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Computer Networks 50 (2006) 599–614

www.elsevier.com/locate/comnet

Cost-optimal design of VoIP networks using the VPN concept

Levente Tamasi, Daniel Orincsay *, Balazs Gabor Jozsa

Ericsson Research, Traffic Analysis and Network Performance Laboratory, P.O. Box 107, H-1300 Budapest, Hungary

Received 1 September 2004; received in revised form 18 May 2005; accepted 23 May 2005Available online 21 July 2005

Responsible Editor: Nelson Fonseca

Abstract

This paper addresses the issue of cost-optimal voice over IP (VoIP) network design. In the applied model, the wholeVoIP network is divided into two logical components: the access network and the transport network. The access net-work consists of VoIP end-points that connect to the transport network through edge routers serving as gateways. Sincemultiple edge routers may be available for any given VoIP node, one task of the design process is to assign a particularedge router to every VoIP node. The edge routers have to be connected in a way that security and availability can beassured for the VoIP traffic. One obvious approach to fulfilling these requirements, which is assumed throughout thepaper, is to define a virtual private network (VPN). Supposing a large volume of VoIP traffic, the cost of the VPN canbe 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 specificationof VoIP regions influences the cost of the final solution to a great extent. Therefore, in this paper a novel approach isproposed in which the edge router assignment process takes the objective function of VPN specification into consider-ation as well. In order to realize the new approach, multiple methods are introduced which are based on the paradigmsof genetic algorithms and simulated annealing. These methods perform a sophisticated optimization of the gatewayassignments using various cost calculation methods. To evaluate the new algorithms, a method based on a well-knowngreedy solution to the problem is used as reference. Moreover, a VPN specification algorithm is presented which utilizesthe stepwise nature of the cost functions. The performance of the presented methods is evaluated with the help ofsimulations. It is shown that the proposed methods outperform the reference algorithm significantly in the simulationscenarios investigated.� 2005 Elsevier B.V. All rights reserved.

Keywords: VoIP; VPN; Cost-optimal; Network design; Stepwise function

1389-1286/$ - see front matter � 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.comnet.2005.05.026

* Corresponding author. Tel.: +36 1 437 7179; fax: +36 1 437 7767.E-mail addresses: [email protected] (L. Tamasi), [email protected] (D. Orincsay), balazs.jozsa@ericsson.

com (B.G. Jozsa).

600 L. Tamasi et al. / Computer Networks 50 (2006) 599–614

1. Introduction

Nowadays, the all-IP concept is favored by theinfocommunication industry, which intends toconduct all types of traffic over the internet proto-col dominant in the networking area. As a part ofall-IP, an increasing number of companies in thetelephony area commit themselves to using thevoice over IP (VoIP) technology. Assuming a largeVoIP network with a huge number of customers, itis necessary to take quality of service (QoS) as wellas economic criteria into account during the designphase.

QoS requirements may be considered in multi-ple ways in the VoIP network. One possible ap-proach is using a best effort IP service, thedrawbacks of which are its incapability to provideQoS guarantees and the consequent fact that theservice level can only be maintained by overprovi-sioning [1]. On the other hand, guaranteeing perflow QoS between all customer end-points, usinge.g., the IntServ architecture, is both expensiveand inefficient. In the current study, a practicallyviable intermediate approach is followed: the VoIPnetwork is divided into two logical components,with a pure IP based service used in the access net-work and QoS guaranteed in the transport network.The access network includes the VoIP nodes, i.e.,the customer end-points that intend to use theVoIP service, while the transport network servesthe purpose of carrying the aggregated VoIP trafficbetween the various access areas. The main partsof the transport network are the edge routers,the transit routers, and the connections betweenthem. Since a VoIP node may reach more thanone edge router so that the transmission path ful-fills the QoS requirements of the telephone service(e.g., limited maximal delay), it is necessary to se-lect the one that will serve as a gateway towardsthe transport network. The VoIP nodes assignedto the same edge router form a so-called VoIP

region.Generally, it is more economical to apply a vir-

tual private network (VPN) instead of deploying abrand-new physical network to realize the trans-port network for a VoIP service (see e.g., [2,3]).The most important advantages of VoIP VPNsare cost efficiency, security, and scalability [4,5].

Therefore, this study follows the VPN approach,which can be applied in different layers of the opensystem interconnection (OSI) model. One possibil-ity is using a Layer 1 (L1) optical VPN (oVPN), inwhich case a network user rents separate opticalconnections from a service provider [6] and installsits own routers at their end-points. This results intotal separation of the users� traffic at the physicallevel, similarly to leased lines. Another novel ap-proach is using a Layer 2 (L2) VPN [7], which pro-vides a data link layer service to customers over awide area network (WAN) using multiprotocollabel switching (MPLS); therefore, hosts connectedby a wide area network appear to be on the samelocal area network (LAN). MPLS can also be usedto realize a traditional Layer 3 (L3) IP VPN. Thelatter two approaches provide logical separationof users� traffic, i.e., at the physical level, the opticalconnections are shared, and the traffic of differentcustomers is only separated at the MPLS level withthe help of label switched paths (LSPs).

To sum up, there are several approaches to real-izing a VoIP VPN. In all cases, however, the costof the VPN depends on the capacity of the corre-sponding devices, i.e., the routers and the connec-tions between them. The area of cost-optimal VPNdesign has been widely studied in the literature,with the topology, the set of traffic demands, andthe cost functions of devices assumed as inputparameters. However, during VoIP networkdesign, the traffic distribution between the VPNnodes cannot be considered a fix input since it lar-gely depends on the specification of VoIP regions.Therefore, two interdependent tasks can be differ-entiated between in the case of VoIP networkdesign: (1) VoIP region specification, i.e., theassignment of each VoIP node to exactly oneVPN edge router and (2) the design of the trans-port network covering the selected VPN nodes.These two tasks can be solved independently byapplying a number of existing methods, in whichcase the objective of the VPN transport networkdesign is disregarded during the VoIP region spec-ification. However, it can be more efficient to havethe cost and quality factors concerning the trans-port network taken into consideration already inthe first task. This approach is followed in thispaper by making several propositions with a view

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to solving the VoIP region specification task of theVoIP network design problem based on the princi-ples of evolutionary algorithms [8] and simulated

annealing [9]. Furthermore, in order to solve theVPN transport network design subproblem, a corenetwork design algorithm (CND) is presented,which is applied after specifying the VoIP regions.This heuristic algorithm exploits the stepwise nat-ure of the cost functions of transport networkdevices and has been shown to be efficient in thearea of cost-efficient VPN specification [10]. Thenumerical investigation of the proposed methodsis performed by means of simulations, using the fi-nal cost of the VoIP network given by CND as themain performance measure. During the investiga-tions, a region specification method based on awell-known greedy algorithm [11] is used asreference.

The rest of the paper is organized as follows.The next section describes the network, traffic,and cost models used. It also includes the formula-tion of the VoIP network design problem. In Sec-tion 3 novel approaches are introduced aimed atsolving the VoIP region specification subproblem.Section 4 describes the core network design algo-rithm proposed for transport VPN design. Section5 presents numerical results obtained from the per-formed simulations. Finally, the conclusions aredrawn.

2. Problem statement

This section introduces the interpretation of theVoIP network design problem considered in thepaper. First, the applied network, traffic, and costmodels are discussed, followed by the formulationof the problem including the optimization objec-tive.

2.1. Network model

The VoIP network is modeled by a graph in thefollowing way. A customer end-point that uses theVoIP service is called a VoIP node. The set of VoIPnodes is denoted by W. The possible routers of theVPN transport network to be composed are calledVPN nodes. The set of VPN nodes is denoted by V.

Further, so-called VoIP edges are given whichconnect the VoIP-VoIP and VoIP-VPN node-pairs. The set of VoIP edges is denoted by F. EachVoIP edge f 2 F has a delay attribute delayf as-signed representing its maximal one-way latency.Based on these edge delay values the delay valuedwv can be determined for each VoIP nodew 2W and VPN node v 2 V pair, representing aguarantee on the maximal latency between them.If a VPN node v is not available for a VoIP nodew, the value of dwv is considered to be 1. In thecurrent interpretation, the QoS requirement thatthe route between the VoIP node and the corre-sponding VPN gateway has to fulfill is the maxi-mal access network latency dmax. Thus, a VPNnode v 2 V is only considered as a candidate gate-

way for a given VoIP node w 2 W if the value ofdwv does not exceed dmax. Since these delay require-ments have to be fulfilled at both end-points of aVoIP call, and the VPN concept guarantees thatlatency limits are satisfied in the transport net-work, the maximum delay requirements of thevoice service (i.e., a one-way delay of 150 ms asrecommended by the ITU-T) can be assured.

VPN nodes are connected by so-called VPN

edges, the set of which is denoted by E. The useof VPN nodes as well as VPN edges is optional;typically only a subset of them is included in thefinal solution of the design. The bandwidth ofVPN nodes and edges is limited; their particularcapacity values are determined during the designphase using the corresponding cost functions (seeSection 2.3). While most VPN specification meth-ods take the maximal capacity constraint of con-nections into account, the capacity aspect ofrouters is often neglected. However, during the de-sign phase this latter factor also has to be consid-ered, i.e., VPN nodes must be handled similarly toVPN edges. For this reason, the VPN nodes aresubstituted by virtual VPN edges for the investiga-tions as shown in Fig. 1. For instance, node u isdecomposed into two nodes uin and uout, which be-long to the incoming and outgoing traffic of theoriginal node, respectively. Henceforth, node uoutis responsible for the traffic originated, while nodeuin manages the traffic terminated by the originalVPN node u. Further, since the traffic transferredby the original node u traverses the virtual edge

Fig. 1. Substituting the VPN nodes with virtual VPN edges: (a) original VPN graph and (b) transformed VPN graph.

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between nodes uin and uout, the capacity constraintof the original router can be easily taken intoconsideration.

2.2. Traffic model

Although a VoIP node may refer to one partic-ular customer owning a VoIP phone, it typicallyrepresents a private branch exchange (PBX)including a VoIP media gateway, which serves anumber of users conducting a significant amountof VoIP calls. Due to the large number of VoIPnodes the generally applied approach of the pipemodel [12] (also known as the trunk model), i.e.,the source–destination pair based handling of traf-fic, is cumbersome. Therefore, the hose model [13]is followed, which defines only the sum incomingand outgoing traffic of a node. Assuming that tele-phone calls are handled, the incoming and out-going traffic are equal corresponding to thesymmetric hose model. Thus, the traffic of anygiven VoIP node w is modeled by a bandwidthdemand value trw that shows the amount ofcapacity needed to satisfy the calls generated(and received) by the VoIP users in the given node.This value can be derived from the number andcalling habits of different VoIP users; however, thisissue is related to the area of traffic modeling, andit is thus beyond the scope of the paper.

Although the hose model based design results innetworks that can accommodate extreme trafficdistributions as well, the high amount of sparecapacity and the consequent extra price make itunacceptable in cost-sensitive situations. There-fore, in the case of the transport VPN the pipemodel is applied, i.e., the traffic between a pairof VPN nodes u, v 2 V is modeled by a bandwidthvalue Truv, which is estimated in the following

way. First, the total hose traffic value of each edgeVPN node is calculated by summing the hose traf-fic values of VoIP nodes in the correspondingVoIP region. Considering that these traffic valuesrepresent large numbers of users and the numberof VPN nodes is relatively low, the pipe model isapproximated by distributing the sum traffic of aparticular VPN node among the other VPN nodesin direct proportion to their total hose trafficvalues.

2.3. Cost model

The relationship between the cost and capacityvalues of VPN nodes and edges can be representedwith the help of monotonic nondecreasing costfunctions. In the simplest case, linear functionscan be used. In this way, every required capacityunit has the same cost value, which gives the slopeof the curve. In the overwhelming majority ofcases, these approximations are inadequate tomodel real cost relations; however, it is a relativelyfrequent approach because of the simplicity of thecomputations involved.

In real-life situations, the various devices, i.e.,the routers and the connections between themhave discrete capacity values and consequently dis-crete cost amounts. These types of cost dependen-cies can be described with so-called stepwisefunctions [14–17] (see Fig. 2). Although this ap-proach makes the VPN design subproblem mathe-matically complex [18], it can fulfill the highaccuracy requirements arising in real-life situa-tions. Moreover, in the applied model each VPNnode v and VPN edge e has an individual costfunction costv and coste, respectively, whichenables special cost modifying factors as well aspolicy reasons to be considered.

cost

cost

cost

cap cap cap1

cap

cost

cost [unit]

capacity [unit]

1

2

3

4

3 42

Fig. 2. Stepwise cost function example.

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2.4. Problem formulation

This section contains the description of theinputs and outputs of the two tasks of the VoIPnetwork design problem. The VoIP region specifi-cation subproblem has the following input param-eters: (1) the set of VoIP nodes W, (2) the set ofpossible VPN nodes V, (3) the set of delay valuesdwv for all VoIP node w 2W and VPN nodev 2 V pairs (derived from the structure of VoIPnodes and edges) and the maximal access networklatency dmax, and (4) the hose traffic values trw forall VoIP nodes w 2W.

As the output of region specification, each VoIPnode is assigned to exactly one VPN node, whichdetermines a set of VPN nodes that are mandatoryelements of the VPN transport network to beformed. This assignment can be used to calculatethe traffic demands between pairs of VPN nodesas described in Section 2.2. Therefore, the trans-port VPN design subproblem takes the followinginput parameters: (1) the set of VPN nodes V

(both the gateways and the possible transit VPNnodes), (2) the set of possible VPN edges E, (3)the bandwidth values Truv for all pairs of VPNnodes u, v 2 V, and (4) the cost functions ofVPN nodes and edges denoted by costv and coste,respectively. As a result of the design process, theVPN transport network is specified including theexact capacity values of all devices. The paths tobe established for the aggregated VoIP traffic de-mands are also given by the applied designmethod.

Aiming at minimizing the overall establishmentcost of the VoIP network, which basically dependson the cost of the VPN transport network, theobjective of the whole design process is to

minXe2E

costeðloadeÞ þXv2V

costvðloadvÞ( )

;

where load refers to the actual capacity need on acertain device, and cost(load) indicates the corre-sponding price of the device.

3. VoIP region specification

This section proposes several methods that arecapable of solving the VoIP region specificationsubproblem. Since it is related to the so-calledset-covering problem widely studied in the litera-ture [19,20], the term covering is used throughoutthe descriptions of various algorithms referringto the situation when a VPN node is selected asa gateway for a VoIP node.

3.1. Greedy covering algorithm (GC)

This section presents greedy algorithms that arebased on a well-known greedy solution to the setcovering problem (see e.g., [11]). The algorithmsconsist of two main steps. In the first step, VoIPnodes with only one candidate gateway each areidentified. Since each of these VoIP nodes has ac-cess to only one VPN node fulfilling the delay

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requirements, the corresponding VPN nodes de-fine a set of gateways that is a mandatory part ofthe solution. Consequently, all VoIP nodes thathave at least one candidate gateway among theseVPN nodes are considered covered. The secondstep of the algorithm is an iteration in which fur-ther VPN nodes are selected one by one basedon a certain utility value. When a particular VPNnode is selected, the uncovered VoIP nodes thatcan access the VPN node fulfilling the delay limitsget covered. The iteration stops if the selectedVPN nodes cover all VoIP nodes. In the following,two utility value variants are presented.

3.1.1. VPN node number based GC (GC-N)

In this variant the utility value corresponds tothe number of yet uncovered VoIP nodes thatcan be covered by the given VPN node. Therefore,this approach aims at minimizing the number ofselected VPN nodes; however, it does not takeany cost factors into consideration.

3.1.2. VPN node cost based GC (GC-C)

The utility value used by this variant is the num-ber of yet uncovered VoIP nodes that the givenVPN node can cover divided by the cost value cor-responding to the first step of its cost function. Theidea behind this utility value is to take the estab-lishment costs of the VPN nodes also into accountduring the iteration.

3.2. Evolutionary covering algorithm (EC)

A common property of the greedy coveringalgorithms presented above is that they assign aVPN node to each VoIP node only once, whichmeans that they do not vary the existing assign-ments. This approach is referred to as constructionmethod, i.e., the algorithm stops when the first fea-sible solution is found. This provides fast regionspecification; however, its drawback is that thereis no possibility for sophisticated optimization.

This section proposes an algorithm that is basedon the well-known paradigm of evolutionary algo-

rithms (also called genetic algorithms) [8], whichenables selection between more feasible solutionsusing complex cost calculation methods (see Sec-tion 3.4). The representation of the VoIP region

specification subproblem applied in the evolution-ary algorithm is the following. An entity defines avalid assignment, where each gene corresponds toa VoIP node, and its value refers to one of its can-didate VPN nodes the particular VoIP node is as-signed to. In each iteration, either a crossover or akilling operation is performed based on the actualpopulation size. In the case of crossover, each ofthe two parents is selected by choosing the entitywith the lowest cost (regarding the actual cost cal-culation method) from a set of randomly selectedentities, and the child inherits each of its genesfrom either of its parents with equal probability.Similarly, the selection of entities that do not sur-vive is performed by killing the oldest entity from anumber of randomly selected entities, and killingthe one with the highest cost (based on the costcalculation method used) from another set of ran-domly selected entities. In the case of both opera-tions, the size of the set of randomly selectedentities is given by a parameter k. Moreover, dur-ing all iterations, mutation is performed, i.e., onegene of an entity is changed randomly, whichmeans that the given VoIP node is re-assigned toanother of its candidate VPN nodes. In orderto create an appropriate initial population, theGC-C algorithm is applied in the following way.Several feasible solutions are sought by GC-C,excluding a different VPN node from the initialset of VPN nodes in each iteration. Naturally,VPN nodes that are mandatory elements of thesolution cannot be excluded. Using this method,several different feasible coverings consisting ofVPN nodes with low establishment cost valuescan be generated to form the initial population.The evolutionary algorithm stops if the cheapestsolution considering the actual cost calculationhas not changed during the last n steps.

3.3. Simulated annealing based covering

algorithm (SC)

This section proposes an algorithm for theVoIP region specification subproblem based onthe principle of simulated annealing [9]. The repre-sentation used is similar to the one presented in theprevious section: a state defines a valid assignmentbetween VoIP nodes and VPN nodes and consists

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of values each of which refers to the VPN node theparticular VoIP node is assigned to. The initial

state is based on a solution by GC-C, whilerandom changes in the state are generated byre-assigning a randomly selected VoIP node toanother of its candidate VPN nodes. States areevaluated using the same cost calculation methodsas in the case of the evolutionary algorithm (seeSection 3.4). A state is accepted with a probabilityof e

C�C0T , where C and C 0 denote the cost of the

previous and current state, respectively, while T

is the temperature of the previous state. This meansthat a state with a higher cost value can also beaccepted by the algorithm; however, the probabil-ity of this event decreases heavily against both thecost difference and the temperature. The annealingschedule takes the form of T 0 = T Æ/, where T is thetemperature in the previous iteration, T 0 is thecurrent temperature, and / denotes the annealing

factor. The initial temperature is denoted by T0.As seen in the case of the evolutionary algorithm,the simulated annealing algorithm terminates if thecost of the cheapest solution has not improvedduring the last n iterations.

3.4. Entity and state cost calculation methods

The quality of the solutions by both EC and SCis heavily influenced by the cost calculation meth-od used for evaluating the entities and states,respectively. Thus, more approaches are investi-gated in this study, as it can be seen in the follow-ing sections.

3.4.1. Cost approximation based methods

(EC-C, SC-C)

The main idea behind the cost approximationbased methods (EC-C and SC-C) is trying to fore-see the final cost of the VPN transport network tobe designed. The set of the aggregated VoIP trafficdemands are routed several times, based on differ-ent random orders. Dijkstra’s shortest path algo-

rithm is applied for this purpose with an edgeweight function that favors devices with low costper unit traffic values. Finally, the algorithm con-siders the price of the cheapest configuration thecost of the entity or state.

3.4.2. Distance weighted traffic based methods

(EC-D, SC-D)

When applying the distance weighted traffic

based methods (EC-D or SC-D), the product ofthe bandwidth requirement and the length of thepossible shortest path (in terms of hop-count) iscalculated for each aggregated VoIP traffic de-mand. Then the cost of the entity or state is spec-ified as the sum of these products regarding thewhole network. This metric aims at reducing thenumber of transit VPN nodes required, especiallybetween edge VPN nodes with higher hose trafficvalues.

3.4.3. Two-level cost metric based variants

(EC-C2, EC-D2, SC-C2, SC-D2)

The two-level variants of the above cost metricswere also investigated in the following way. Thenumber of the selected VPN edge routers servesas primary metric, while the value computed bythe cost approximation or distance weighted trafficmethods is normalized by the initial value of themetric, scaled by an importance factor s, and usedas a secondary metric. These metrics generallyfavor assignments where the number of gatewaysis low, however, they may also select a larger num-ber of edge VPN nodes if the gain in the secondarymetric is significant enough.

3.4.4. Interconnection based methods

(EC-I, SC-I, EC-TI, SC-TI)

The interconnection based methods (EC-I andSC-I) aim at reducing the total network cost byselecting a group of heavily interconnected edgeVPN nodes, thus diminishing the number of therequired transit VPN nodes. The degree of inter-connection is defined as the number of VPN edgesconnecting the selected VPN nodes directly, di-vided by the maximal possible number of edges be-tween them, which corresponds to the case whenthe selected VPN nodes are fully meshed. The costof an entity or state is then defined as the numberof selected VPN nodes, divided by the degree ofinterconnection.

In the case of the traffic weighted interconnectionbased methods (EC-TI and SC-TI), each VPN edgebetween the currently selected VPN nodes is as-signed a weight defined as the sum hose traffic of

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the two VPN nodes it connects. The weights of allVPN edges between the selected VPN nodes aresummed, and this sum is divided by itsmaximal pos-sible value corresponding to a fully interconnectedgroup of VPN nodes. The cost of the entity or stateis defined as the number of selected VPN nodesdivided by the above ratio. The idea behind thismetric is to favor assignments where VPN nodeswith higher hose traffic values can transmit theirtraffic on direct links, while taking the number of se-lected VPN nodes into consideration at the sametime. Note that the above interconnection basedmethods (EC-I and SC-I) can be viewed as special-izations of these methods where all VPN edgesbetween the selected VPN nodes have unit weights.

4. Transport VPN design

This section describes the core network design(CND) algorithm proposed as a solution to thetransport VPN specification subproblem definedin Section 2. The outline of the algorithm is givenin Section 4.1, followed by a detailed descriptionof its phases.

4.1. Algorithm outline

The algorithm presented for transport VPN de-sign is a heuristic method which outperformed [10]a reference algorithm based on the principle ofgreedy randomized adaptive search procedures

(GRASP) [21], a method which was shown to beable to solve the location and dimensioning prob-lems arising in the field of cost-optimal VPN spec-ification efficiently [22]. Note that although CNDis used to solve the transport VPN specificationsubproblem in this study, it may be applied inthe case of any underlying networking technologythat supports explicit routing and bandwidth res-ervation (e.g., ATM or MPLS).

Fig. 3. The three phases of the core ne

The process can be divided into three subse-quential phases (see Fig. 3). The algorithm startswith the initial capacity estimation (ICE) phase,whose task is to estimate the approximate capacityconditions. The main phase is the iterative routingoptimization (IRO), which searches for an appro-priate network configuration based on the initialestimations. Although this second phase alreadyprovides an economical solution to the VPN spec-ification subproblem, a cheaper configuration canbe reached with the help of the last phase calledposterior capacity refinement (PCR).

Generally, two types of search methods can bedifferentiated between. The first two phases (ICEand IRO) perform global search, utilizing compre-hensive information about the current networkstructure and the traffic demands. The purposeof this is to diminish the whole state space in away that its remaining part approaches the opti-mal solution. Then the third phase (PCR) per-forms a local search aimed at finding the mostfavorable solution in the reduced state space.

4.2. Initial capacity estimation

The main purpose of the initial capacity estima-tion (ICE) phase is to assess the necessary devicecapacities by analyzing the set of traffic demands.Thus, prior information can be provided for IROby supplying a partially dimensioned network asan initial state. Therefore, the remaining task ofIRO is to finalize the dimensioning of devicesand the routing of demands. Although ICE typi-cally does not give a full solution to the task, itspecifies a favorable starting configuration basedon a global picture of the transport VPN designsubproblem.

The operation of ICE is based on an iteration(see Fig. 4). In Step 1, the traffic demands to beaccommodated are shuffled randomly. Then inStep 2, they are routed one after another (in the

twork design (CND) algorithm.

Fig. 4. Steps of the initial capacity estimation (ICE) phase.

L. Tamasi et al. / Computer Networks 50 (2006) 599–614 607

above order) using Dijkstra�s shortest path searchalgorithm with the following edge weight function:newDeviceCost

newDeviceTraffic, where newDeviceCost is the cost of thegiven device if it is involved in the path of the ac-tual demand, and newDeviceTraffic is the sum traf-fic that the device has to manage in the above case.This weight function favors devices with low costper unit traffic values with a view to keeping theoverall network cost at a low level. In Step 3, thetotal network cost and device capacity values cor-responding to the accommodation calculated inStep 2 are stored. These steps are repeated a prede-fined number of times (see Step 4), which is set to100 during the experiments. Finally in Step 5,those accommodations are determined whose totalnetwork cost is worse than the best cost valueencountered during the above iterations at mostby a predefined percentage (set to 10% duringthe simulations), and the capacity values of the de-vices are specified in a way that each device is as-signed the lowest value of the ones saved duringthe above accommodations. This idea is based onthe assumption that if several random accommo-dations with low total network cost values needa certain amount of capacity on a particular de-vice, then it is probable that the optimal accommo-dation will also need as much bandwidth.

Fig. 5. Steps of the iterative routin

4.3. Iterative routing optimization

The main phase of the algorithm, namely theiterative routing optimization (IRO) phase isbased on an algorithm that can accommodate agiven set of traffic demands in a graph with capac-ity limits. In this study, the algorithm proposed in[23] is used for this purpose. As it was shown in[23], this algorithm performs well in terms of feasi-bility, i.e., it finds a solution for a given probleminstance, supposing that there is a valid solution.An important advantage of IRO is that the routingoptimization procedure applied can be substitutedby any other method fulfilling the same task.

The steps of the IRO process are shown inFig. 5. In Step 1, IRO attempts to accommodatethe traffic demand set considering the actualcapacity constraints. If the algorithm terminateswith success (Step 2), i.e., all demands are accom-modated, IRO finishes. Otherwise, the capacity ofa particular device is increased by one capacitystep in the following way. In Step 3, the remainingdemands that could not be fit into the graph underthe actual capacity conditions are accommodated,disregarding the capacity constraints. The deviceto be extended in Step 4 is the one on which thecapacity violation, i.e., the extra capacity required

g optimization (IRO) phase.

608 L. Tamasi et al. / Computer Networks 50 (2006) 599–614

by the actual accommodation is the largest. Afterthe capacity increase, Step 1 follows again withthe updated capacity limits.

4.4. Posterior capacity refinement

As it was discussed in Section 4.1, after the IROphase a suitable solution to the VPN specificationsubproblem is already available. However, this re-sult might be improved with the help of posteriorcapacity refinement (PCR). This greedy methodis based on a local search procedure, which meansthat the process concentrates only on one part ofthe network at a time.

The idea behind PCR is to reduce the size of de-vices that are underutilized in the sense that if arelatively small amount of traffic was removedfrom them, a device with lower capacity and con-sequently lower cost level would suffice. For exam-ple, if the traffic to be managed on a connection is170 Mbps, then two 155 Mbps devices have to beinstalled in parallel, while if traffic on the particu-lar connection could be reduced by about 10%,one 155 Mbps device would be sufficient, whosecost would be the half of the original. The remain-ing 10% of the traffic should be redirected ontoother connections utilizing their spare capacity, ifpossible.

Fig. 6 shows the operation of the PCR method.In Step 1, the devices are sorted by their relativestep utilization, i.e., the utilization of the capacityrange belonging to the current cost value. The rea-son is that in the case of a device with a lower rel-ative step utilization, it is more probable that if itscapacity is decreased by one step, the traffic de-mands can still be satisfied under these tightercapacity conditions. Next in Step 2, the devices

Fig. 6. Steps of the posterior capa

are shrunk one by one in the above order, andthe accommodation of the traffic demands is at-tempted by IRO in Step 3. If, after the shrinkingof a particular device, IRO results in a configura-tion that is cheaper than the best overall cost sofar (Step 4), the process restarts from the sortingstep. Otherwise, the solution before the capacitydecrease step is restored in Step 5. The process isterminated if the overall cost could not beimproved since the last sorting (Step 6).

5. Results

In order to investigate the performance of theproposed algorithms, simulations were carriedout using artificial problem instances. First, theautomated method of problem instance generationis described; then, the performed simulation sce-narios are presented including the analysis of thenumerical results.

5.1. Problem instance generation

During the simulations the aim was to createproblem instances that provide a good representa-tion of real-life situations. The first task was togenerate the topology of the network, includingthe VoIP nodes and edges as well as the possibleVPN nodes and edges. For this purpose a randomVoIP graph generator method was applied that isbased on the Barabasi–Albert model [24,25]. Thisapproach is based on the power laws of Internettopology [26,27], and nowadays it is frequentlyused to model wide area communication networks.Topologies of various sizes were examined; how-ever, results are presented only for networks with

city refinement (PCR) phase.

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500 VoIP nodes and 50 possible VPN nodes. Thedelay values of VoIP edges were specified ran-domly using a distribution that generates valuesproportionally to the lengths of edges, i.e., the dis-tances between their end-points. The maximum ac-cess network latency dmax was set to 50 ms for theinvestigations, as was the guarantee on the maxi-mal delay in the transport VPN. These valuesassure that the ITU-T recommendation for amaximal one-way delay of 150 ms is compliedwith.

The traffic demands of VoIP nodes were gener-ated randomly in the following way. First, the max-imal number of parallel calls was generated foreach VoIP node in the interval [1,2N]. The valueof N refers to the average number of maximal par-allel calls, and it was shifted from 32 to 256. Thenthe number of parallel calls had to be transformedinto a bandwidth value based on the codec type andpacketization overhead (RTP/UDP/IP header)actually used. Assuming the use of the ITU-Trecommendation G.711 PCM codec, which canprovide the highest voice quality, with silence sup-pression having an activity factor of 55% and apacketization time of 5 ms, this resulted in a callbandwidth of 64 kbps. Thus, the investigated aver-age VoIP node traffic (trw) interval was 2–16 Mbps.Note that the actual codec type only affects thebandwidth calculation; moreover, since the averageVoIP node traffic interval is relatively wide, the re-sults presented can apply to various codec types.

The cost functions of VPN edges were based onthe Synchronous Transfer Mode (STM) standardsreferring to a physical layer approach as describedin Section 1, while in the case of VPN nodes twodifferent device sizes were assumed (see Table 1).As the cost values of these functions only represent

Table 1The capacity and cost steps of VPN nodes and edges

Capacity Cost

1 Gbps 1510 Gbps 45

155 Mbps 10311 Mbps 20622 Mbps 301244 Mbps 60

ratios, they can be considered cost units. In thecase of VPN edges, the capacity values 311 Mbpsand 1244 Mbps refer to the situation when twoconnections of the same size are deployed in paral-lel. The cost function of VPN edges is based on theassumption that the deployment of two devices ofsimilar capacity is reasonable, while it is worthinstalling a device of a larger capacity instead ofinstalling three parallel devices of a given size.

Since in real-life situations the cost functions ofdevices may deviate from the average, each costfunction was distorted randomly during the simu-lations. The original costs were multiplied or di-vided (with equal probability) by 1 + r, where r

is a random variable with a uniform distributionin the interval [0, 1).

In order to get accurate results, numerous net-work topologies and traffic distributions wereexamined for each network size resulting in a con-fidence interval size of 2% at a significance level of95%.

5.2. Optimization of parameters

The first simulation scenario targeted the opti-mization of the parameters of EC and SC. Itturned out that in the case of EC the parametervalue combination of k = 3 and s = 500, where k

and s refer to the size of the sets of randomlyselected entities and the importance factor of thesecondary metric, respectively, can provide themost favorable results. In the case of SC, the com-bination of the initial temperature T0 = 10,annealing factor / = 0.9995, and the importancefactor s = 500 proved to be the best choice. There-fore, these parameter value combinations wereused throughout the next simulation scenarios.The value of the parameter n used in the stop con-dition of the methods was fine-tuned indepen-dently for all variants of both algorithms.

5.3. Total network cost

The most important performance indicator isthe total cost of the resulting network, which isshown in Fig. 7 for the variants of the evolutionaryalgorithm EC. As it can be seen in the figure, algo-rithms EC-C and EC-C2 performed similarly. By

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Fig. 7. Total network cost using EC.

610 L. Tamasi et al. / Computer Networks 50 (2006) 599–614

applying EC-I, about 2–3% improvement can beachieved. The use of EC-D results in more eco-nomical configurations in the higher traffic inter-vals. EC-TI provided the lowest total networkcost in the case of lower average VoIP node trafficvalues, while EC-D2 proved to be the best algo-rithm as it outperformed all other variants in thetraffic interval between 6 and 16 Mbps. Theimprovement may reach 15% compared to EC-Cand EC-C2 at higher traffic volumes.

Fig. 8 shows the results of applying the differentvariants of the simulated annealing based algo-rithm SC. It can be seen that the results providedby SC-I, SC-C and SC-C2 converge in the highertraffic intervals. About 7–11% improvement canbe gained by applying SC-D in the average VoIPnode traffic interval between 12 and 16 Mbps. Asin the case of EC, the methods based on the two-level distance weighted traffic and the trafficweighted interconnection metrics (SC-D2 andSC-TI) provided the best results. However, thegap between the results of the two methods wasrelevantly smaller than in the case of EC at everyaverage VoIP node traffic value investigated.

Fig. 9 shows the total network cost for the twovariants of the greedy covering algorithm GC aswell as the two best variants of EC and SC. As itcan be seen in the figure, GC-C provided 3–5%lower network costs than the simplest algorithmGC-N. The sophisticated optimization algorithmsEC and SC proved that more efficient results canbe achieved by selecting from multiple feasiblesolutions, as they outperformed the greedy cover-ing algorithms in almost all cases. While the twovariants of the evolutionary algorithm ECachieved better results than the methods basedon simulated annealing at lower average VoIPnode traffic values, above 12 Mbps the results ofEC and SC converge. However, EC-D2 provedto be the best algorithm overall providing animprovement of 7–20% compared to the greedyalgorithm GC-N over the traffic intervalinvestigated.

5.4. Number of VPN nodes

Besides the cost of the VPN transport network,its size is also an important attribute, which can be

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Fig. 8. Total network cost using SC.

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Fig. 9. Total network cost using the different algorithms.

L. Tamasi et al. / Computer Networks 50 (2006) 599–614 611

0

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Fig. 11. Running time values of the different algorithms.

612 L. Tamasi et al. / Computer Networks 50 (2006) 599–614

described well by the number of VPN nodes. Thus,in this scenario the algorithms were comparedfocusing on this basic measure. Fig. 10 presentsthe number of VPN nodes used in the final trans-port network differentiating between the edge andtransit nodes for the two variants of the greedycovering algorithm GC as well as the best two vari-ants of EC and SC. Since these measures did notshow relevant change against the change of aver-age VoIP node traffic, results are presented onlyfor the 10 Mbps value.

An important observation is that in the case ofboth EC and SC the number of edge VPN nodesis higher for the two-level distance weighted traf-fic based variant than the traffic weighted inter-connection based method, while the relationbetween the total network cost values of thetwo variants is exactly the opposite. This meansthat the sophisticated selection of VoIP trafficaggregation points is more important than keep-ing their number as low as possible. Anotherpoint to note is that in the case of the methodsbased on EC and SC, the ratio of transit VPNnodes is significantly smaller than in the case ofthe greedy algorithms. This can be explained bythe fact that both the two-level distance weightedtraffic and the traffic weighted interconnectionmetric aim at diminishing the number of transitVPN nodes, by reducing the length of the short-est path and increasing the degree of interconnec-tion between the edge VPN nodes with higherhose traffic values, respectively.

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transitedge

Fig. 10. Number of edge and transit VPN nodes using thedifferent algorithms.

5.5. Running time

Although in the case of off-line network designthe running time has only secondary importance, itis worth examining this factor also in order tomake the investigations complete. Fig. 11 depictsthe values for the two versions of the greedy cover-ing algorithm GC and the best two variants of ECand SC measured on a Sun Ultra Enterprise 420Rmachine with an Ultra II 450 MHz processor and1 GByte RAM. As it can be seen, the GC algo-rithms were very fast as they provided results with-in 1 min on average. Another important point tonote is that for both cost calculation methodsshown the running time values of the simulatedannealing based algorithm SC were higher thanthose of the evolutionary algorithm EC. This canbe partly attributed to the fact that the runningtime of the VPN specification method presentedin Section 4 depends heavily on the number ofedge VPN nodes selected.

6. Conclusions

This paper addressed the topic of cost-optimalVoIP network design. The whole design problemconsists of two main tasks: the specification ofthe VoIP regions and the design of the VPN trans-port network. A novel approach was proposedaimed at improving the cost efficiency by takingthe objective of transport VPN design into consid-eration during region specification. Various algo-rithms were proposed that realize the approach

L. Tamasi et al. / Computer Networks 50 (2006) 599–614 613

based on the paradigms of evolutionary algo-rithms and simulated annealing, which perform asophisticated optimization of the VoIP regions.Moreover, a VPN specification method utilizingthe stepwise nature of cost functions was pre-sented.

In order to evaluate the performance of thealgorithms, numerous simulations were carriedout. It turned out that significant reduction intotal network cost can be achieved by applyingsophisticated cost evaluation in the VoIP regionspecification phase. Based on the performed simu-lations, the evolutionary algorithm using the two-level distance weighted traffic metric seems to bethe best choice.

Possible future work in the area includes theinvestigation of situations where other types oftraffic demands with high bandwidth require-ments, e.g., video telephony, are likewise handled.Another direction is to take reliability issues alsointo consideration during VPN transport networkdesign.

Acknowledgments

This work was partially supported by projectIKTA-0092/2002 of the Ministry of Education,Hungary. The authors would also like to thankGabor Magyar and Gergely Tamasi for theirinsightful suggestions and comments, and the peo-ple at Ericsson Research Hungary for their valu-able remarks.

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Levente Tamasi received his M.Sc.degree from the Budapest University ofTechnology and Economics (Hun-gary), where he is currently a Ph.D.student at the High Speed NetworksLaboratory of the Department ofTelecommunications and Media Infor-matics. He also works as a researchfellow at the Traffic Analysis andNetwork Performance Laboratory ofEricsson Research Hungary. His main

interests are design and optimization problems in wide area

Daniel Orincsay received his M.Sc.degree in 2000 from the BudapestUniversity of Technology and Eco-nomics, where he is currently finalizinghis Ph.D. Parallelly, he also works as aresearch fellow at the Traffic Analysisand Network Performance Laboratoryof Ericsson Research Hungary. Hismain interests are traffic engineeringand performance optimization in highspeed networks.

Balazs Gabor Jozsa received his M.Sc.degree in computer science from theBudapest University of Technologyand Economics (Hungary) in 2000. Heis currently finishing his Ph.D. disser-tation at the High Speed NetworksLaboratory (HSNLab) of the sameuniversity. Meanwhile, he works as aresearch fellow at Ericsson TrafficAnalysis and Network PerformanceLaboratory in Budapest, Hungary. His

main interests are traffic engineering, routing and performance