Tài liệu Pricing communication networks P8 doc

For example, the resources that are required to produce a particular model of personal computer are fixed before its manufacturingstarts, whereas a connection whose service contract spec

Charging Guaranteed Services

In Section 2.1.5 we defined a guaranteed service as one for which there is a contract betweenthe service provider and the customer This contract specifies obligations for both parties.The service provider agrees to provide a service with certain quality parameters so long asthe customer’s traffic satisfies certain constraints

In general, a contract for a guaranteed service may allow some flexibility Certain contractparameters, such as maximum peak rate, may be renegotiated and allowed to change theirvalues during the life of the service For example, the contact might specify that the networkguarantees no information loss so long as the user sends at no more than a maximum rate

of h Mbps The value of h may be renegotiated at the beginning of every minute to be

some value between 1 and 2 Thus there is a part of the contract which guarantees no cellloss at a rate of 1 Any extra rate above this must be negotiated One possibility is thatthe extra rate must be bought in a bandwidth auction This auction is run by the networkoperator so as to better utilize spare capacity A second possibility is that the operator posts

a price p.t/ and lets the user choose how much bandwidth in excess of 1 he wishes to buy.

He sets p.t/ to reflect the present level of congestion in the network Seeing p.t/, the user

must choose the amount of bandwidth in excess of 1 he would like

Chapter 10 is about charging flexible contracts and pricing methodology that gives usersincentives to make such choices optimally However, in this chapter we restrict attention

to guaranteed services whose contracts do not allow the users such flexibility We supposethat all contract parameters are statically defined at the time the contract is established.Equivalently, we restrict attention to that portion of the contract which has no flexibilityand for which the network is bound to provide some minimal requirements, known at thetime the contract is established and persisting throughout its life In the example above, thisportion of the contract is the obligation to provide a 1 Mbps rate at no cell loss We use ideas

of previous chapters to develop a theory of charging for such contracts We do this in variouseconomic contexts, such as the maximization of the social welfare or the supplier’s profit.Most interesting guaranteed services have contracts that specify minimum qualities ofservice that the network must provide, such as minimum throughput rate, maximum packetdelay or maximum packet loss rate This means that the network must reserve resources tomeet the requirements of the active service contracts, and if network resources are finite, thenetwork must operate within its technology set Recall from Chapter 4 that the technologydefines the set of services and their quantities that it is within the network’s capability

to provide at one time In this chapter we analyse, in different economic contexts, the

Pricing Communication Networks: Economics, Technology and Modelling.

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

ISBN: 0-470-85130-9

form of prices that result from considering the particular structure of the constraints oftechnology sets.

An important distinction between service contracts for communications services andsome other economic commodities is that the former do not specify fully the resourcesthat are required to produce a unit of output For example, the resources that are required

to produce a particular model of personal computer are fixed before its manufacturingstarts, whereas a connection whose service contract specifies only an upper bound on theconnection’s maximum rate may use buffer and bandwidth in a way that can only beknown to the network once the connection ends The fact that some information is knownonly ‘a posteriori’, rather than ‘a priori’, makes the problem of pricing service contractsquite complex We will see that by including component of usage in the tariff we canproduce a charge that more accurately reflects the actual resource consumption This type

of charge can provide a customer with the incentive to change his prospective networkusage in a way that benefits overall system efficiency Perhaps he might smooth his trafficand make it less bursty, or use some sort of compression scheme to reduce its total volume

If there is no usage component in the charge then customers have no incentive to conserveresources; instead, they may be wasteful of resources and behave in ways that reduce theoverall efficiency and capacity of the network We argue that flat rate pricing can lead toexactly this sort of waste, and that pricing methods which include a usage charge are to bepreferred

Chapter 4 presented the concept of an effective bandwidth as a proxy for the quantity

of network resources consumed by a bursty connection In Section 8.1 we discuss marketmodels for which it is or is not appropriate to use effective bandwidths as the basis forpricing network connections In Section 8.2 we investigate the more complex problem ofconstructing tariffs for service contracts We discuss the pros and cons of flat rate pricingand give justifications for using tariffs that take account of actual network resource usageand charge proportionally to effective bandwidths

As we see in Section 8.3, it is important that the tariffs for service contracts be incentivecompatible A network can be more competitive and fairer to its users if it presents themwith a range of tariffs, each of which is intended for a specific user type In the simplestcase, a network might offer two different tariffs: one for heavy users and one for light users(as we did in Example 5.5.3) The network cannot prevent a heavy user from choosing thetariff that is intended for light users, but it can construct the tariffs so that heavy users payless on average if they choose the tariff that is intended for them, rather than the tariff that isintended for light users This gives users the incentive to make choices that are informative

to the operator, who can tell whether the a customer’s consumption of network resource

is more likely to be heavy or light, before any resources are actually consumed Thisinformation can help the operator to dimension and operate his network more efficiently,for the benefit of all his customers At the end of Section 8.3 we explain the competitiveadvantage of such tariffs, and consider some related problems of arbitrage and splitting.Section 8.4 describes three simple pricing models that make use of this type of pric-ing Section 8.5 presents a simple example to illustrate the long-term interaction betweentariffing and the load on the network

8.1 Pricing and effective bandwidths

A simple example will illuminate the relationship between the prices for services and theireffective bandwidths Suppose a network operator offers two contract types to his customers

PRICING AND EFFECTIVE BANDWIDTHS 197and wishes to choose a point within his technology set that maximizes his customers’ total

utility, u.x1; x2/ Here x i is the quantity of the service contract i that he supplies Suppose that the optimum point is achieved for some prices p D p1; p2/ At these prices the

demand x.p/ D x1.p/; x2.p// is a feasible point in his technology set Note that x must

be on the boundary of the technology set If it is not, then a decrease in prices will increase

x and hence u (as it is nondecreasing in x1; x2) Recall also that the inverse demandfunction satisfies @u=@x i D p i , i D 1; 2 That is, prices are the derivatives of u Now

on the boundary of the technology set there is a possible substitution of services that isdefined by the effective bandwidth hyperplane that is tangent to the set’s boundary at the

operating point x The network operator can substitute small quantities of service types i and j for one another, in quantities Ž and ŽÞi=Þj respectively, and still be feasible Can

such a change (which in practice is realized by perturbing prices) increase the value of u? The answer lies in the values of the partial derivatives of u Their ratio provides a rate

of substitution for services which leaves the utility unchanged Recalling that these partialderivatives are the prices, we see that unless the ratio of prices equals the ratio of the

effective bandwidths of the services, one can find a feasible perturbation of x that strictly

increases the utility

Suppose, for instance, that near to x the customers benefit 10 times as much from a small

increase in the quantity of service 1 as from the same increase in the quantity of service 2.That is, @u=@x1D10@u=@x2 Again recall that@u i =@x i D p i , so p1D10 p2 Then u can

be increased by x1!x1CŽ unless this requires x2 to be decreased by 10Ž or more, i.e.unless Þ1=Þ2 ½ 10 Similarly u can be increased by increasing x2 ! x2CŽ unless this

requires x1 to be decreased by Ž=10 or more, i.e unless Þ1=Þ210 This means that thecoefficients of substitution in the ‘network container’ (the effective bandwidths, Þ1, Þ2)must have the same ratio as @u=@x1 :@u=@x2, equivalently as p1: p2 We now continueour discussion by deriving prices in a more general economic context

Consider a model in which there are k service contract types, each of which corresponds

to a traffic stream with known statistical properties Let x i p/ be the number of services

of type i that are demanded when prices are p D p1; : : : ; p k /, and let x.p/ be the vector whose i th component is x i p/ One may think of x.p/ as arising from a population of user maximizing a net benefit of u.x1; : : : ; x k/ Pk x k p k Our aim is to construct appropriateprices under models of both monopoly and perfect competition amongst service providers

To illustrate, we do a complete analysis for a single link network The basic results arethat for perfect competition, the optimal prices are proportional to the effective bandwidths

of the traffic streams We remind the reader that perfect competition conditions hold whenthe network is not a single enterprise and consists of a large number of smaller capacitynetworks operated by different network providers with no individual market power In thiscase, the capacity of the network is the aggregate capacity of all such network providers

We also recall that perfect competition results in social welfare maximization For imperfectcompetition, prices can be arbitrary This is easy to see in the case of a monopoly For somedemand, the monopolist may maximize his profit in the interior of the technology set ofthe network He finds it more profitable to keep prices high by restricting the quantities ofservices he makes available Hence, effective bandwidths become irrelevant Social welfaremaximization may be the goal of a monopolist who can perform price discrimination Usingpersonalized pricing he may be able to recover the surplus of each of his customers byimposing an appropriate subscription fee

For simplicity, we consider first the case of a single contract type and seek to characterizethe structure of the optimal price As in Section 6.5 we find the optimal quantity of contract

to sell by solving a problem of maximizing a weighted sum of consumer surplus and supplierprofit:

maximize

x 2X

ý

u x/  xp.x/ C ½ðx p x/  c.x/Ł

where c.x/ is the variable cost of providing a quantity of the service x, and x is constrained

to lie in the technology set of the network, X Note that for½ D 1 this is the problem ofmaximizing social welfare We can rewrite this as in (6.6), as an equivalent problem,

D 1 we have the problem of maximizing social welfare So increasing
is associatedwith increasing competition

If we assume that the technology set is specified by the single constraint g1.x/  b1, wemust maximize the Lagrangian

p xŁ/



1 C 1 
ž

If xŁlies in the interior, then¼ D 0 and the optimal price satisfies

p xŁ/



1 C1 
ž



This is equivalent to (6.8) that we obtained in Section 6.5 In this case the price depends both

on the service’s elasticity of demand and the degree of competition (where for
D 1 we

have the familiar marginal cost pricing rule) Why would one expect xŁto be in the interior

of the acceptance region? There are two independent reasons The first is that the variable

cost function c x/ increases rapidly with x, and hence it does not make economic sense to

fully load the network The other reason may be that there is little competition (
is close

to zero), and hence profits are maximized by supplying services in lesser quantities thanthe technology set would actually permit Observe that if social welfare is to be maximizedrather than profit, and variable costs are small, then the network should provide as muchservice as possible, within the constraints of its technology set

An interesting special case is when marginal variable cost c0.x/ is zero This is often a

reasonable assumption for communication networks that operate with a fixed infrastructure.Then the term in parentheses on the left hand side of (8.3) must be zero and this suggests

PRICING AND EFFECTIVE BANDWIDTHS 199that the optimal price and the operating point are completely determined by the degree ofcompetition and the price elasticity of demand, as summarized by
and ž (recalling that ž,

the price elasticity of demand, is a function of p) In other words, the revenue maximizing

price of the service does not depend on the amount of resources it consumes in the network,but only on its demand The marketing department should construct the tariff for the servicefrom market research There is no need to consult the engineering department and to betterunderstand what use the service contract actually makes of network resources

If the constraint of the technology set is active, then ¼ > 0 in (8.2) In this case theprice depends also on the shadow cost and the derivative of the constraint However, if themarket is highly competitive (so
is approximately 1) and there is a negligible marginalvariable cost, then we obtain (approximately)

p xŁ/ D ¼g0

Thus the price has a simple form, which we can exploit further Since g1.x/ is a constraint

of the technology set, we can use the results from Section 4.5 to approximate g1.x/ D b1

locally at xŁ by xŁÞ.xŁ/ D C, where C is the effective capacity of the link, and obtain

Another practical approach is to use tatonnement to find the appropriate prices This

requires no a priori knowledge of the value of ¼ We only need to know the relativevalues of the effective bandwidths The tatonnement proceeds in an iterative fashion asfollows Pick a set of prices in proportion to the effective bandwidths This corresponds

to choosing a value of ¼ Determine whether for these prices the demand lies inside oroutside the technology set and then respectively inflate or deflate all prices by the samesmall percentage Repeat this step, until the demand lies just inside the technology set

In practical terms, given that the network operator wishes to solve (8.1), the value ofthe shadow price ¼ is the amount he would be willing to pay to increase by one unit the

constant b1 of the binding constraint In our case, this corresponds to increasing C, the effective capacity of the link If the price for increasing C in the actual market is less

than ¼ then there is an incentive is to expand the network Observe that ¼ depends upondemand The greater the demand for services, the greater ¼ will be

In general, if there are multiple contract types, then contract types can be substitutes andcomplements for one another If the price for one contract type increases, the demands for

other contract types can increase and decrease In the general case, maximizing L gives in

place of (8.2), and generalizing (6.7),

Example 8.1 (Pricing minimum throughput guarantees) Consider a single link that can

carry Q bytes in total within a period of length T The contract of a transport service is defined in terms of the maximum number of bytes, say q, that the network will transport

on behalf of the contract during this period In other words, the network guarantees a

throughput rate of q =T over the time window of length T Such a contract does not specify

any other performance guarantee Let us suppose that each contract that is accepted by thenetwork is required to make all the bytes that it wishes to have transported available at

the beginning of the period T (since it would clearly be very troublesome if the data were

available only towards the end of the period) How should the network price this contract?

Should prices be in proportion to q?

Based on our previous discussion, the answer depends on competition aspects In asocial welfare optimization context, prices of contracts should be proportional to effectivebandwidths Let us discretize the size of the possible contracts and enumerate them so

that q i is the size of a contract of type i , i D 1; : : : ; k Now the technology set of

the network is P

i x i q i  Q, where x i is the number of contracts of type i Hence

the effective bandwidth is Þi D q i , and the optimal prices are of the form p i D ½q i

In other words, ½ is the price per byte, and is the same for all contracts irrespectively

of their size Clearly, such a simple charging scheme is not optimal when the networkoperator has market power He may use volume discounts to effect price discrimination

in selling his service and so obtain larger revenues from his customers If the operatorcan use personalized pricing, then he will wish to make each user a take-it-or-leave-

it offer

In concluding this section, we observe that we have not yet spoken about one furtherimportant aspect of the pricing problem that is special to the nature of transport servicesand makes pricing decisions even more complex This concerns arbitrage By their nature,transport service contracts can be combined and re-sold in smaller units For instance, onemay buy a contract with a large effective bandwidth and resell it to other customers interms of a number of different contracts with smaller effective bandwidths The traffic ofthese customers must be multiplexed and then demultiplexed at the end, at some cost.However, if there is little competition and marginal variable cost is near 0, the implication

of (8.3) is that prices should be computed solely on demand assumptions But these pricescan be impractical This is because high prices for certain services provide the incentivesfor customers to buy cheaper service types and then disguise them as the expensive servicetypes, i.e to use them to transport the data of the applications which would otherwisebuy the expensive services Such an incentive is reduced if prices reflect actual resourceconsumption Alternatively, network operators may avoid such commoditization of theirtransport services by combining them with other offerings such as security, reliability andglobal availability Personalizing a service according to the customer’s needs is an importanttool for achieving greater revenues Hence in practice, revenue maximizing operators willchoose prices that are related to effective bandwidths to provide for a stable environment

in which to offer services Such choices must also take account of demand, personalization

PRICING AND EFFECTIVE BANDWIDTHS 201capabilities, and the cost of service resale by third parties We return to these issues inSection 8.3.5.

Finally, we extend our results to the general case of pricing contracts for connectionsover a network instead of single link

8.1.1 The Network Case

We let L be a set of links and R be a set of routes, a route being a set of links Connections are made over routes, and use contracts from a finite set of contract types, K Suppose that

a connection using route r has contract type k Then, as in Section 4.13, we can assume

for simplicity that the effective bandwidth Þk that is consumed by a contract is the same

on each link of the route, and so depends only upon the type of the contract Denote by

C j the effective capacity of link j

Let x r k be the demand for contracts of type k over route r , and assume that this demand arises from the users’ aggregate utility function u.fx r kg/ In this case, taking account of(4.28), the social welfare maximization problem becomes

kÞk x r k/ As in the single link case, we take the derivative with respect

to x r k and find that the optimal price for contracts of type k on route r is given by

charge per unit of time of a unit of effective bandwidth along route r This again suggests

that optimal prices should be proportional to effective bandwidths The price for a contract

over route r is equal to the product of the effective bandwidth of the contract and the price

of a unit of effective capacity along route r

Such prices can be computed by a tatonnement Each link of the network posts its pricefor effective capacity These lead to prices for contracts along all routes The demandfor contracts adjusts itself to these prices Each link now increases or decreases its pricedepending on whether or not there is excess demand for effective capacity at that link.Iterating this procedure, prices eventually converge to ones that achieve the optimum

in (8.8)

As a simple application, consider the following approach for pricing guaranteed qualityservices using the Integrated Services architecture described in Section 3.3.7 To establishthe contract, the originating node declares, in addition to its quality of service requirements,its maximum willingness to pay (per unit time) for the connection In the process ofestablishing the connection, bandwidth is reserved at each link, and the available budget

is decremented by the cost of the bandwidth at each link If it is found that the budget

is sufficient, then the connection is established and the price is set to the sum of thesecosts Otherwise, the connection is rejected, or it is allowed to renegotiate a reducedbandwidth requirement The links constantly update prices to reflect available capacity.Prices should rise if the available capacity becomes small, say less than 10% of the totallink capacity

8.2 Incentive issues in pricing service contracts

In practice, service contracts specify constraints which restrict the maximum amount of

resource usage This contrasts with other economic goods for which the resource use isspecified exactly For example, a traffic contract might specify a maximum access rate or

a leaky bucket constraint The fact that a traffic contract only constrains the maximumresource consumption creates a number of interesting incentive issues In this section, wediscuss the impact of the structure of tariffs on actual resource usage This motivates the

construction of tariffs that combine a priori and a posteriori contract information.1 Suchtariffs include an element of usage charge and make sense from the viewpoint of both thenetwork and users Let us consider the user’s viewpoint first

Consider a simple model for a user application that needs a contract to transport data

with a constant rate x through the network (In general, x may be an effective bandwidth.)

If all network applications were of this type, differing only in the value x, and this were a

known parameter, things would be simple Each user would request a contract that exactly

fits the needs of his application, and pay appropriately Unfortunately, in practice, x is not

known and so we must model it as a random variable For instance, the application may

be known to produce data at a rate, x, which randomly takes a value in the range [x1; x2],independently chosen each time the user starts the application What contract should the

user select? One possibility would be for him to play safe and buy a contract for x2 Butthis contract may be very expensive A second possibility is for him to purchase a contract

for a rate y between x1 and x2, which would be sufficient most of the time However,

the downside it that when x exceeds y, the policing mechanisms of the network will trim

the rate and the application will experience unacceptable performance This will reduce thevalue of the service to the customer The user may also feel that he is charged unfairly

every time x is less than y, since he pays for y even though he does not use it Such a user would benefit from a contract that allows his applications to use the range of rates up to x2

(to reflect a priori information, that x2is known), but charges him something that reflects

the actual rate he uses (the a posteriori information about x).

Consider now the network’s perspective We have argued in Section 8.1 that charging

in proportion to the effective bandwidths may be the optimal approach under appropriatemarket conditions However, there are subtleties in the conversion of an effective bandwidthinto a charge As we have already discussed, these subtleties arise because contracts specify

a range of possible effective bandwidths, rather than a unique one An additional complexity

is that users may alter their traffic generating applications in response to the incentives thatare provided by whatever effective bandwidth definition is used to price the contract.Let us investigate two extreme possibilities Consider first the problem of designing an

effective bandwidth pricing scheme that is based only on a priori information That is, it

does not take account of the actual traffic that is carried under the contract For simplicity,suppress the coefficient¼ from the effective bandwidth charge, and assume that the networkhas all the information it needs to compute the effective bandwidths

The a priori information that might be available for all connections of type j , could

include the fact that all connections of this type are subject to the same traffic contract

Perhaps this contract is defined in terms of leaky bucket parameters The a priori

1A priori information consists of the contract’s static parameters and knowledge of the amount of resources that connections using this type of contract have consumed in the past The a posteriori information includes the

amount of resources that the connection actually consumed; it may include statistics about the traffic that was generated during the connection’s life.

INCENTIVE ISSUES IN PRICING SERVICE CONTRACTS 203

information might also include data on past connections of type j For example, one might estimate the effective bandwidth of connections of type j in the following way Suppose that we have seen n j connections of type j We take the kth connection that we have seen

of type j , divide its duration T k into intervals of length t, and then compute

where X j k[.i 1/t; it] is the number of bytes of traffic that was measured from connection

k in the interval [ i  1/t; it] (with i D 1 denoting the start of the connection) This would

give us an empirical estimate of the expectation

may differ significantly between two connections of this type.) We can now simply charge

each newly admitted connection of type j an amount per unit time equal to the empirical

estimate QÞj s; t/ That is, each connection of type j is charged proportionally to the average

effective bandwidth of past connections of the same type

This is really the same as flat rate pricing, in which all users pay an identical rate ofcharge, calculated from the average resource usage of previous similar users It is also thecharging method of an all-you-can-eat restaurant In such a restaurant, each customer ischarged not for what he eats, but for the average amount that similar customers have eaten

in the past; (we say ‘similar customer’, because some restaurants have a lower price forchildren or different prices depending on the time of day) The existence of all-you-can-eatrestaurants demonstrates that this charging scheme is viable It is analogous to the chargingscheme used when local telephone calls are unmetered, or when the only cost a student pays

to browse the WWW is the cost of waiting for a free seat in the computer room However,all-you-can-eat restaurants are not for everyone They encourage diners to overeat; theytend to serve only the lower quality part of the market Customers with small appetites mayfeel that they are overcharged Others are put off by the bare-bones, help-yourself, no-frillsambiance

We can identify two problems with a flat charging scheme The first concerns a user

who has connections of type j but whose traffic usually has an effective bandwidth that is

less than the average for this type Such a user may feel that he is being overcharged, and

subsidizing other users of connection type j whose traffic usually has a greater effective

bandwidth than his Consequently, he may defect to a service provider who uses a chargingmethod that is more favourable to him The second problem is that customers have anincentive to overconsume Since the charge does not depend on usage, customers have

no incentive to use applications in ways that conserve resources Network resources will

be wasted, and probably congestion will increase The result is that the typical contractwill have a larger effective bandwidth, and this must eventually be reflected in a greatercontract price As before, customers with light usage may change providers, and ultimately

the network will be left with only the heaviest users This is known as the adverse selection

problem Thus, it is clear that a flat pricing scheme has severe problems Similar problems

occur with a form of peak rate pricing, in which the operator defines the effective bandwidth

as the greatest effective bandwidth that can result under the given contract

Having examined one extreme, let us examine the other: a charge based completely on

a posteriori measurements For example, one might charge the kth connection of type j

This is the effective bandwidth of this connection measured a posteriori Apart from the

difficulty of interpreting this complicated tariff to users, there is the following conceptualflaw Suppose that a user requests a connection policed by a high peak rate, but then

actually transmits very little traffic over the connection Then the a posteriori estimate of

the effective bandwidth given by (8.11) will be near zero, and hence the charge near zero,even though the a priori expectation may be much larger, as assessed by either the user

or the network The network bears too much of the risk inherent in uncertainty about theuser’s traffic, since the network may have to allocate at least some resources on the basis

of a priori information about the connection.

Our discussion of the two extreme cases above has highlighted the flaws in two possibleapproaches to charging A third approach, which we believe to be the most reasonable,attempts to circumvent these flaws It creates a charge that is close to the actual effective

bandwidth of the connection Like the first approach, it takes account of a priori information

in the contract This ensures that some charge is made for resources that must be reservedeven if they are not used Like the second approach, it also takes into account actual usage.This ensures users have an incentive not to overconsume

The key idea of the approach is that the charging scheme is framed in terms of a menu ofseveral tariffs The user chooses in advance the tariff from which he would like his charge to

be computed Clearly, he will choose the tariff under which he expects the smallest charge.This is the one for which he would expect the smallest average charge, given what he knowsabout his likely use under the contract The network can use the information about the tariffselection to better estimate the effective bandwidth of the particular contract Hence, thenetwork can do a better job of call acceptance, utilize its resources better, and in principleprovide more services This alignment of incentives between the individual choices made

by users and the network’s goal of optimizing its performance is what we call the incentivecompatibility property of the charging scheme We explain more details in the next section

8.3 Constructing incentive compatible tariffs from effective bandwidths

In this section we present an incentive compatible charging scheme It is based on the

effective bandwidth concept It avoids the problems of a charge that is based only on a

priori, or only on a posteriori, information The key idea is to approximate the effective

bandwidth by an upper bound that depends on both a priori and a posteriori information,

i.e upon both the static parameters of the contract and actual measurements This gives agood approximation of the actual effective bandwidth of the traffic stream produced by thecontract We bound the effective bandwidth by a set of linear functions of parameters that

are measured a posteriori, with coefficients that depend on the static parameters known

a priori These linear functions become the basis for simple charging mechanisms In

particular, users are offered the set of linear functions as tariffs If the user knows theexpected value of the parameters that are to be measured, he can choose the tariff thatminimizes his expected charge Even if he does not know these expected values precisely,

CONSTRUCTING INCENTIVE COMPATIBLE TARIFFS 205better estimates of them can help him to select a better tariff Although this method can

be used for arbitrary measurements, we illustrate it by considering simple measurements ofthe contract’s duration and the volume of bytes carried under it

There are other important issues that we also discuss We show by an example thatproviders who use such effective bandwidth schemes have a competitive advantage overthose who use flat rate schemes We also discuss, as at the end of Section 8.1, issues ofcontract arbitrage, resale and splitting By their nature, transport contracts do not specifythe ownership of the bytes carried Hence, a customer may himself become a transportservice provider by selling parts of his transport capability to other customers Pricingschemes that leave open this possibility are usually not desirable, since they are vulnerable

to competitive entry

8.3.1 The Time-volume Charging Scheme

We illustrate our approach by describing how one class of traffic might be charged Supposethis class of traffic uses a traffic contract under which the user must send at no more than a

maximum rate h (the a priori information) Imagine that a connection uses this contract and sends data at a mean rate m (the a posteriori information) It can be shown that amongst possible traffic of mean rate m and peak rate no more than h the traffic with the greatest

effective bandwidth is one that is periodically on and off, and has on and off phases of longduration As we have seen in Example 4.5, this type of traffic has an effective bandwidthgiven by

Here, s and t are defined by the operating point of the multiplexer.

Think ofÞon-offas a function of m, where without confusion we can write it asÞon-off.m/,

a concave function of m Note that the network does not know the value of m when the contract is established Now for our traffic contract, parameterized by the peak rate h, we define a family of tariff lines, parameterized by the parameter m, each of which takes

the form

f m M/ D a.m/ C b.m/M which as a function of M lies above the curveÞon-off.M/ and is tangent to it at m D M Note that a.m/ and b.m/ also depend upon h, s and t through the definition of Þon-off in (8.12),but because these are fixed we do not indicate the dependence on them explicitly The user

chooses a tariff, or, equivalently states a value of m The final charge is T [a m/ C b.m/M], where M is the measured mean rate of the user’s traffic Equivalently, the charge is

a m/T C b.m/V , where V D T M is the volume of traffic carried (measured in cells

or bytes) (see Figure 8.1)

Does such a scheme really charge for effective bandwidths? Can we make the user reveal

his mean rate, m, through his choice of tariff? If he does not know m, can we give him an

incentive to estimate it at the time the connection is set up?

One can easily see from Figure 8.1 that a user’s expected charge is minimized when he

chooses the tariff with m D E[M], i.e when the parameter of the tariff equals the expected value of the measured mean rate of the connection In the figure, we suppose E[M] D 1 The choice of the tariff f m M/, with m D E[M] D 1, produces an average charge of 2T The choice of f 0.M/ produces an average charge of 2:4T This is the notion of ‘incentive

the mean rate, M, for a fixed peak rate h The user is free to choose any tangent to this curve, and

is then charged a.m/ per unit time and b.m/ per unit volume He minimizes his average charge rate

compatibility’: the tariffs are designed so that if a user knows his M and chooses amongst

the tariffs in a self-interested way, he will choose the tariff that reveals the true value of

his M.

In practice, the user may not know his M in advance, but he has the incentive to make

a good estimate of it If he can make a good estimate, he will be rewarded by beingcharged less than he would be otherwise The network operator is provided with someinformation about the likely mean rate of the connection He can use this information tohelp reserve resources appropriately Thus, the risk that the network reserves the wrongamount of resources is more evenly shared between the provider and the user

By giving the user a set of tariff choices as above, we obtain several desirableconsequences:

ž The total charge takes the very simple form a m/T C b.m/V To charge for time and

volume is perhaps the simplest usage-based scheme one could imagine, yet it is firmlybased in the theory of effective bandwidths

ž The tariff coefficients depend upon known traffic contract parameters, h, s and t, and so

can be easily computed

ž The charge accounts both for resource reservation (which is charged by the timecomponent) and actual usage (which is charged by the volume component)

ž The charge requires only simple accounting It should be simple to measure T and V

ž By allowing a user to specify m to be used in his tariff, a new dimension is added to the

traffic contract Thus, users obtain added-value from the fact that they can choose to becharged in a way that fairly reflects their actual resource usage

Note that, in this example, the tariff coefficients a.m/ and b.m/ depend upon the traffic contract through the single parameter h and on the operating point through s and t One

can repeat the analysis for contracts involving more than one static parameter For example,

if a contract is policed by K leaky buckets with static parameters fh k D ²k; þk /; k D

1; : : : ; K g, then we can take these into account using an effective bandwidth approximation