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DTIA: Differentiated Traffic-based Interconnection Agreement Ruzana Davoyan Department of Mathematics and Computer Science University of Mannheim, 68131 Mannheim, Germany rdavoyangmail.uni-mannheim.de Abstract- This paper presents a new model, called would both benefit equally. As a result, networks have little or differentiated traffic-based interconnection agreement (DTIA) no economic incentive to increase capacity to terminate traffic for reciprocal compensation between providers. In particular the [7]. Second, lack of pricing at the peering points leads to the model aims to achieve the twofold goal of i) determination of an overuse of the network resources and eventually IXPs original initiator of transmission, and ii) compensation of the overue cofethen interconnection costs. For that purpose, traffic is differentiated become congested. into two types, called native and stranger. In comparison to the Traditionally, before interconnection the provider existing financial settlement, under which the payments are calculates whether the interconnection benefits would based on the net traffic flows, the proposed model governs cost outweigh the costs [8]. In case of telephony, the study [9] compensation according to the differentiated traffic flows. argued that both calling and called parties benefit from the Besides, we describe a traffic management mechanism that call, and consequently, should share the interconnection costs. supports the proposed traffic differentiation approach. In the Internet, under symmetry of traffic flows, the Analytical studies were provided using Nash bargaining solution termination costs are set to zero, since it is assumed that the to investigate how the interconnection payments between termination fees are roughly the same, and the peering providers depend on the presented approach.teniainfsarroglthsm,adtepeig arrangement is used. However, because no termination cost is charged, BAK is considered inefficient in terms of the cost I. INTRODUCTION compensation [10]. If traffic is unbalanced, interconnection The Internet is a system of interconnected networks, which arrangement is governed by the financial compensation in a are connected either through a direct link or through an unilaterally or bilaterally negotiated basis to recover the costs intermediate point, called Internet exchange point (IXP) to of the network. The survey and discussion on interconnection exchange traffic. Currently the Internet provides two types of with two-sided benefits are provided in [11-12]. interconnections: peering and transit [1]. Peering is the Various aspects of interconnection of ISPs have been arrangement of traffic exchange on the free-settlement basis, analyzed by [9], [13-15]. This work is focused on private called bill-and-keep (BAK), so that the Internet service peering arrangement and addresses the problem of cost providers (ISPs) do not pay each other and derive revenues sharing between providers. Generally, when providers are from the respective customers [2]. It is fair and efficient under asymmetric in terms of size, peering model is not appropriate, symmetry of traffic flows as well as termination charges and since it is assumed that providers incur different costs and costs. In transit model one party, such as the downstream benefit differently. It was shown in [16] that peering as a provider pays the upstream provider to deliver the traffic result of bargaining process can take place also when between the customers. Negotiation process over being a providers are asymmetric. When analyzing economics of transit or peered customer reflects on the assessment of the interconnection, existing literature considers intercarrier actual cost of traffic exchange and was studied in [3-4]. compensation based on the flows of traffic. However, it was Peering offers several advantages in terms of interconnection cited in [5] that traffic flows are not a reasonable indicator to costs and quality of data transmission, however, limits access share the costs, since it is not clear who originally initiated to the network. As cites in [5] according to the estimates, 80% any transmission and therefore, who should pay for the costs. of the Internet traffic is routed via private peering. In some In other words, compensation between providers cannot be cases, however, in order to recover the infrastructure costs, solely done based on the traffic flows. instead of peering with the smaller ISPs, the larger ISPs offer This paper presents a new cost recovery model, called transit arrangements that might be expensive, but give access differentiated traffic-based interconnection agreement (DTIA). to the whole Internet. In comparison to the existing negotiated-financial settlement Due to rapid growth of the Internet traffic, bottleneck [3], under which the payments are based on the net traffic occurs at IXPs among the networks [6]. The reasons of flows, this study proposes to determine an original initiator of peering bottleneck at the interconnection points are mostly transmission in the IP networks by means of traffic economic. First, there is no money exchange between peers, differentiation and to compensate the interconnection costs since originated traffic volumes are symmetric and providers according to the differentiated traffic (DT) flows. More 978-1-4244-2336-1/08/$25.OO © 2008 IEEE 681

[IEEE 2008 International Symposium on Communications and Information Technologies (ISCIT) - Vientiane, Laos (2008.10.21-2008.10.23)] 2008 International Symposium on Communications

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DTIA: Differentiated Traffic-based InterconnectionAgreement

Ruzana DavoyanDepartment of Mathematics and Computer Science

University of Mannheim, 68131 Mannheim, Germanyrdavoyangmail.uni-mannheim.de

Abstract- This paper presents a new model, called would both benefit equally. As a result, networks have little ordifferentiated traffic-based interconnection agreement (DTIA) no economic incentive to increase capacity to terminate trafficfor reciprocal compensation between providers. In particular the [7]. Second, lack of pricing at the peering points leads to themodel aims to achieve the twofold goal of i) determination of an overuse of the network resources and eventually IXPsoriginal initiator of transmission, and ii) compensation of the overue cofetheninterconnection costs. For that purpose, traffic is differentiated become congested.into two types, called native and stranger. In comparison to the Traditionally, before interconnection the providerexisting financial settlement, under which the payments are calculates whether the interconnection benefits wouldbased on the net traffic flows, the proposed model governs cost outweigh the costs [8]. In case of telephony, the study [9]compensation according to the differentiated traffic flows. argued that both calling and called parties benefit from theBesides, we describe a traffic management mechanism that call, and consequently, should share the interconnection costs.supports the proposed traffic differentiation approach. In the Internet, under symmetry of traffic flows, theAnalytical studies were provided using Nash bargaining solution termination costs are set to zero, since it is assumed that theto investigate how the interconnection payments between termination fees are roughly the same, and the peeringproviders depend on the presented approach.teniainfsarroglthsm,adtepeigarrangement is used. However, because no termination cost is

charged, BAK is considered inefficient in terms of the costI. INTRODUCTION compensation [10]. If traffic is unbalanced, interconnection

The Internet is a system of interconnected networks, which arrangement is governed by the financial compensation in aare connected either through a direct link or through an unilaterally or bilaterally negotiated basis to recover the costsintermediate point, called Internet exchange point (IXP) to of the network. The survey and discussion on interconnectionexchange traffic. Currently the Internet provides two types of with two-sided benefits are provided in [11-12].interconnections: peering and transit [1]. Peering is the Various aspects of interconnection of ISPs have beenarrangement of traffic exchange on the free-settlement basis, analyzed by [9], [13-15]. This work is focused on privatecalled bill-and-keep (BAK), so that the Internet service peering arrangement and addresses the problem of costproviders (ISPs) do not pay each other and derive revenues sharing between providers. Generally, when providers arefrom the respective customers [2]. It is fair and efficient under asymmetric in terms of size, peering model is not appropriate,symmetry of traffic flows as well as termination charges and since it is assumed that providers incur different costs andcosts. In transit model one party, such as the downstream benefit differently. It was shown in [16] that peering as aprovider pays the upstream provider to deliver the traffic result of bargaining process can take place also whenbetween the customers. Negotiation process over being a providers are asymmetric. When analyzing economics oftransit or peered customer reflects on the assessment of the interconnection, existing literature considers intercarrieractual cost of traffic exchange and was studied in [3-4]. compensation based on the flows of traffic. However, it wasPeering offers several advantages in terms of interconnection cited in [5] that traffic flows are not a reasonable indicator tocosts and quality of data transmission, however, limits access share the costs, since it is not clear who originally initiatedto the network. As cites in [5] according to the estimates, 80% any transmission and therefore, who should pay for the costs.of the Internet traffic is routed via private peering. In some In other words, compensation between providers cannot becases, however, in order to recover the infrastructure costs, solely done based on the traffic flows.instead of peering with the smaller ISPs, the larger ISPs offer This paper presents a new cost recovery model, calledtransit arrangements that might be expensive, but give access differentiated traffic-based interconnection agreement (DTIA).to the whole Internet. In comparison to the existing negotiated-financial settlementDue to rapid growth of the Internet traffic, bottleneck [3], under which the payments are based on the net traffic

occurs at IXPs among the networks [6]. The reasons of flows, this study proposes to determine an original initiator ofpeering bottleneck at the interconnection points are mostly transmission in the IP networks by means of trafficeconomic. First, there is no money exchange between peers, differentiation and to compensate the interconnection costssince originated traffic volumes are symmetric and providers according to the differentiated traffic (DT) flows. More

978-1-4244-2336-1/08/$25.OO © 2008 IEEE

681

specifically, traffic is differentiated into two types, referred to traffic, and the receiver (the terminator) is the part thatas native that is originally initiated by the provider's own receives traffic.customers and stranger, which is originally initiated by the In telephony the initiator is considered as the originator andcustomers of a rival network. Moreover, each ISP is charged based on the transaction unit, namely a "callcompensates fully the termination costs incurred from minute" for using the terminating network. In the Internet, itdelivering native traffic, and partially the termination costs might be argued that TCP session can be considered as a call,incurred from carrying stranger traffic. Thus, in comparison to where the initiator of a session pays for the entire traffic flow.the telephony, according to the proposed agreement, an However, considering actual use of the network resources,initiator of transmission is not considered as a cost causer, financial settlement should be done at the IP level, accountingwho should cover the joint costs, but rather both parties share each packet of a flow. In this case, money flow directionthe costs. coincides with the traffic flow direction. In summary, session-

Besides, the traffic management mechanism that supports based accounting, which faces with technical difficulties, isthe traffic differentiation approach was presented. The major more complicated than a simple packet-based accounting,advantage of the described mechanism is that a provider has under which the volume of the exchanged traffic in bothnot to inspect the IP header of a packet in order to determine directions should be measured. Therefore, generally,how it should be accounted. Hence, a significant reduction in providers adopt the negotiated-financial settlement, wherecomputational costs is achieved by proposing the membership payments are based on the net traffic flows. For detailedlabel, which allows accounting the volume of a particular discussion see [3], [13], [18].traffic type.

Analytical studies based on the bargaining model were III. DIFFERENTIATED TRAFFIC-BASED INTERCONNECTIONprovided to determine how the intercarrier compensation AGREEMENTpayments depend on DT flows. The key consequence of the The principle that we follow is that both parties deriveobtained results show that the net interconnection payment benefits from the exchanged traffic and should share thebetween asymmetric providers under asymmetry of traffic

interconnection costs. Considering a system withoutflows can be zero. Therefore, symmetry of costs structure is externalities [5], [19], the costs should be shared based on thenot required for peering. In addition, comparative analysis of benefits obtained by each party. However, in real world it isthe agreements based on the net traffic flow and differentiated impossible to measure the benefits of both parties' andtraffic flow compensation were presented.theffi rest cofmthenpaperisorganizedasfollows.Setion weerconsequently, to share the costs. When content is not equallyThe rest of the paper iS organtzed as follows. Section I distributed between providers, traffic imbalance occurs, andpexamns fDTIA. Section IV describes the design of traffic therefore, costs and revenues are not shared evenly. Indeed,presents DTIA. Section IV describes the design of traffic. the network that sends more traffic incurs lower cost, than themanagement mechanism. Section V provides analytical network that receives more traffic [20]. As cited in [21],studies. Finally, Section VI concludes this paper. traffic flow is dominant towards a customer requested the

11.FINANCIAL SETTLEMENTS content and generates 85% of the Internet traffic. This impliesthat inbound traffic is much more compared to outbound

Generally, providers arrange the financial settlements in traffic of content request.order to determine the distribution of the interconnection costs According to [5], the traffic flows are not a good meter for[3], [17]. To examine financial settlements in the Internet, costs sharing, since "it is impossible to determine whofirst, consider a telephony system where Alice makes a call to originally initiated any given transmission on the Internet".Bob. Accepting the call, Bob incurs termination costs to its On the other hand, providers are unwilling to inspect the IPprovider that should be covered either directly by billing Bob header of a packet, since "the cost of carrying an individualor indirectly by billing calling party's carrier. As cited in [10], packet is extremely small, and the cost of accounting for each"existing access charge rules and the majority of existing packet may well be greater than the cost of carrying thereciprocal compensation agreements require the calling packet across the providers" [1 8].party's carrier, ..., to compensate the called party's carrier for In order to determine a party that originally initiated anyterminating the call". Thus, an initiator of the call, i.e. Alice transmission, we differentiate traffic into two types, referredpays to the subscribed provider for the entire call, since Alice to as native, which is originally initiated by the provider'sasked to reserve the circuit. In contrast to the telephony, in the own customers, and stranger that is originally initiated by theInternet, Alice does not make any reservation of the circuit, customers of the peered network. Indeed, outgoing traffic ofand usually packets between Alice and Bob are routed ISPi that is the same as rival provider's incoming traffic mayindependently via different paths. As cited in [13] "at this be i) either a part of transmission initiated by a customer ofpoint, it is very important to distinguish between the initiator ISPi, ii) or a part of transmission initiated by a customer of theand the sender, and likewise between the destination and the peered network. Hence, it is assumed that the providerreceiver". The initiator is the part that initiates a call or a compensates the termination costs i) fully, if the exchangedsession, and the destination is the part that receives a call. In traffic is native, and ii) partially, if the originated traffic iscomparison, the sender (the originator) is the part that sends stranger. More specifically, the private peering networks

settle DTIA, whereby each partner is compensated for the

682 2008 International Symposium on Communications and Information Technologies (ISCIT 2008)

termination costs that it incurs in carrying traffic according to stream with the requested data, where the label value of eachthe DT flows. packet is set to the same as in the request one. The similar

procedure follows on the inverse path with only differenceIV. TRAFFIC MANAGEMENT MECHANISM that ISPi considers incoming traffic as native, initiated by its

The proposed traffic management mechanism includes own customers.

described below marking, negation, and duplication V. THE MODEL OF DTIAoperations. It is assumed that the networks trust each other aswell as that each node supports truthful labeling of all packets. Analytical studies are based on the bargaining process thatThe reason for proposing this assumption is that cooperation is explored using Nash bargaining solution. The intuitionbetween peers engaged interconnection under mutual benefits behind this principle is that peering is long term and repeatedis natural and reasonable solution. The key aspect of the process, arranged under mutual benefit, and hence,proposed agreement is based on the traffic differentiation into sustainable cooperation between the interconnected providerstwo types, which are identified by a 1-bit field in the IP is reasonable. This approach was studied in [16]. In analysispacket header, referred to as a membership label (ML). All two types of the customers, namely consumers, i.e. end-usersnodes within the network support packet marking, where each and websites are considered [14]. Actually, traffic isnode sets the ML field of native packet to '1' and the packet exchanged 1) between consumers, 2) between websites, 3)of stranger traffic to "0". The assignment of the label to "1" is from websites to consumers, and 4) from consumers todone once, when a node originally initiates a transmission. websites. Generally, traffic between consumers, between

It is obvious, that native traffic with regard to one network websites, and from consumers to websites is negligible.is strange with regard to the other. Hence, in order to Recently, peer-to-peer (P2P) traffic has increased rapidly. Thedifferentiate the exchanged traffic between the networks the significant part of the Internet traffic, comprised of FTP, Web,ML field negation is necessary. We distinguish providers' and streaming media traffic, is from websites to consumers. Inborder nodes, which maintain connection with peered network order to demonstrate how intercarrier compensation paymentsand refer to as the provider-to-provider border (PPB) nodes. depend on DT types, we focus on traffic exchange i) fromThe PPB nodes perform negation (i.e. NOT operation) of the consumers to websites, and ii) from websites to consumers.label of outgoing traffic. In addition, in order to carry out Traffic between consumers and between websites is neglected,intercarrier compensation based on the DT flows, each PPB since it does not have any significant impact on the results ofnode keeps two counters (one for inbound and another for the analysis. To simplify the analytical studies the followingoutbound traffic), which calculate the volume of a particular assumptions were made throughout the paper:type of traffic, i.e. native or stranger. The volume of the other Assumption 1 Let ai E(O,1) network i's market share fortype of traffic can be easily defined by subtraction of the

c

counted volume frm the total one.consumers and ,6 (O01) its market share for websites. It iscounted volume from the total one.lA consumer can request a webpage either from a assumed that there exist two providers i.j= 1,2 and ai+ aj =I1

subscribed network or from a rival network. As a result, Ji +,/j =1.traffic originated by the endpoint of transmission (e.g. Assumption 2 The number of consumers and websites in thedestination), can be part of the transmission initiated either by market is given by N and M respectively. Each customerthe network's customer or by the customer of a peered chooses only one provider to join, because of homogeneity ofnetwork. In order to identify traffic originated by the theoses.transmission endpoint, the duplication of the label is the services.necessary. Thus, any transmission endpoint duplicates the Assumption 3 For simplicity a balanced calling pattern,label of the request packet. Therefore, the label of webpage where each consumer requests any website in any networktraffic is the same as that of the request packet. All nodes with the same probability is considered. Each consumerwithin the network support duplication of the ML field. It is downloads a fixed amount of content.obvious that incoming network traffic marked by '1' is a part We start by examining a scenario, when ISP, fails to signof transmission initiated by its own customers. An example an interconnection agreement with ISPj. The utility or benefitthat helps to understand how the above described traffic of joining ISP.for each consumer is u(f8 ,M)=f(J3), and eachmanagement mechanism works iS described below.

website's utility is h(ai, N) = g(ai). The presence of networkFor simplicity consider a model consisting of ISPi, ISPj, positive externalities assumes that f'(.)>o and g'(.)>O [19].

and their customers, where each provider calculates native In case of disagreement between providers, the total traffictraffic volumes. Assume that a customer of ISPi requests data volume generated by ISPi is given byavailable on ISPj. Let Ni be the PPB router of ISPi, which tinat=aifliNM+aifliNMx (1)receives a packet marked by '1'. Before forward it to ISPi, NJ where the first component is volume of traffic exchangednegates the ML field and increases the counter for outgoing from consumers to websites, the second one denotes volumenative traffic. The PPB node N2 of ISP1 reads the label of the of traffic exchanged from websites to consumers, and x is thereceived packet and then forwards it to the destination, e.g. average amount of traffic generated by each website. It isthe N3 node. After receiving the packet, N3 sends a packet

2008 International Symposium on Communications and Information Technologies (ISCIT 2008) 683

assumed that each consumer originates one unit of traffic per incremental costs increase as the network size decreases. Byeach request of website. substituting (10) in (12), it can be obtained that

Let network i's marginal costs of origination and oj -Hlj =0.5[t7-'(2a, +C) -ct)-t'-t(2aj +c7 -c)]termination are cl > 0 and cit>0 respectively, where ci°=c +0=5[ttsi(2b,+c±-ct)-tst7(2bj +co-c)] (13)and ci is the total marginal cost [14]. We do not consider The net interconnection charge can be interpreted as twofixed network cost and assume that transportation cost is independent components i) one for native traffic business,normalized to zero, since peering model is considered. The which is denoted by Ao-7, and ii) another for stranger trafficprofit of ISPi from on-net traffic is defined by

business that is denoted by Austr.;Ti = [aiNf (6)+ 6,Mg(ai)]-Citinat (2)Suppose that ISP, obtained an agreement with ISPj. It is Proposition 1 If ai =aj and 13, =1 then the net

assumed that providers' market shares for customers do not interconnection payments are zero.change in case of interconnection. In this case each user's Proof: Since the networks are symmetric in terms of sizeutility is u(18,M)= f(13), and each website's utility is given by therefore, ct = ct . From the conditions (3)-(6), (13), the neth(a,N)=g(a) . The volumes of the differentiated traffic transfers are given by i-Hi= j-Hj = 0.exchanged from ISPi to ISPj are given by . .

=i ai,8jNM (3) Proposition 2 If a, a1 and , >/3 then ISPj subsidizest '" =a,lNMx (4) ISP1 for native traffic.

where tnat and tstr denote native and stranger traffic volumes I t c Jwith respect to ISPi. Similarly, the traffic volumes from ISPj Native From the conditions (3), (5) follows that tj"<t'to ISPj are given by Considering the component for the native traffic business, it is

ta =a1J3NM (5) obtained that A7=n0.5[t (2ai +cJ°-Ct )_tnat (2aj +co -c5)]> .sJJtr1NMx (6) Here, ISPi gets higher profit from native traffic exchange and

t) jnatia)j N dM strangrxtraffi subsidizes for it to ISPj.where jit and t,s'tr are native and stranger traffic volumes with Stranger: On the other hand, from the conditions (4), (6), it

respect to ISPj. The total traffic volumes are defined by can be obtained that t >t7 . The net payment for stranger=t.. +t..~ ~~~ ~ ~ ~ ~~~~~~~~~~~~~st 2.+c c -tt 2j c c

t,=Z',(7) traffic is defined by A ojst = 0.5[t7(2b, ±c) -c)-t(2b +c° -c)]

tj1=t jt (8) This case is not straightforward and depends on (tSc,-t'c7),Let ai and bi are network i's access charges for where

terminating native and stranger traffic respectively, where wo *fhtjr/et> /ai >b, , since the provider compensates partially the costs of =0 if t:/t)1=,)/1, (14)terminating stranger traffic. To carry out analysis, it is >Of /tJi <)/Jciassumed that each network access charge for terminatingnative traffic is set to the termination marginal cost, i.e. ai =ct. Proposition 3 If 13i =13j and ai > aj then ISPi (ISPj)The access charge for terminating stranger traffic determines subsidizes ISPj (ISPd for stranger (native) traffic.how the costs are shared between consumers and websites. It Proof: Since ai > aj then ct < c.is defined by bi = ai, where 0.5 <.<1, and £ is the same for

' . ' . . ~~~~~~~~~~~Native.From the conditions (3), (5) follows that t nat > t nat . Theboth networks. The higher access charge for terminating N,stranger, the higher per unit charge to websites. However, in net charge for native traffic is given byorder to simplify analysis, it is assumed that £=0.5 . The A t = 0.5[tiit(2a icJ -Cf)-t7 (2ai±ci -ci)]<0profit of ISPi obtained interconnection is calculated as follows Here, ISPj gets higher incremental profit from native traffic

fli = Tj +±o, (9) exchange and subsides for it.where vi is the incremental profit ISPi gets from the Stranger. From the conditions (4), (6) follows that t7j<tiinterconnection and is given by The component for the stranger traffic business is given by

, = Nf(13)+l3Mg(a)+tiJat(-c-a(_) Ausr =0.5[tstr(2bi + -ct)-ts(2bj +co -ct)]>°±tjt(-c7 -b1)±t7at(ai -c)t) i(bi-<) (10) where ISPj receives the net interconnection charge for

The outcome of i's network according to the bargaining game stranger traffic from ISP1.[22] is defined by Assuming that a,> a1 and fSi > /3j, the following cases for

i=0.5(H ±t+T,- s)=0.5(b,+1)+.z (11) r tffic volumes are obtained from the conditions (7)-(8): 1)IfThe >ou thenISPo receives the net payment from ISPi that isgm > te, 2) t,e <t1, , and 3) t,j = t1, The cases 1) and 2) are

A1 -H1 =0.5(ov,-cr)=0.5Acri (12) analogous to those described above. The last case whenIt is assumed that network externalities exhibit constant tA=tinis analyzed below.returns to scale, wherefl(i) = 0 and g 7()i=0 , meaning thatthe networks have the same incremental revenues, while the Proposition4atfa>j2 >aji1,an i > tji,and te t_ then xai - are

Proof: The result is obtained from the conditions (3)-(8).

684 2008 International Symposium on Communications and Information Technologies (ISCIT 2008)

Corollary 1 If a, > aj, /8i > /3j, and t~ tji then tna =tnat and agreements based on the net traffic flows and DT flowsst = st compensation.tii tji ~~~~~~~~~~~~Inorder to calculate specific outcomes, we impose the

Proposition 5 If ai > a, , /3i > /8j , and t~ tji then ISP, following values of termination costs i) ct =ct =1 in Cases Isubsidizes ISPjfor stranger traffic. and v, ii) ct =1 , ct =2 in all other cases. Other parameters areProof: Since a, >aj and f6i >/8j then ct < ct x=35 , N=100 , and M=60. The market shares for Case VNative. The net interconnection charge for native traffic when were obtained so that the size of each network is equal tot6 =tg is given by 0.5(N±M)= 80. The net payment based on the net traffic flow

A07 =05t(a c c)t(a c ]ois defined by: 05, -Hlj=0.5[t1, (2ai ±c)-eft)-t~ (2aj ±c -&)]

Here, the incremental profits of the providers are equal.Stranger. Considering stranger traffic business when tstr = tst TABLE IIji ~~~~PROVIDERS' OUTCOMEs AcCORDING To DTIAwe get that Aust" =0.5[tstr(2b, +co -ct)-tst-(2bj +co-ct)]>0 .___________________________Under symmetric stranger traffic, ISPj receives the net a, (-, f if)~ t ~ ty. Ao Ao

Case 1: ai=aj l6=/,f c=C>Cinterconnection charge. 0.5 0.5 0.5 0.5 1500 52500 1500 52500 0 0Case 11: a,=aj86>68 ,c

Assuming that a, > aj , ,6, < ,6j and recalling that costs are 0.5 0.5 0.9 0.1 300 94500 2700 10500 3600 -36750higherfor thsmaler netork thn thefollowng cass for 0.5 0.5 0.8 0.2 600 84000 2400 21000 2700 -21000higher for thesmaller network then the following cases for ~~0.5 0.5 0.7 0.3 900 73500 2100 31500 1800 -5250

termination costs are possible: 1) ct > ct , 2) ct < ct , and 3) 0.5 0.5 0.677 0.323 970 71061 2030 33939 1591 -15910.5 0.5 0.6 0.4 1200 63000 1800 42000 900 10500

-i ct. The cases 1) and 2) are similar to those described Case III: ai > ai A3 =,l cit < cti i~~~~~~~~~~~~~~~~~.. . . 70 00 0 40 30 95above. The last case when networks are equal in terms of size 0.8 0.2 0.5 0.5 2400 210500 600 84000 -2700 732500is considered below. 0.7 0.3 0.5 0.5 2100 31500 900 73500 -1800 57750

0.6 0.4 0.5 0.5 1800 42000 1200 63000 -900 42000

Proposition 6fIf ai > aj, 83, </31, and ct = ct then ISP, (ISPj) Case IV: ai >aj /i >6 ci<<c'0.9 0.1 0.9 0.1 540 18900 540 18900 0 9450

subsidizes ISPj ([SPd for stranger (native) traffic. 0.8 0.2 0.8 0.2 960 33600 960 33600 0 16800Proof: Native: From the conditions (3), (5) follows that 0.7 0.3 0.7 0.3 1260 44100 1260 44100 0 22050

t na > tnat. Thnetpay ent or ntiv trafic s dfine by0.6 0.4 0.6 0.4 1440 50400 1440 50400 0 25200j7>7.Tentpymn o aietafi sdfndb CaseV: ai >a 8/</8j c>'=c'

7na 05tnt(2 +CO t(2 ] 0.7 0.3 0.167 0.833 3500 10500 300 122501 -3200 56001ji i U\ 0.65 0.35 0.25 0.75 2925 18375 525 102375 -2400 42000

Hence, ISPj compensates ISP1. 0.6 0.4 0.333 0.667 2400 28000 800 84000 -1600 28000

Stranger. From the conditions (4), (6) follows that tstr < tst 0.55 0.45 0.417 0.583 1924 39407 1126 67337 -798 13965

Considering the business for stranger traffic, it can be TABLE IIIobtained that A<s =0. 5[tst (2b, + co -ctf)-tst(2bj + co - ct)]> 0. COMPARATIVE RESULTS OF THE AGREEMENTs BASED ON THE NET TRAFFIC

In this case, ISPj gets the net payment for stranger traffic FLOWS AND DT FLOWS COMPENSATION

exchange from ISP1. Case a /3A t tj Netpayment(A a,/2)Traffic flows DT flows

TABLE I I: a aj /3, / 0.5 0.5 54000 54000 0 0RESULTS OF DTIA ci =C

a / ct na Ao7nat st II: aCa,= /3A4 0.5 0.9 94800 13200 -122400 -33150cft<c 0.5 0.8 84600 23400 -91800 -18300

a =a1 /i,Jc[c.1=.7 cJ = 7t07 0.5 0.7 74400 33600 -61200 -3450

= 81/>/83 c<Ct tnat< t; na 7nt> 7nt tst > tS is conditional, 0.5 0.677 72030 35970 -54091 0ai =aj i ii ji ii ji ji defined by (14) 0.5 0.6 64200 43800 -30600 11400ai aj i 8jCtCt na >tna na <.7 at sr <t l s > .

s Ill: a,>aj , =686 0.9 0.5 13200 94800 122400 85650

/3>/i c<<c5 ~~~~~~~~~~~~~~~J~ ~ ~ ~ ~~~~c'C 0.8 0.5 23400 84600 91800 70800t~ "tvij 0.6 0.5 43800 64200 30600 41100

a>81/</i, c>Ct tna >tna If Ct =Ct t <t;r If<=IV: a >aj !>/q 0.9 0.9 19440 19440 0 9450eft <c. 0.8 0.8 34560 34560 0 16800

ci<C (~o7 <o§7 07 >J7S 0.7 0.7 45360 45360 0 22050ct t 0.6 0.6 51840 51840 0 25200

_________________________________=________ V: a,>ai !</,8 0.7 0.167 14000 122801 108801 52801ci=Cj 0.65 0.25 21300 102900 81600 39600

0.6 0.333 30400 84800 54400 26400Discussion of the results 0.55 0.417 41330 68462 27132 13167

Table I summarizes the outcomes of the analytical studies.TalTTcnan rvies aktsae for- conumrs an The observed results showed that under certain market

providers decide to interconnect without monetary transfers One open issue that is not addressed in this study is(see Table III Case II). incentive compatibility. The technical part of the paper

Considering Case II and Case III, it can be noticed that requires the networks to truthfully label the packets. However,according to the agreement based on the net traffic flows strategic agents have an incentive not to be truthful. How tocompensation, the net payment that subsidizes the smaller incorporate the truthful aspect in packet marking strategyISPj in Case II equals to the net payment that subsidizes the requires further investigation.bigger ISPi in Case III (see Table III). DTIA assumes that incontrast to the bigger provider, the smaller one gets more ACKNOWLEDGMENTcompensation, since it incurs more costs. Thus, it can be The author would like to thank Prof Wolfgang Effelsbergconcluded that compensation based on traffic volumes is not

and Kristina Davoian for their useful comments and helpfulstraightforward; determination of an initiator of transmissionby means of traffic differentiation encourages a more fair costsharing between providers.

In addition, taking into account the fact that no valid REFERENCESmathematical modeling of the evolution in the traffic [1] W. Norton, "Internet service providers and peering", draft 2.5, Equinixdistribution between networks exists, the most research works White Papers, 2001.make the Assumption 3. Hence, it is more reasonable to [2] C. Courcoubetis, R. Weber, "Pricing communication networks:

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