Tài liệu Pricing communication networks P12 ppt

Network service providers often negotiate special interconnection agreements and tariffs so they can provide the best service to their end-customers.. If that customer network is a direc

Interconnection

Two parties that are connected to different networks are able to communicate with

one another if there is interconnection of the two networks The positive network

externalities that result when networks are connected are an economic force driving interconnection between network providers Modern access technology strengthens inter-network connectivity by providing universal access A customer using a wireless access system can access the network from any physical location

Interconnection is important if networks are to offer truly global services Network service providers often negotiate special interconnection agreements and tariffs so they can provide the best service to their end-customers These play a vital role in ensuring the smooth operation of today’s worldwide Internet They also provide substantial income for network operators who have invested in building large backbone networks By buying interconnectivity, a small network can appear larger to its customers, without investing in costly and rapidly changing infrastructure This helps it to offer services that can compete with those offered by a network that has invested in greater geographical coverage There are important incentive issues involved in offering interconnection services Unless prevented by the contract, the network that provides the service may be tempted to discriminate in favour of traffic that originates from its own end-customers and against traffic that originates from end-customers of its ‘customer’ network If that customer network is a direct competitor in the market for retail services, then the interconnection service provider has an incentive to offer a poorer quality of transport to the interconnection traffic than to his own internal traffic A carefully chosen interconnection charge can correct this inequality

by making transport quality a measured part of the contract

In this chapter we introduce some important concepts in interconnection services Sec-tion 12.1 reviews types of interconnecSec-tion agreement and pricing In SecSec-tion 12.2 we briefly consider the effect of competition on service differentiation and in Section 12.3 we consider the factors that motivate networks to interconnect or not Section 12.4 is about the asymmet-ric information problem that can arise when one network buys interconnection service from another Section 12.5 describes how an incentive contract can be used to solve this problem

12.1 The market structure

12.1.1 Peering Agreements

Once interconnection is in place, a network service provider can use the infrastructures

of a number of other networks to provide services to any of his customers However,

Pricing Communication Networks: Economics, Technology and Modelling.

Costas Courcoubetis and Richard Weber Copyright  2003 John Wiley & Sons, Ltd.

ISBN: 0-470-85130-9

it is only reasonable that he should transfer part of the charge that he makes to his customer to those other providers whose networks are used to provide the customer’s

service Traditional telephone networks use the so-called accounting rate system to share

charges Interconnection charges are computed on a per call basis, and the network in which the call originates pays a predefined charge to the network that terminates the call (and possibly to intermediate networks) This is implemented by each carrier computing his ‘traffic balance’ with the other carriers over a certain time period, and then paying in proportion to it

In today’s data networks, things are different First, since customers are connected to the Internet and data flows in all directions, there is no notion of charging on a per call basis

Second, interconnection is achieved by there being a number of Network Access Points

(NAPs), at which many different networks interconnect with each other As a function

of the interconnection agreements between network providers, and routing decisions in the interior of the network (which may depend on how network congestion and topology changes), data can flow unpredictably through intermediate networks In present Internet practice there are two ways that traffic is exchanged between data network providers The

first is peering, in which traffic is exchanged without payment, and the second involves interconnection charges for transit traffic.

Peering agreements have some distinct characteristics Peering partners exchange traffic

on the bilateral basis that traffic originates from a customer of one partner and terminates

at a customer of the other partner This allows customers of the two networks to exchange information Note that peering agreements are only bilateral; so a peering partner does not agree to act as an intermediary to accept traffic from a partner and transmit it to a third network Peering traffic is exchanged on a settlement-free basis, also known as ‘sender-keeps-all’ The only costs involved in peering arise from the equipment and transmission capacity that partners must buy to connect to some common traffic exchange point Peering agreements do not specify that a network should provide any minimum performance to the traffic originating from his peer; such traffic is usually handled as ‘best-effort’

Network providers consider several factors when negotiating peering agreements These include the customer base of their prospective peer and the capacity and span of the peer’s network Clearly, some providers have greater bargaining power than others It may be of

no advantage for a provider with a large customer base to peer on an equal terms with a provider with a small customer base

The second type of interconnection agreement is a transit agreement It has important

differences with peering Now one partner pays another partner for interconnection and so becomes his customer The partner selling transit services will route traffic from the transit customer to its own peering partners as well as to other customers He provides a clearly defined transport service for the transit traffic of the first network, and so can charge for

it in a way that reflects the service contract and the actual usage This charge, if rightly set, is billed to the customer of the network in which the traffic originated, and becomes one of the components of his total charge Observe that transit is not the same service as peering Refusing peering in favour of transit is not a means of charging for a service that was otherwise provided for free When regional ISPs pay for transit they benefit from the infrastructure investments of national or global backbones without themselves having to make the same investments Transit gives an ISP customer access to the entire Internet, not just the customers of its peering partners To fulfil his obligations, a transit provider must either maintain peering arrangements with other backbones or pay for transit to another backbone provider who maintains peering relationships

THE MARKET STRUCTURE 281

The Internet connectivity market is hierarchical, with three main levels of participants: end-users, ISPs and Internet Backbone Providers (IBPs), as shown in Figure 3.12 At the bottom of the hierarchy are the end-users, individuals and business customers They access the Internet via ISPs At the top of the hierarchy are the IBPs, who own the high speed and high capacity networks which provide global access and interconnectivity They primarily sell wholesale Internet connectivity services to ISPs ISPs then resell connectivity services,

or add value and sell new services to their customers However, IBPs may also become in-volved in ISP business activities by selling retail Internet connectivity services to end-users Two markets can be identified in the Internet connectivity value chain: the wholesale market, and the retail market for global access and connectivity to end-users There are two main types of contracts and they can be distinguished by their pricing: contracts for primary Internet access between end-users and ISPs, and contracts for interconnection between ISPs and IBPs In the early days, when the Internet exclusively served public sector purposes of research and education, interconnection was a public good and its provision was organized outside competitive markets Today interconnection is primarily commercial, yet its basic architectures remain the same Network externalities generate powerful incentives for interconnection They also provide incentives for potential opportunistic exploitation

12.1.2 Interconnection Mechanisms and Incentives

To better understand the difference between transit and peering, let us examine the mechanisms which networks use to exchange traffic One such mechanism is the routing

protocol BGP (Border Gateway Protocol ) It is primarily used at the borders of carriers’

networks, i.e at the gateways (the edge routers) between a carrier’s network and other networks that are attached to it Consider two networks, A and B, which are connected with a link running BGP There are two principal types of information carried between the two edge routers of the networks: announcements and withdrawals Announcements (also called ‘advertisements’) are packets containing lists of new destinations (network addresses) which are reachable via this link Withdrawals are packets containing lists of destinations which can no longer be reached via this link In making announcements, one network is soliciting from another network packets whose destination can be reached through the first network So if network A advertises network C to network B, it signals its willingness to receive traffic from network B that is destined for network C By advertising destination networks, and hence by being willing to receive and forward traffic to these networks, network A is offering a service to network B This service may be offered for a price Let

us see now the difference between transit and peering

In the case that A offers a transit service to B, network A advertises to B all the destinations he can reach (probably the whole Internet) Such information can be used freely by B and advertised to any other neighbouring network, say network D, that he can also reach all the above destinations (through A) In that respect, this routing information is transitive, since all destinations reachable through A are also reachable through B from any network connected to B (if B allows it) For this service A charges B a fee; in most cases, this charge is based on measuring the volume of data crossing the link AB, having as origin

or destination the networks advertised by B Similarly, B advertises to A all its destinations,

so that A can advertise these further and the rest of the world can know how to reach them

In the case of peering between A and B, a similar and bidirectional process takes place, the difference being that routing information is not transitive This means that B will use the information about the destinations reachable through A only for the benefit of its own customers (and its customers from transit agreements), and will not further advertise these

direct peering connection

1

2

4

3 5

9

8

peering point (NAP)

Figure 12.1 An example of interconnection agreements Networks 1, 2, 3, 4 offer transit services

to networks 5, 6, 7, 8, 9, and peer at a peering point A peering agreement must be established between each pair of peering networks As a provider of a transit agreement a network advertises all networks it can reach (through other peers or customers) In a peering agreement a network advertises only those networks he can reach which are also his customers If the traffic between networks 5 and 6 is substantial, it may be cost-effective for them to peer and incur the cost of the direct connection 5–6 By doing so, the traffic between 5 and 6 will follow the direct route instead

of going through (and hence be charged by) the transit providers 1 and 2

destinations to other neighbouring networks Observe that B has no incentive to advertise A’s destinations to other than his own customers To do so would result in B carrying for free traffic that is destined for A’s customers, but which does not benefit B’s customers Consider the example in Figure 12.1 Four large networks, 1–4, offer transit services to smaller networks, 5–8 For instance, network 2 offers transit service to networks 6 and 7 To

do so, networks 1–4 peer at a peering point Each network must make a peering agreement with each of the other networks Let us consider networks 1 and 2 and the information exchanged between their edge routers Network 1 advertises network 5 to network 2, and network 2 advertises networks 6 and 7 to network 1 Similarly, when networks 2 and 3 peer, network 2 advertises networks 6 and 7 to network 3, and network 3 advertises network

8 to network 2 Observe that network 2 does not advertise to network 3 the information obtained from network 1 concerning the reachability of destination 5 To do so would be to invite to carry traffic at no charge from 8 to 5 Thus, under peering, full-meshes of peering relationships must be created between peers even if these are peering at the same peering point However, as network 2 charges its customers 6 and 7 for transit service, it does advertise to 6 and 7 all the destinations that are advertised through its peers

When should one prefer peering to transit? First, note that peering cannot completely substitute for transit This is because transit services usually offer global Internet access (advertise all possible destinations), whereas peering is useful for only a fixed set of destinations Nonetheless, peering relationships can reduce the amount of traffic that is served through transit agreements and so reduce transit charges Of course there is a cost

to establishing a peering relationship A network provider must decide whether a peering agreement is worthwhile by estimating its effects on the traffic serviced under the transit agreements Consider again Figure 12.1 Networks 5 and 6 observe that they have substantial traffic between one another If networks 5 and 6 peer then they can save transit charges that they would otherwise have to pay to networks 1 and 2 But to peer, 5 and 6 must pay for a new connection, either directly connecting them (private peering), or through some peering point They should decide to peer if the cost of doing so is less than savings they can make because their local traffic no longer needs to flow through the transit providers

1 and 2 After establishing a new peering relationship, the transit contract can continue to act as a backup, to can carry traffic between peers whenever the direct peering connection

is out of order This means that the peering connection can tolerate a certain amount of downtime and so can be safely implemented with inexpensive facilities and technology

THE MARKET STRUCTURE 283

12.1.3 Interconnection Pricing

Much study has been given to interconnection pricing for telecommunications networks and many intricate issues have been identified Many of these issues remain equally relevant for communication networks which offer a broader set of services Let us look as some details

Two common regimes for interconnection pricing are calling-party’s-network pays (CPNP) and bill-and-keep CPNP regimes presently account for the majority of

interconnection agreements for traditional voice traffic In this regime, the calling party’s local exchange carrier (LEC) or interexchange carrier (IXC) pays the called party’s local network for the cost of processing and allocating resources to terminate the call More specifically, the calling party’s LEC collects a charge from the calling party and then pays a transport and termination charge to the called party’s network In the case of long-distance, the calling party’s IXC collects a charge from the calling party and pays an originating access charge to the calling party’s LEC and a terminating access charge to the called party’s LEC

In ‘bill-and-keep’ regimes the calling party’s carrier does not pay any termination charge

to the called party’s carrier Instead, the termination cost is recovered from the end-customer This means that an end-customer has the incentive to choose among competing carriers The resulting competition means that bill-and-keep regimes achieve better economic efficiency

than do CPNP regimes (where the terminating carrier is a de facto monopolist)

‘Bill-and-keep’ regimes are also fairer As both the calling and called parties benefit from a call, it is fair that they should share its cost Of course there are subtleties as to how the cost should

be shared Let us investigate these issues further

As we say, a fundamental problem with CPNP is that the LEC who terminates calls is a

de facto monopolist Because end-customers usually receive their access service from just

one provider, any interconnecting LEC or IXC who carries the call prior to it reaching the terminating network has no choice over the terminating carrier Thus, each terminating carrier, no matter its size, has monopoly power over termination to its own customers A long distance IXC does not enjoy such a monopoly because there are usually a number

of competing IXCs that can carry the call between the LECs of the calling and called parties The problem with CPNP is that a terminating carrier can safely raise termination prices without losing customers, since the called party does not share any part of the termination charge Furthermore, there are usually geographic rate-averaging requirements, which mean that call prices cannot depend in a very detailed way upon precisely how they are terminated For example, calls from Greece to all UK destinations should be priced the same, even though they may be terminated by different local carriers in the UK If one of such terminating carrier raises his price, then this will raise the average termination price, but his identity will be hidden Since it is only the average termination charge that affects the bill of the calling party, that party will have little or no incentive to complain to the called party and encourage him to switch to a local carrier with a smaller termination charge Thus, CPNP denies customers the ability to choose the most cost-efficient network provider Customers must pay part of the charges of all the networks involved in the interconnection service, even though some of these may be artificially inflated and uncompetitive By comparison, ‘bill-and-keep’ provides better incentives, because a LEC with high access charges will lose customers when they see those charges in their bills

Another issue with CPNP is that interconnection charges tend to be traffic sensitive, typically being calculated on a per-minute or per-call basis These inter-network charges are typically reflected in the traffic-sensitive retail prices charged to customers Customers facing such tariffs are given traffic-sensitive incentives to reduce usage, even when the

network may actually have large amounts of unused capacity and so there is no need for congestion pricing This may significantly reduce the economic efficiency of the overall system

To prevent LECs behaving as monopolists, it is common for access charges to be regulated Typical regulatory frameworks are rather complex and treat different classes

of interconnecting parties and types of services in different ways, even when there may

be little difference in the costs that they generate For instance, the regulatory regime can depend on whether the interconnecting party is another local carrier, an interexchange carrier, or a subscriber This complexity in the regulatory framework creates regulatory arbitrage opportunities that motivate entrepreneurs to invent new ways to provide services The availability of new services can be highly beneficial unless these are motivated solely

by artificial differences in regulatory rules For instance, Internet telephony is not subject to LEC access charges (either originating or terminating) for that part of the call that is placed over the IP protocol In this respect (besides being more cost-efficient), IP telephony is more competitive than traditional long-distance telephony (where the long-distance carrier must pay access charges) Pressure from Internet-based technologies should cause interconnection regimes based on CPNP to collapse Looked at another way, so long as interconnection regimes based on CPNP continue to exist, they act as a spur to the introduction of new disruptive technologies such as IP telephony

‘Bill-and-keep’ may be unfair to a large network that interconnects with smaller networks

A smaller network, with smaller operating costs, may be able to offer lower prices to its customers Yet because of interconnection with the large network its customers can reach the same population of customers as those of the large network A way to remedy this could

be to split the cost of the interconnection facilities so that customer prices are the same

for both networks This is the idea of facility-based interconnection cost sharing, which

contrasts with the usage-based prices that CPNP computes on a per call basis Another interesting idea is to make the calling party’s network pay all the cost of the call up to the point that it reaches the called party’s network, which then does not receive any payment for terminating the call That final part of the cost is paid by the called party In this scenario, the originating network also pays for the long-distance part of the call, and so has the incentive to choose a lost-cost IXC, since the long-distance charge will be seen in the bills of its customers

The reader may wonder why charging for interconnection has evolved differently in the Internet than in traditional telephony A principal reason is the difference in the market structure The market for local Internet service that is offered by ISPs is highly competitive, whereas the market for backbone connectivity is less competitive, reversing to some extent the trends of the telephony market No ISP can survive by charging high access prices So peering, which is a type of ‘bill-and-keep’, is widely used In the market for backbone con-nectivity, competition encourages IBPs to adopt a similar peering strategy for terminating each others’ traffic, except that their customers are now ISPs The limited competition in the IBP market justifies nonnegligible prices in the transit contracts paid by ISPs to IBPs Note that ISPs have the incentive to operate as efficiently as possible, since they pass on the cost of their local network and its transit agreements directly to their customers, who can easily switch ISP if they feel they are not receiving the best value for money

12.2 Competition and service differentiation

We can use standard models of oligopoly to analyse competition in networks that offer guaranteed services In these networks, capacity determines the quantity of services that

INCENTIVES FOR PEERING 285

can be sold However, when networks offer elastic services, then we must be more careful

in modelling competition, as congestion must now be taken into account

The desire of competing networks to discriminate between consumers who differently value various aspects of the offered services motivates the production of services with different qualities of service These differing services can be realized by dividing a network into subnetworks with different congestion levels and profit can be increased thereby However, when more services are offered they will be partly substitutable, and the resulting increase in competition can reduce the profits of all the competing network operators

It is therefore interesting to ask to what extent a competitive market induces service differentiation by making it advantageous for competing networks to offer many types

of service The answer is very sensitive to assumptions Consider the market for access services If a customer can subscribe to multiple services, and so benefit from multiple levels of quality, then it is probable that competing networks will wish to provide services

at multiple quality levels, i.e levels of congestion However, if a customer can subscribe to just one quality level, then competition effects can outweigh service differentiation effects, and each competing network will wish to offer just one class of service, at a price that depends upon its congestion level Of course this assumes competition If network operators collude, then they can maximize profits by each producing at multiple quality levels In any case, if an access network wishes to distinguish itself by a certain quality level, it must guarantee that quality by buying appropriate interconnection agreements Thus, the intermediate networks’ quality of service can be a constraining factor on the competitiveness

of an access network

12.3 Incentives for peering

Whether or not peering between two networks is beneficial depends on how their customers value those things that differentiate the networks, such as size and location Network size is very important to users who wish to access a large customer base and buy or sell services through the network Similarly, location is important to customers that find it easier to access one network than another A network provider can make his network look more attractive by providing good performance to the traffic of his own customers, and worse performance to traffic that originates from outside

Simple economic models of competition suggest that, as a function of customer preferences, either all or no competing networks may want to peer, or smaller networks may want to peer while larger ones do not The case in which no network wants to peer occurs when most customers are more interested in network size than location Here, the market is modelled by a game whose equilibrium solution is asymmetric, in the sense that competing networks grow to different sizes However, if customers are more interested in location, then networks may wish to peer, since by increasing their customer bases, they add value to what they provide and can charge more for it If both size and location are important then peering can benefit smaller networks, but not larger ones This is because, in

a competitive scenario, smaller networks can introduce access charges Peering eliminates the advantage of network size and can encourage customers of larger networks to move to smaller and cheaper ones

In practice, it is typical for a network provider to specify conditions for peering that depend

on the other network’s size and geographic span He might also specify a ‘peering charge’ that compensates him for his loss of income when he peers with another network Of course it

is very difficult to determine this charge In practice, it is often made a function of the access speed of the connection between the two networks at the NAP where peering takes place

12.4 Incentive contract issues

Interconnection agreements may not always provide sufficient incentives for partners to collaboratively realize the full potential of positive network externalities In the present best-effort Internet, interconnection agreements tend to be rather simple, specifying a maximum rate and perhaps a volume charge However, newer Internet applications increasingly require specific network performance guarantees, and so new types of interconnection contract are needed that can account for both quality and volume These contracts must give the peering network the appropriate incentives to allocate the effort required for the contracted quality This contrasts with the present practice of flat contracts that do not include incentives for effort

It is difficult to devise interconnection contracts because of asymmetric information about variables We can discuss this using the terminology of the principal-agent model , in which

a principal (the contractor who sets the terms of the contract) wishes to induce some action from an agent (the contractee who executes the contract) There are variables, such as

peak rate, average throughput and number of bytes, that can be observed and verified by both principal and agent However, there are other variables that cannot be observed by the principal For example, a principal who buys from an agent a contract for interconnection may not be able to tell what minimum bandwidth the agent dedicates to his traffic, or the priority class to which his traffic is assigned These are variables of the ‘effort’ provided

by the agent It is technology that dictates what is observable and what not Sometimes, the effort of the agent may be observable, but the context in which this effort is exercised may not be known at the time the contract and the incentives are defined

Information asymmetry can provide significant advantage to the contractee, who naturally tends to expend the least effort he can to fulfil his contractual obligations The contractor

takes a risk known as moral hazard There is an adverse selection problem when, at the

time the contract is agreed, the agent knows some important information that the principal does not For instance, if the principal is the provider of the interconnection service and the agent is the network generating the traffic, the agent knows how he values ‘heavy’ or

‘light’ use of the contract If he intends to make heavy use of the interconnection service,

it is to his advantage not to reveal this to the principal He would rather be charged the cost of a contract that is targeted at the average customer

In practice, there are many important ways that information asymmetry can occur and can influence the performance that is obtained from an interconnection contract:

ž Perhaps an ISP signs an interconnection agreement, but subsequently does not maintain

or upgrade his network capacity The result is that the interconnection traffic receives poor service As peering agreements are presently based on best-effort services, one party cannot easily tell whether or not the other party is properly managing his network

ž An ISP carrying a high load of local traffic might actively discriminate against packets that enter his network from an interconnected partner The damaging effect of the discrimination may be camouflaged as natural congestion, and it can be hard for his partner to detect the true cause

ž A client party cannot easily predict the traffic load that a network offering interconnection service carries on its backbone It is hard for that party to know the other party’s available spare capacity, his resource allocation and routing policies, or whether he effectively uses statistical multiplexing and overbooking Resource allocation and traffic multiplexing can strongly affect network performance

In negotiating peering or transit agreements, all the above are critical However, information about these issues is not readily available, and ISPs have little incentive to reveal it Present market practices only partly address the problem Large ISPs exert their

MODELLING MORAL HAZARD 287

bargaining power to extract information from smaller partners However, the requirements and terms of their agreements are private and undisclosed to third parties

12.5 Modelling moral hazard

To model asymmetric information problems in the market for Internet connectivity, three fundamental parameters must be defined: effort, outcome, and the cost of providing effort The effort of a network service provider is defined in terms of how he treats his client’s traffic; e.g how an IBP treats the traffic of client ISPs Quantitatively, it can

be described in terms of the resources that he allocates and the scheduling policies he applies to serving the client’s traffic When multiplexing traffic from different sources and applications, the network manager can assign different priorities to different flows of packets according to subjective criteria, such as the type of application being served (e.g email vs videoconferencing), the identity of the sender or recipient, and the revenue generated by the traffic transferred

The dangers inherent in being unable to verify the level of effort can be reduced by using pricing mechanisms that provide the IBP with suitable incentives to exert the effort required

to ensure the required performance In effect, such mechanisms make the IBP responsible for the effort he provides by making his profit depend upon the outcome, after accounting for uncertain conditions Performance indicators, such as average delay or packet loss, could

be used to measure the observable outcome in an interconnection agreement

Effort has a cost This cost could be defined as the opportunity cost of not serving (or reducing the quality of service for) other client ISPs of the same network An alternative but equivalent definition of this cost is based on the negative externality (congestion) imposed

on the network and its other users It is quite difficult to estimate this cost, as it depends

on parameters that an IBP may not reveal Often, a key component in the cost of serving the interconnection traffic is the load of ‘local traffic’ in the network, i.e., the traffic that originates from the network’s other customers and which it is already contracted to carry Information about this load may be available to the network provider before he must decide how to treat transit traffic from an ISP with whom he peers The cost of allocating effort to the traffic of the new contract is negligible when the local traffic load is small, but increases quickly as the local load becomes greater and exceeds a certain threshold This threshold may depend upon the total available capacity, the multiplexing algorithms used, and the burstiness of the traffic In principle, the greater the amount of effective bandwidth that is allocated to the specific contract, the less bandwidth is available for the rest of the traffic, resulting in some opportunity or congestion cost

For an incentive contract to be successful, one must be able to quantify reasonably well the expected cost to the contractee of the required effort, and the value of the resulting quality to the contractor These issues are illustrated in the following example There is information asymmetry at the time the contract is established A rational service provider will provide the minimum possible effort, unless he is given appropriate incentives

In our simple model, we assume that some network conditions are unobservable (implying

an unobservable cost to the agent), but that the provider’s effort is observable The latter assumption is reasonable since interconnection contracts are typically of long duration, and

so a customer ISP should be able to rather accurately estimate the parameters that he needs

to infer the effort allocated by the contracted ISP Only if contracts were of short durations, say a connection’s life, might such estimation be inaccurate and effort unobservable For simplicity, we focus on the modelling issues and the resulting optimal incentive schemes, omitting the complete analysis

y ∈{y1, y2}

a ∈{aL, aH}

aC

(1 − a)C

x

Figure 12.2 A model for an agent’s effort He operates a link serving two queues: one for the transit traffic and the other for his internal traffic The effort given to the transit traffic is measured

by the fraction of capacityÞ dedicated to serving the first queue The rate of internal traffic at the

time the contract is instantiated is random, taking values y1, y2with probabilities p1, p2,

respectively, with y1< y2

Example 12.1 (A principal-agent problem) Consider a transit agreement between two

network service providers, using the formulation of the principal-agent model Suppose a principal, P, contracts with an agent, A, for transport of a packet flow through A’s network

We model A’s network by two queues; one is dedicated to A’s internal traffic and the other

is dedicated to P’s transit traffic (see Figure 12.2)

The service capacity of the network is C, of which ÞC is allocated to the P’s transit

traffic For simplicity, we restrict the choice ofÞ to two values, ÞL,ÞH, whereÞL < ÞH Thus,Þ is the effort that is provided by A in the context of his contract with P We suppose that A has no control over the rate of his internal traffic at the time he begins serving P’s traffic He can control the fraction of his capacity that he will allocate to it, and he knows the distribution of the future rate of his internal traffic at the time he agrees the contract with the principal These are reasonable assumptions for many practical situations The contract defines a service to be provided at some later point in time, and statistical information is available on the future state of the network Let us denote the rate of the internal traffic

by y, and suppose that it is known that it will take one of the two values y1and y2, with

probabilities p1 and p2D1  p1, respectively, where y1< y2

The cost of allocating capacity to P’s flow is the extra delay experienced by packets of

A’s internal flow Assuming, for simplicity, that this is a M=M=1 queue, we can calculate the cost using the fact that if a flow of rate y is served at rate C then the average packet

delay is 1=.C  y/ Taking
as the monetary value of the cost of one time unit’s delay, this implies a rate of delay cost of
y=.C  y/ per unit time Thus, the cost of allocating

a fraction Þ of the available effort to the contract with P is

c y; Þ/ D
y

1

.1  Þ/C  y 

1

C  y

½

Let c.i j/ denote c.y i; Þj /, i 2 f1; 2g, j 2 fL; Hg It can be proved that

c.2H/  c.2L/ > c.1H/  c.1L/ > 0

In other words, a change from low to high effort is more costly to A when the system has

a greater internal load Of course, such a change benefits P, since it reduces the average

delay of his packets Denote by r L and r H respectively the monetary value of the service received by P when the effort levels are low and high

Our task is to design an incentive contract in which P pays A an amount w.Þ/ This payment is determined after the completion of the service and depends on the level of effort

Þ allocated by A, which we suppose P can estimate both accurately and incontestably Perhaps P measures the average delay of his traffic and then uses the delay formula for the

M =M=1 queue to compute the effort that was provided by A.