Intercarrier Compensation between Providers of Di
erent Layers: Advantages of Transmission Initiator
Determination

Ruzana Davoyan, Wolfgang Effelsberg

► To cite this version:

Ruzana Davoyan, Wolfgang Effelsberg. Intercarrier Compensation between Providers of Di erent Layers: Advantages of Transmission Initiator Determination. 9th International IFIP TC 6 Networking Conference (NETWORKING), May 2010, Chennai, India. pp.373-384, 10.1007/978-3-642-12963-6_30. hal-01059116

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# Work in Progress: Intercarrier Compensation between Providers of Different Layers: Advantages of Transmission Initiator Determination

Ruzana Davoyan and Wolfgang Effelsberg

Department of Mathematics and Computer Science
University of Mannheim, Germany

{ruzana.davoyan,wolfgang.effelsberg}@informatik.uni-mannheim.de

**Abstract.** This paper addresses the important issue of providing balanced allocation of the interconnection costs between networks. We analyze how beneficial is the determination of the original initiator of a transmission to the providers of different layers. The introduced model, where intercarrier compensation is based on the differentiated traffic flows, was compared with the existing solution, which performs cost compensation based on the traffic flows. For our analysis we considered both unilateral and bilateral settlement arrangements.

**Key words:** Interconnection arrangement, intercarrier compensation, Internet economics.

## 1 Introduction

The Internet is a system of interconnected networks, which are connected either through a direct link or an intermediate point to exchange traffic. Currently, the Internet provides two basic types of interconnections such as peering and transit, and their variations. Peering is the arrangement of traffic exchange on the free-settlement basis, so that Internet service providers (ISPs) do not pay each other and derive revenues from their own customers. In transit, a customer ISP pays a transit ISP to deliver the traffic between the customers. Emergence of new types of ISPs (with large number of customers and great amount of content) led to appearance of new types of models, such as paid peering and partial transit.

Traditionally, before interconnecting, provider calculates whether the interconnection benefits would outweigh the costs [1]. Simple economic principle suggests sharing the costs between all parties. In the case of telephony, the study [2] argued that both calling and called parties benefit from the call, and consequently, should share the interconnection costs. In the Internet, under symmetry of traffic flows, the termination costs are set to zero, since it is assumed that the termination fees are roughly the same, and a peering arrangement is used. However, because no termination cost is charged, settlement-free model is considered
inefficient in terms of cost compensation [3]. Generally, if providers are asym-
metric in terms of size, peering is not appropriate, since providers incur different
costs and benefit differently. In such a case, an interconnection arrangement is
governed by the financial compensation in a bilaterally or unilaterally negotiated
basis. In the bilateral settlement arrangements, the payments are based on the
net traffic flow. In the unilateral settlement arrangements, a customer provider
pays for sent and received traffic, even though traffic flows in both directions.
This causes the existence of imbalance in allocation of the interconnection costs.
In particular, smaller providers in high cost areas admit higher subscription fees.
There exists a large body of literature that discusses interconnection challenges
[1, 4-6]. Various pricing schemes have attempted to provide sustainable con-
ditions for smaller ISPs [7-8]. These models make different trade-offs between
the two objectives of interconnection pricing, viz., competition development and
profitability. Hence, no single model has a clear advantage over the others. As
cited in [9], it was recommended to establish bilateral settlement arrangements
and to compensate each provider for the costs that it incurs in carrying traffic
generated by the other network. However, it was argued that traffic flows are
not a reasonable indicator to share the costs, since it is not clear who origi-
nally initiated a transmission and, therefore, who should pay for the costs. In
other words, compensation between providers cannot be solely done based on the
traffic flows, which provide a poor basis for cost sharing [9]. Recently provided
analytical studies in [10-11], investigated the impact of the original initiator of
a transmission at the wholesale and retail levels in the case of private peering
arrangements. Further, we extended studies by examining the benefits of the
customer providers only, which purchased transit services [12]. However, the re-
maining literature on the economics of interconnection considers the intercarrier
compensation based only on the flows of traffic [2, 13-16].

The main objective of this paper is to explore the role of the determination
of a transmission initiator on ISPs of different layers. The paper differs from the
prior reported studies in that it considers how beneficial is the traffic differenti-
ation to *all providers*, such as transit and customer, and it examines customer
ISPs, which *operate in different cost areas*. Our studies involve the earlier in-
troduced model, called Differentiated Traffic-based Interconnection Agreement
(DTIA) that distinguishes traffic into two types to determine the transmission
initiator in the IP networks and to compensate the costs. In contrast to the ex-
isting solutions [17], in which the payments are based on traffic flows (TF), we
compensate differently for a particular traffic type. Unlike telephony, where the
transmission initiator covers the entire costs, imposing uniform retail pricing, the
proposed model distributes the joint costs between all parties and supports the
diversity of existing retail pricing schemes in the Internet. Comparative studies
were provided for the agreements based on the traffic flows and differentiated
traffic flows compensations. We considered both unilateral and bilateral settle-
ment models. The rest of the paper is organized as follows. Section 2 discusses
existing financial settlements. Section 3 describes the motivation for traffic differ-
entiation. Section 4 provides analytical studies. Section 5 concludes this paper.
## 2 Financial Settlements

Generally, providers arrange financial settlements in order to determine the distribution of the interconnection costs [17]. Before examining financial settlements within the Internet, we consider the telephone system. As an example, assume a scenario, where Alice makes a call to Bob. Accepting the call, Bob incurs termination costs to its provider that should be covered either directly by billing Bob or indirectly by billing the calling party's carrier. As cited in [3], "existing access charge rules and the majority of existing reciprocal compensation agreements require the calling party's carrier, [...], to compensate the called party's carrier for terminating the call". Thus, the initiator of the call, i.e., Alice pays to a subscribed provider for the entire call since Alice asked to reserve the circuit. In contrast to the telephony example, establishing a connection in the Internet does not require any reservation of a circuit. Usually packets between Alice and Bob are routed independently, sometimes even via different paths. Therefore, as cited in [18], "it is very important to distinguish between the *initiator* and the *sender*, and likewise between the *destination* and the *receiver*." The initiator is the party that initiates a call or a session, and the destination is the party that receives a call. In contrast, the sender (the originator) is the party that sends traffic, and the receiver (the terminator) is the party that receives traffic. In telephony, the initiator is considered to be the originator and is charged based on the transaction unit, namely a "call minute" for using the terminating network. Even though it may be argued that a TCP session can be considered as a call, where the initiator of a session pays for the entire traffic flow, such a model deals with technical issues, considerable costs, and implies uniform retail pricing. Currently, the Internet uses the packet-based accounting model, under which the volume of the exchange traffic in both directions is measured, and adopts a small set of interconnection arrangements. Specifically, in the *service-provider* (unilateral) settlement, namely transit and paid peering business relationships, a customer ISP pays to a transit ISP for sent and received traffic. In the *settlement-free* agreement, namely peering relationships, providers do not pay each other. In some cases ISPs adopt the *negotiated-financial* (bilateral) settlement where the payments are based on the net flow of traffic. For detailed discussion see [17-19].

## 3 Motivation for Traffic Differentiation

The principle that we follow is that both parties derive benefits from the exchange of traffic and, therefore, should share the interconnection costs. Considering a system without externalities [20], the costs should be shared based on the benefits obtained by each party. However, in the real world, it is impossible to measure the benefits of parties and so to share the costs. If content is not equally distributed between providers, traffic imbalance occurs, and hence, costs and revenues are not shared evenly. As cited in [21], traffic flow is dominant towards a customer requested the content and generates 85% of the Internet traffic. This implies that inbound traffic is much more compared to outbound
traffic of content request. In telephony for example, it is acceptable that more
than 50% of rural network's revenue could come from the incoming calls. In
contrast, in the Internet, customer networks pay for the entire traffic flows. It
was recommended to compensate each provider for the costs that it incurs in
carrying traffic based on the traffic flows. However, traffic flows are not a good
measure for costs sharing, since "it is impossible to determine who originally
initiated any given transmission on the Internet" and therefore, provide a poor
basis for cost sharing [9]. On the other hand, providers are unwilling to inspect
the IP header of a packet, since "the cost of carrying an individual packet is
extremely small, and the cost of accounting for each packet may well be greater
than the cost of carrying the packet across the providers" [19].

The DTIA model presented in [22] manages inter-provider cost compensa-
tion considering the original initiator of a transmission. In order to determine a
party that originally initiated a transmission, we differentiated traffic into two
types, referred to as *native*, which is originally initiated by the provider's own
customers, and *stranger* that is originally initiated by the customers of any other
network. Indeed, outgoing traffic of ISPᵢ that is the same as adjacent provider's
incoming traffic may be i) either a part of a transmission initiated by a customer
of ISPᵢ, ii) or a part of a transmission initiated by a customer of any other
network. Furthermore, we suggest that providers compensate differently for a
particular type of traffic, where stranger traffic is charged at a lower rate than
native traffic. More specifically, each provider settled DTIA compensates the
cost of carrying traffic according to the differentiated traffic flows. For detailed
description of the DTIA model and its traffic management mechanism see [22].

4 The Model of Interconnection

In our analysis we follow an assumption done in [13] to capture traffic imbalance and therefore, consider two types of the customers, namely websites (who host information and content) and consumers (who use information and content provided on websites). Actually, traffic is exchanged between consumers, between websites, from websites to consumers, and from consumers to websites. According to the proposed approach, a node (customer) in a P2P network is considered as a consumer as well as a website simultaneously, since it can act as a client and as a server. Thus, traffic generated from websites to consumers and vice versa along with Web, FTP and streaming media traffic captures P2P traffic. Traffic between consumers captures VoIP traffic that tends to be symmetric, and email exchange that is much smaller than traffic generated from websites to consumers. To focus on explicit monetary transfers between providers and traffic asymmetry in its simplest way, we consider traffic exchange i) from consumers to websites, and ii) from websites to consumers. To simplify analytical studies the following assumptions were made throughout the paper:

**Assumption 1.** Let $\alpha_i \in (0, 1)$ network *i*'s market share for consumers and $\beta_i \in (0, 1)$ its market share for websites. The market consists of only one transit and two customer ISPs, *i* and *j*, where $i \neq j = 1, 2$ and $\alpha_i + \alpha_j = \alpha$, $\beta_i + \beta_j = \beta$.
**Assumption 2.** Balanced calling pattern, where each consumer requests any website in any network with the same probability is considered<fnref n="1" />. Each consumer originates one unit of traffic per each request of website. The number of consumers and websites in the market is given by N and M respectively.

We examine a scenario, in which ISP$_i$ and ISP$_j$ exchange traffic through the transit ISP$_k$. The amount of the differentiated traffic originated from ISP$_i$ with destination to ISP$_j$ and vice versa is given by

$$t_{ik}^{nat} = \alpha_i \beta_j N M \qquad t_{jk}^{nat} = \alpha_j \beta_i N M \qquad (1)$$

$$t_{ik}^{str} = \alpha_j \beta_i N M x \qquad t_{jk}^{str} = \alpha_i \beta_j N M x \qquad (2)$$

where $t_{ik}^{nat}$ ($t_{jk}^{nat}$) denotes the amount of outgoing native traffic (exchanged from consumers to websites) and $t_{ik}^{str}$ ($t_{jk}^{str}$) is the amount of stranger traffic (exchanged from websites to consumers) with respect to ISP$_i$ (ISP$_j$). The variable $x$ denotes the average amount of traffic caused by requesting a website. It is known that P2P traffic asymmetry is typically caused by less capacity provisioned in the upstream direction. Thus, upstream/downstream P2P traffic flows can be asymmetric, which implies that $x$ is different for the customers subscribed to different ISPs. However, this does not affect the results of our studies. The total amount of traffic originated by ISP$_i$ and ISP$_j$ are $t_{ik} = t_{ik}^{nat} + t_{ik}^{str}$ and $t_{jk} = t_{jk}^{nat} + t_{jk}^{str}$.

## 4.1 Unilateral Settlement Arrangements

We start by considering a unilateral settlement arrangement, where transit ISP charges the customer providers for every unit of traffic sent and received. Let $c_i^k$ and $c_j^k$ are the marginal costs of the connectivity of ISP$_i$ and ISP$_j$ correspondingly. These providers operate in different cost areas so that $c_i^k < c_j^k$, where marginal costs exhibit increasing returns to scale (i.e., ISP$_i$ > ISP$_j$). ISP$_k$ charges the customer ISPs $a_k$ and $b_k$ for every unit of native and stranger traffic respectively, where $a_k > b_k$ (ISPs pay less for stranger traffic). In particular, in DTIA we consider that a customer ISP i) compensates fully the imbalance in the connectivity costs between endpoints, if the exchanged traffic is native, and ii) does not compensate this difference, if the originated traffic is stranger. The difference in the costs of the exchanged traffic between the points is defined by

$$\Delta = c_j^k - c_i^k \qquad (3)$$

**Proposition 1.** The access charge for stranger traffic is set to the lowest cost of the connectivity, i.e., $b_k = c_i^k$.

*Proof.* Interconnection costs between the customer providers are covered by the access charges. Since native traffic for ISP$_i$ is stranger for ISP$_j$, the sum of fees for native and stranger traffic are equal to the whole costs, that is

$$c_i^k + c_j^k = a_k + b_k \qquad (4)$$

<footnote n="1">¹ Due to the lack of mathematical models on how traffic between ISPs is distributed, many works make a statistical assumption, such as balanced calling pattern.</footnote>
In the DTIA model, a provider compensates the imbalance in the costs expressed by (3) fully only for native traffic. This cost difference is not compensated for the stranger traffic. Consequently, it can be written that

$$a_k = b_k + \Delta \qquad (5)$$

By substituting (3) and (5) in (4), it can be obtained that access rate for stranger traffic is set to the lowest cost of the connectivity, that is $b_k = c_i^k$. Obviously, that the access charge for native traffic is defined by $a_k = c_i^k + \Delta$. □

We investigate the payments of the customer providers in the classical and DTIA models. The payments of ISP$_i$ and ISP$_j$ to transit ISP in DTIA are given by

$$f_{ik} = a_k(t_{ik}^{nat} + t_{jk}^{str}) + b_k(t_{ik}^{str} + t_{jk}^{nat}) \qquad (6)$$

$$f_{jk} = a_k(t_{jk}^{nat} + t_{ik}^{str}) + b_k(t_{jk}^{str} + t_{ik}^{nat}) \qquad (7)$$

The sum of these payments presents the incremental revenue of the transit ISP $\pi_k = f_{ik} + f_{jk}$. The net payments of the customer ISPs according to the traffic flow based compensation are denoted by $\tilde{f}_{ik}$ and $\tilde{f}_{jk}$ and calculated as follows

$$\tilde{f}_{ik} = c_i^k(t_{ik} + t_{jk}) \qquad (8)$$

$$\tilde{f}_{jk} = c_j^k(t_{ik} + t_{jk}) \qquad (9)$$

**Proposition 2.** The payments of larger (smaller) providers are higher (less) in DTIA than these in the classical model.

*Proof.* Considering the net payments of the larger ISP$_i$, from (6) and (8) follows that $\tilde{f}_{ik} - f_{ik} = (b_k - a_k)(t_{ik}^{nat} + t_{jk}^{str}) < 0$, i.e., $f_{ik} > \tilde{f}_{ik}$. Similarly, comparing the payments of ISP$_j$ in the DTIA and classical models given by (7) and (9) we obtain that $\tilde{f}_{jk} - f_{jk} = (a_k - b_k)(t_{ik}^{nat} + t_{jk}^{str}) > 0$. This gives that $f_{jk} < \tilde{f}_{jk}$. □

## 4.2 Bilateral Settlement Arrangements

This subsection examines bilateral settlement models, where each provider (including customer ISP) is compensated for the costs of carrying traffic.

**Reciprocal Access Charges** In the following lines we explore the case when the customer providers charge the transit provider reciprocal access charges and vice versa. Let b be the access payment that ISP$_k$ subsidizes ISP$_i$ and ISP$_j$ for every unit of sent traffic, where $b < c_j^k$. The marginal connectivity costs of the customer providers charged by ISP$_k$ can be written as follows

$$c_i^k + c_j^k = c_k + \sigma \qquad (10)$$

where $c_k$ is the marginal transportation cost of ISP$_k$; $\sigma$ is an arbitrary constant.

**Proposition 3.** The access charge for stranger traffic set by ISP$_k$ is equal to $b_k = c_k + b$ (i.e., the total costs of ISP$_k$).
*Proof.* The costs of ISP$_k$ are comprised of the marginal transmission cost and the payment to access customer provider's infrastructure, i.e., $c_k + b$. The bilateral settlement model is attractive to ISP$_k$ only if its own costs are covered. These costs correspond to the minimum level of access charge set by ISP$_k$, that is

$$c_k + b = \min\{a_k, b_k\}$$

In DTIA provider compensates less the costs of carrying stranger traffic, thus

$$b_k = c_k + b \qquad (11)$$

Obviously, that the access charge for native traffic set by the transit provider is increased by the arbitrary constant and calculated as follows $a_k = b_k + \sigma$. □

The net interconnection payments from ISP$_i$ and ISP$_j$ to ISP$_k$ are defined by

$$f_{ik} = a_k t_{ik}^{nat} + b_k t_{ik}^{str} \qquad f_{jk} = a_k t_{jk}^{nat} + b_k t_{jk}^{str} \qquad (12)$$

Analogously, the net transfers of ISP$_k$ to the customer providers are given by

$$f_{ki} = b(t_{jk}^{nat} + t_{jk}^{str}) \qquad f_{kj} = b(t_{ik}^{nat} + t_{ik}^{str}) \qquad (13)$$

It can be noticed that the transit ISP is charged based on the rate for stranger traffic, because we consider that it does not have any customers of its own.

Before examining the payments of the customer ISPs in the DTIA and classical models with bilateral settlements, we consider access charges and net payments in the classical solution. Let $\tilde{b}$ be the payment paid by ISP$_k$ to the customer providers for sending traffic. In the model with bilateral settlements, the access charge set by the transit provider is defined by $\tilde{a}_k = c_i^k + c_j^k + \tilde{b}$. Assume that ISP$_k$ has users, thus $b$ (in DTIA) is the rate charged by the customer ISPs for unit of stranger traffic only, while $\tilde{b}$ (in the classical model) is payment for unit of traffic. As a result, we obtain that $\tilde{b} \ge b$. The payments of ISP$_i$ and ISP$_j$ are

$$\tilde{f}_{ik} = \tilde{a}_k t_{ik} \qquad \tilde{f}_{jk} = \tilde{a}_k t_{jk} \qquad (14)$$

**Proposition 4.** *The net payments of the customer providers in the DTIA model are less than these in the classical model.*

*Proof.* Considering the payments of ISP$_i$ and ISP$_j$ given by (12) and (14) follows

$$\tilde{f}_{ik} - f_{ik} = t_{ik}^{nat}(\tilde{a}_k - a_k) + t_{ik}^{str}(\tilde{a}_k - b_k) > 0 \qquad (15)$$

$$\tilde{f}_{jk} - f_{jk} = t_{jk}^{nat}(\tilde{a}_k - a_k) + t_{jk}^{str}(\tilde{a}_k - b_k) > 0 \qquad (16)$$

□

**Non-reciprocal Access Charges** We continue with examination of the bilateral settlement model with asymmetric access fees. Let $b_i$ and $b_j$ ($b_i < b_j$) are the access rates for every unit of traffic received by ISP$_i$ and ISP$_j$ correspondingly.
Following the results of Proposition 3, fees that the transit provider charges the customer ISPs for native and stranger traffic can be rewritten as

$$ 
\begin{aligned}
a_{ik} &= c_i^k + c_j^k + b_j & a_{jk} &= c_i^k + c_j^k + b_i \\
b_{ik} &= c_k + b_j & b_{jk} &= c_k + b_i
\end{aligned}
$$

The net payments from ISP$_i$ and ISP$_j$ to the transit ISP$_k$ and vice versa are

$$ f_{ik} = a_{ik}t_{ik}^{nat} + b_{ik}t_{ik}^{str} \qquad f_{jk} = a_{jk}t_{jk}^{nat} + b_{jk}t_{jk}^{str} \qquad (17) $$

$$ f_{ki} = b_i (t_{jk}^{nat} + t_{jk}^{str}) \qquad f_{kj} = b_j (t_{ik}^{nat} + t_{ik}^{str}) \qquad (18) $$

The following lines explore the payments of customer ISPs in the classical and DTIA models. For this purpose, we consider access charges and payments in the classical solution. The access rates that ISP$_k$ charges ISP$_i$ and ISP$_j$ are

$$ \tilde{a}_{ik} = c_i^k + c_j^k + \tilde{b}_j \qquad \tilde{a}_{jk} = c_i^k + c_j^k + \tilde{b}_i $$

where $\tilde{b}_i$ and $\tilde{b}_j$ ($\tilde{b}_i \ge b_i$, $\tilde{b}_j \ge b_j$) are access fees set by the customer providers correspondingly. The net payments of the customer providers are given by

$$ \tilde{f}_{ik} = \tilde{a}_{ik}t_{ik} \qquad \tilde{f}_{jk} = \tilde{a}_{jk}t_{jk} \qquad (19) $$

**Proposition 5.** The interconnection payments of the customer providers are less in DTIA than these in the classical model.

*Proof.* Examining the payments of ISP$_i$ and ISP$_j$ given by (17) and (19) follows

$$ \tilde{f}_{ik} - f_{ik} = t_{ik}^{nat}(\tilde{a}_{ik} - a_{ik}) + t_{ik}^{str}(\tilde{a}_{ik} - b_{ik}) > 0 \qquad (20) $$

$$ \tilde{f}_{jk} - f_{jk} = t_{jk}^{nat}(\tilde{a}_{jk} - a_{jk}) + t_{jk}^{str}(\tilde{a}_{jk} - b_{jk}) > 0 \qquad (21) $$

□

## 4.3 Discussions

Tables 1-3 report the results of analytical studies, which examined how beneficial is the determination of a transmission initiator to the providers of different layers. The comparison results between unilateral settlement models are presented in Table 1. Tables 2 and 3 demonstrate the comparison of bilateral settlement arrangements with symmetric and asymmetric access charges. The analyses considered all available market states in terms of providers’ market shares, where ISP$_i$ >ISP$_j$. The following parameter values were imposed to calculate the specific outcomes: $c_i^k = 0.4$, $c_j^k = 1.5$, $c_k = 0.9$, $b = 0.5$, $b_i = 0.3$, $b_j = 0.5$, $x = 35$, $N = 100$, and $M = 60$. In order to simplify analyses we assume that $\tilde{b} = b$, $\tilde{b}_i = b_i$, and $\tilde{b}_j = b_j$. The parameters are chosen to satisfy a condition that providers operate in different cost areas. However, the specification is clearly arbitrary. It is important to note, that our conclusions do not heavily depend on
the chosen parameter values. The results obtained for a number of other param-
eter sets have not produced significant changes. Network i's total incremental
cost of connectivity is defined by $r_i = f_{ik} - f_{ki}$. Network k's profit obtained from
interconnection is $r_k = (f_{ik} + f_{jk}) - (f_{ki} + f_{kj})$.

Comparative results obtained for arrangements with unilateral settlements demonstrated that in the presented model the payments are decreased for the smaller ISP and are increased for the larger ISP. This is achieved by different access rates charged for the distinguished traffic flows. Specifically, the payments of ISPᵢ are increased due to native traffic compensation, while the payments of ISPⱼ are decreased due to stranger traffic compensation. Further, the results showed that in DTIA the more outgoing traffic the lower costs of the provider. In particular, incoming and outgoing native traffic are directly proportional. Hence, the network that sends more native traffic incurs higher costs than the network that receives this traffic. This is explained by the higher access charges for native than stranger traffic. The costs of both customer ISPs are equal only in the case when their native and stranger traffic volumes are symmetric correspondingly. Finally, the results indicated that the revenues of the transit provider in the classical model based on the traffic flows compensation and DTIA are equal.

The key consequences provided below are based on the analytical studies, which explored bilateral settlement arrangements. In DTIA, the payments paid by the customer providers are decreased and these of transit provider remain the same. Specifically, providers ISPᵢ and ISPⱼ compensate based on the differentiated traffic flows, where the access charge for stranger traffic flow is lower than the access charge set in the classical model. As a consequence, the total incremental costs of the customer providers (rᵢ and rⱼ) are also decreased. On the other side, profits of ISPₖ obtained from the interconnection (i.e., the differences between received and paid payments, rₖ) are lower than these in the traffic flow based compensation model. However, as mentioned earlier, it was argued that traffic flows provide a poor basis for Internet interconnection cost sharing.

The provided studies examined a model consisting of one transit and two customer ISPs. One question that arises here is on the robustness of the obtained results for more realistic scenarios, which consider more transit and customer ISPs. From Propositions 2, 4 and 5 it can be noticed that the results depend only on the access charges of both DTIA and classical models. More specifically, in the unilateral settlement arrangements, the results rely on the inequality (a_k - b_k) > 0. Analogously, the results given by (15) and (16) depend on the inequalities (\tilde{a}_k - a_k) > 0 and (\tilde{a}_k - b_k) > 0, while results expressed by (20) and (21) are based on (\tilde{a}_{ik} - a_{ik}) > 0 and (\tilde{a}_{ik} - b_{ik}) > 0. Hence, the provided conclusions remain the same. Obviously, in the extended scenarios, access charges are obtained by solving a system of linear equations.

# 5 Summary and Conclusions

In this paper we proposed models and their analysis, which are based on the
DTIA strategy for inter-provider cost compensation. The goal for this was to ex-
<table><caption>**Table 3.** Comparative Results of Bilateral Settlement Models (Non-reciprocal Access Charges).</caption><thead><tr><th rowspan="2">Case</th><th colspan="2">f<sub>ik</sub></th><th colspan="2">f<sub>jk</sub></th><th colspan="2">f<sub>ki</sub></th><th colspan="2">f<sub>kj</sub></th><th colspan="2">r<sub>k</sub></th><th colspan="2">r<sub>i</sub></th><th colspan="2">r<sub>j</sub></th></tr><tr><th>DTIA</th><th>TF</th><th>DTIA</th><th>TF</th><th>DTIA</th><th>TF</th><th>DTIA</th><th>TF</th><th>DTIA</th><th>TF</th><th>DTIA</th><th>TF</th><th>DTIA</th><th>TF</th></tr></thead><tbody><tr><td>I</td><td>133020</td><td>227520</td><td>18540</td><td>29040</td><td>3960</td><td>47400</td><td>100200</td><td>205200</td><td>129060</td><td>223560</td><td>-28860</td><td>-18360</td><td></td><td></td></tr><tr><td></td><td>119040</td><td>203040</td><td>30480</td><td>51480</td><td>7020</td><td>42300</td><td>100200</td><td>205200</td><td>112020</td><td>196020</td><td>-11820</td><td>9180</td><td></td><td></td></tr><tr><td></td><td>105060</td><td>178560</td><td>42420</td><td>73920</td><td>10080</td><td>37200</td><td>100200</td><td>205200</td><td>94980</td><td>168480</td><td>5220</td><td>36720</td><td></td><td></td></tr><tr><td>II</td><td>21180</td><td>31680</td><td>114060</td><td>208560</td><td>28440</td><td>6600</td><td>100200</td><td>205200</td><td>-7260</td><td>3240</td><td>107460</td><td>201960</td><td></td><td></td></tr><tr><td></td><td>35160</td><td>56160</td><td>102120</td><td>186120</td><td>25380</td><td>11700</td><td>100200</td><td>205200</td><td>9780</td><td>30780</td><td>90420</td><td>174420</td><td></td><td></td></tr><tr><td></td><td>49140</td><td>80640</td><td>90180</td><td>163680</td><td>22320</td><td>16800</td><td>100200</td><td>205200</td><td>26820</td><td>58320</td><td>73380</td><td>146880</td><td></td><td></td></tr><tr><td>III</td><td>26112</td><td>42912</td><td>46416</td><td>84216</td><td>11484</td><td>8940</td><td>52104</td><td>106704</td><td>14628</td><td>31428</td><td>37476</td><td>75276</td><td></td><td></td></tr><tr><td></td><td>44616</td><td>74016</td><td>62328</td><td>112728</td><td>15372</td><td>15420</td><td>76152</td><td>155952</td><td>29244</td><td>58644</td><td>46908</td><td>97308</td><td></td><td></td></tr><tr><td></td><td>56952</td><td>94752</td><td>72936</td><td>131736</td><td>17964</td><td>19740</td><td>92184</td><td>188784</td><td>38988</td><td>76788</td><td>53196</td><td>111996</td><td></td><td></td></tr><tr><td></td><td>68568</td><td>114768</td><td>70944</td><td>127644</td><td>17406</td><td>23910</td><td>98196</td><td>201096</td><td>51162</td><td>97362</td><td>47034</td><td>103734</td><td></td><td></td></tr><tr><td>IV</td><td>27756</td><td>46656</td><td>23868</td><td>42768</td><td>5832</td><td>9720</td><td>36072</td><td>73872</td><td>21924</td><td>40824</td><td>14148</td><td>33048</td><td></td><td></td></tr><tr><td></td><td>49344</td><td>82944</td><td>42432</td><td>76032</td><td>10368</td><td>17280</td><td>64128</td><td>131328</td><td>38976</td><td>72576</td><td>25152</td><td>58752</td><td></td><td></td></tr><tr><td></td><td>64764</td><td>108864</td><td>55692</td><td>99792</td><td>13608</td><td>22680</td><td>84168</td><td>172368</td><td>51156</td><td>95256</td><td>33012</td><td>77112</td><td></td><td></td></tr><tr><td></td><td>74016</td><td>124416</td><td>63648</td><td>114048</td><td>15552</td><td>25920</td><td>96192</td><td>196992</td><td>58464</td><td>108864</td><td>37728</td><td>88128</td><td></td><td></td></tr><tr><td>V</td><td>16248</td><td>20448</td><td>181704</td><td>332904</td><td>45396</td><td>4260</td><td>148296</td><td>303696</td><td>-29148</td><td>-24948</td><td>177444</td><td>328644</td><td></td><td></td></tr><tr><td></td><td>23340</td><td>33840</td><td>151860</td><td>277860</td><td>37890</td><td>7050</td><td>130260</td><td>266760</td><td>-14550</td><td>-4050</td><td>144810</td><td>270810</td><td></td><td></td></tr><tr><td></td><td>37422</td><td>59472</td><td>116046</td><td>211596</td><td>28854</td><td>12390</td><td>112224</td><td>229824</td><td>8568</td><td>30618</td><td>103656</td><td>199206</td><td></td><td></td></tr></tbody></table>

plore how the determination of a transmission initiator affects different providers, operated in different cost areas and arranged interconnection with unilateral and bilateral settlements (Tables 1-3). The results obtained from the analytical studies showed that DTIA was able to find better results (in terms of interconnection payments) than the classical solution for the both models. More specifically, the proposed scheme diminishes the existing inequity in allocation of the interconnection costs. From the comparison between unilateral settlement models follows that the costs of the smaller provider are decreased. This stimulates the retail prices fall in the market, where the provider operates and consequently, the development of the infrastructure in terms of subscribed customers. The growth of the smaller ISP leads to balance the volumes of a particular traffic type, and as a result, reduces the imbalance in cost allocation. Obviously, that revenue of the larger ISP obtained from retail market will be increased. From the perspective of a transit provider, its revenues obtained from the customer providers remain the same in the DTIA and classical models.

In the bilateral settlement arrangements, the net payments of both customer ISPs in the DTIA model are decreased. This leads to the decrease in the incremental revenue obtained by the transit provider. Finally, the comparison between the existing model with unilateral settlement and DTIA with bilateral settlement showed that our approach generally performed better for both smaller and larger ISPs in terms of reduced net payments. For the smaller provider, DTIA is
dominated in all cases over the classical model, and for the larger provider only
in Cases II and V. Obviously, that the profits of the transit provider in bilat-
eral settlement model are decreased, since it along with other ISPs shares the
interconnection costs. Resuming, the provision of a model, which compensates
providers while exploiting their infrastructures, is advantageous for sustainable
environment. From this point of view the proposed DTIA model is beneficial.

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