffic demands of VoIP nodes were generated
randomly in the following way. First, the number of
maximal parallel calls was generated for each VoIP
node in the interval [1, 2n]. The value of n refers to
the average number of maximal parallel calls, and it
was shifted from 96 to 256. Then the number of parallel calls had to be scaled due to the actually used codec type and packetization overhead (RTP/UDP/IP
header). Assuming the use of ITU-T recommendation
G.711 PCM codec—that can provide the highest voice
quality—with silence suppression having activity factor of 55% and 5 ms packetization time, the investigated VoIP traffic (trw) interval was 6 to 16 Mbps.
The cost functions of VPN edges were based on the
STM standards, while in the case of VPN nodes three
different size devices were assumed. The detailed description of the used cost functions can be found in
[1].
4.2
Optimization of parameters
The first simulation scenario targeted the optimization
of parameters of the evolutionary algorithm EC. It
turned out that parameter value combination k=3,
n=1000, s=500 can give a good tradeoff between the
quality and running time measures, therefore this parameter value combination was used throughout the
next simulation scenarios.
4.3
Total network cost
The most important performance indicator is the resulting total cost of the network. As it can be seen in
Fig. 2, the simplest method GC-N provided the most
expensive solution. Taking the establishment cost of
VPN nodes into account (GC-C), about 3% improve-
Total network cost [unit]
2000
4.5
GC- N
GC- C
1800
EC-C
1600
EC-D
EC-C2
EC-D2
1400
1200
1000
6
8
10
12
14
16
Average VoIP network traffic [Mbps]
Fig. 2 Total network cost using different algorithms
ment can be achieved. Algorithms EC-C and EC-C2
performed similarly, and they decreased the total network cost by further 7–9% compared to GC-C. Applying EC-D more economical configurations can be
obtained in the higher traffic intervals. EC-D2 proved
to be the best algorithm as it outperformed all other
approaches in all examined test cases. The improvement compared to the simplest method GC-N varied
from 15–25% depending on the traffic volume.
Although in the case of off-line network design the
running time has only secondary importance, it is
worth examining also this factor in order to make the
investigations complete. As it can be seen in Table 1,
GC algorithms were very fast as they provided results
within one minute on average. EC-C and EC-C2 had
similar results again, but one order of magnitude
higher compared to GC. Basically, the time consumption of region specification is low in the case of distance weighted traffic based algorithms EC-D and
EC-D2. However, EC-D2 resulted in higher overall
running time due to the fact that the running time of
the final VPN design step carried out by CND highly
depends on the number of VPN gateways.
Design
algorithm
Running
time [min]
Table 1
4.4
Number of VPN nodes
Besides the cost of the VPN transport network its size
is also an important attribute, which can be described
well by the number of VPN nodes. Thus, in this scenario we compared the algorithms focusing on this
basic measure. Fig. 3 presents the number of used
VPN nodes in the final transport network differentiating the edge and transit types. Since these measures
did not show relevant change against the change of
average VoIP node traffic, results are presented only
for the 12 Mbps value.
We can see that as the total network cost decreases,
the total number of VPN nodes decreases. The exception is EC-D, whose result differs relevantly from the
other ones as it uses much more VPN gateways. The
reason for this could be the lower impact of VPN
node number on the entity cost values compared to
the other cases. Another observation is that the number of VPN edge nodes shows increasing tendency.
This means that the sophisticated selection of VoIP
traffic aggregation points is more important than
keeping their number as low as possible.
Number of VPN nodes
50
ed g e
t rans it
40
Running time
5
GC-N
GC-C
EC-C
EC-C2
EC-D
EC-D2
1
1
12
11
19
6
Running time values
Conclusion
This paper addressed the area of cost-optimal VoIP
network design. The whole design problem consists
of two main tasks: the specification of VoIP regions,
and the design of the VPN transport network. We
have proposed a novel approach aiming at improving
the cost efficacy by taking the objective of transport
network design into consideration during the region
specification.
We have presented various new algorithms that realize the novel approach. In order to evaluate their performance, numerous simulations have been carried
out. It has turned out that significant reduction in total
network cost can be achieved by applying sophisticated cost evaluation in the VoIP region specification
phase. Based on the performed simulations the evolutionary algorithm—using VPN node number and distance weighted traffic based cost approximation—
seems to be the best choice.
Our future work includes the investigation of such
situations where also other types of traffic demands
having high bandwidth requirement—such as video
telephony—are handled. Another direction is to take
also reliability issues into consideration during the
VPN transport network design.
30
Acknowledgment
20
10
0
GC-N
Fig. 3
GC-C
EC-C EC-C2
Design algorithm
EC-D
EC-D2
Number of edge and transit VPN nodes
The authors would like to thank Gábor Magyar for his
insightful suggestions and comments. Further, the
authors are grateful to the members of project IKTA
and people in Ericsson Research Hungary for their
valuable remarks.
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