IEEE TRANSACTIONS ON SERVICES COMPUTING, 201X 1

Spot Transit: Cheaper Internet Transitfor Elastic Traffic

Hong Xu, Member, IEEE, and Baochun Li, Senior Member, IEEE

Abstract—We advocate to create a spot Internet transit market, where transit is sold using the under-utilized backbone capacity ata lower price. The providers can improve profit by capitalizing the perishable capacity, and customers can buy transit on demandwithout a minimum commitment level for elastic traffic, and as a result improve their surplus (i.e., utility gains). We conduct asystematic study of the economical benefits of spot transit both theoretically and empirically. We propose a simple analyticalframework with a general demand function, and solve the pricing problem to maximize the expected profit, taking into account thepotential revenue loss of regular transit when spot transit traffic hikes. We prove the price advantage of spot transit, as well asthe profit and surplus improvements for tier-1 ISPs and customers, respectively. Using real-world price data and traffic statisticsof 6 IXPs with more than 1000 ISPs, we evaluate spot transit and show that significant financial benefits can be achieved in bothabsolute and relative terms, robust to parameter values.

Index Terms—Network economics, Internet transit, bandwidth pricing

F

1 INTRODUCTION

Internet transit has traditionally been traded withlong-term contracts, where the tier-1 Internet Ser-vice Provider (ISP) specifies pricing and the transitcustomers commit a minimum level of bandwidthconsumption. Two facts make this market inefficientfor today’s Internet. First, tier-1 ISPs typically over-provision the backbone and have a portion of thecapacity under-utilized most of the time [13], whichrepresents a bulk of the missing revenue opportunities.Second, the transit customers are increasingly unwill-ing to purchase transit due to sheer costs of serving theever increasing traffic volumes. Cisco estimates thatbusy-hour Internet traffic will increase fivefold by 2015while average traffic will increase fourfold [12].

In this paper, we advocate that a spot Internet transitmarket should be created, where the unused transitcapacity is sold at a lower price to compliment thetraditional contract-based market. To serve the spottraffic, the tier-1 ISP uses its under-utilized capacitythat are otherwise wasted. It provides no Quality-of-Service (QoS) guarantee or support for spot transit.This enables the ISP to adopt a lower price and earnextra revenue from the available, yet perishable, band-width resource. It can also stop routing the spot trafficat any time, when capacity is needed for regular transitor to handle network failures.

The transit customers, on the other hand, have theflexibility to buy transit on demand at a discount. Spottransit is ideal for elastic traffic [33]. For example, data

• Hong Xu is with Department of Computer Science, City Universityof Hong Kong, Kowloon, Hong Kong. Email: henry.xu@cityu.edu.hk.Baochun Li is with Department of Electrical and Computer Engineer-ing, University of Toronto, Toronto, Ontario M5S 3G4, Canada. Email:bli@ece.toronto.edu.

centers can use it for the bulk backup and replicationtraffic across the Internet [11], [19]. Eyeball ISPs canuse it at demand valleys to support time-dependentpricing [16]. A lower broadband access price can beadvertised at valley periods, encouraging users to de-fer time-insensitive applications, and reduce the costlypeak demand. In short, they can cope with trafficfluctuations in a more flexible and cost efficient way.

Moreover, small ISPs that originally rely on variousforms of peering or buying from transit resellers [35],[39] can now purchase spot transit to offload theelastic traffic, and enjoy the reachability of a tier-1backbone with lower costs. The barrier of minimumcommitted data rates no longer exists. Since it doesnot differentiate based on protocol or user type, spottransit is also less susceptible to network neutralityconcerns spawned by some instances of paid peering[1], [39].

In this paper, we are primarily interested in theeconomic aspect of the market, in particular, pricing,profit for tier-1 ISPs, and consumer surplus, i.e. utilitygains, for transit customers. Pricing is critical as it di-rectly affects the incentives of both sides to participate.We take the liberty to envision that a spot market istechnically feasible, and conduct a systematic study ofthe economical benefits of spot transit.

The unique challenge of pricing here arises froman intriguing interplay between the spot and regulartransit traffic, whose bits share the same backboneinfrastructure. When the tier-1 ISP tries to lower theprice to attract demand, it is certainly possible thatthe increased spot traffic hogs up the network andcauses performance degradation to the regular traffic.Therefore, the risk of demand overflow and its impacton profit have to be taken into account.

We solve the spot transit pricing problem for ex-pected profit maximization of a tier-1 ISP under the

classical additive random demand model [31], whichwe validate against real inter-domain traffic. Further,we prove that spot transit improves both profit andconsumer surplus, as long as it is cheaper than regulartransit. It is therefore a win-win solution for both sides.We emphasize that all our results are obtained with ageneral demand function that captures the basic prop-erties of any demand function. Essentially, the benefitsof spot transit only depend on the characteristics ofelastic traffic.

To quantitatively understand the potential of spottransit, we perform an extensive empirical evaluationbased on traffic traces collected from 6 Internet eX-change Points (IXPs) in America, Europe, and Asia.The dataset of each IXP contains aggregated trafficstatistics from more than 100 ISPs with peak demandbetween 1200 Gbps and around 200 Gbps. We use twocanonical demand functions with real transit prices,empirical demand elasticity data, and a range of modelparameters. We find that, spot transit typically can be15%-30% cheaper, and provide more than 60% profitimprovement for tier-1 ISPs and more than 10% sur-plus improvement for customers. In dollar terms, theprofit and surplus gains are on the order of millions(monthly) for large IXPs and hundreds of thousandsfor smaller ones. The benefit is robust: 10% profit andsurplus improvements are still observed even in theworst case.

We make three original contributions in this paper.First, we propose spot transit, a transit market thatallows customers to buy underutilized transit capacityon demand at a discounted price (Sec. 2). Second, wepropose a simple analytical framework that strikes abalance between economic theory and realistic aspectsof Internet transit. With a general demand function(Sec. 3), we characterize the optimal price as a functionof the provision cost, overflow penalty, demand elas-ticity, and the predictability of traffic. We theoreticallyestablish the price advantage and efficiency gains ofspot transit (Sec. 4). Third, we empirically evaluatespot transit using real traffic statistics and price data.We obtain realistic parameters for demand functionsby fitting empirical traffic data into canonical economicmodels, and demonstrate the significant benefits ofspot transit (Sec. 5). Towards the end, we also discussissues about implementing such a market (Sec. 6).

2 BACKGROUND AND MOTIVATIONThe Internet backbone consists of a small number oftier-1 ISPs, each owning a portion of the global infras-tructure, and can reach the entire Internet solely viasettlement-free interconnection, i.e. peering. They pro-vide transit services to transit customers for monetaryreturns. It is widely known that the tier-1 backboneis largely under-utilized (under 50%) due to over-provisioning [13]. Over recent years, though traffic hasbeen growing at a 40%–50% annual rate [12], [18],backbone capacity has been increasing worldwide at

an equivalent pace [37]. As a result, underutilizationcontinues, with average and peak link utilization onmajor backbone lines virtually unchanged [36].

The under-utilized backbone capacity represents abulk of missing revenue opportunities for tier-1 ISPs.Network capacity is inherently a perishable resource:bandwidth that is not used is lost forever. On theother hand, despite the constant decline of transitprices [37], customers face enormous transit costs dueto the rapid-growing traffic. New forms of peering[39] and smart traffic engineering schemes [19], [40]are continuously being developed to cut the transitbill. This demonstrates the inefficiency of the currentmarket, and calls for novel solutions that offer betterways of trading transit.

Motivated by these observations, we propose tocreate a spot transit market, where the unused capacityis sold at a discount without SLAs regarding networkavailability, route stability, etc. Transit customers canpurchase spot transit on-demand without entering acontract first. The spot transit market compliments theregular contract based market. It suits well to servethe elastic traffic, such as the bulk replication andbackup traffic across datacenters and most residentialbroadband traffic, because it can tolerate delay andloss and is much more price sensitive [39].

D

p

p0 = 5

p1 = 3

D0 = 100

D1 = 226.4

D

p

SurplusSurplus

RevenueRevenue

(a) Regular transit at $5/Mbps (b) Spot transit at $3/Mbps

Fig. 1. The benefits of the spot transit market. Itimproves the social welfare by improving the revenuefor tier-1 ISPs, and surplus for transit customers. Thedemand curve shown is D = 1313.26 · p�1.6.

To intuitively see the potential of the spot transitmarket, Figure 1 shows a typical iso-elastic demandcurve [24], [39] for a tier-1 ISP’s elastic traffic. Wechoose the demand function such that at a regulartransit price of $5/Mbps, the elastic traffic is 100 Gbps.The revenue is $500,000 per month. If the demandwere to be served by the spot transit market, since thetier-1 ISP does not need to provide QoS guarantees,it can afford a lower price of, say, $3/Mbps, with a40% discount. At such a low price, demand rises toaround 226.4 Gbps, and our tier-1 ISP collects around$680,000. Thus, by creating the spot transit market andoptimizing price, the tier-1 ISP attains a 36% profitincrease. This represents a strong financial incentive.

The spot transit market also benefits transit cus-tomers in terms of consumer surplus, which is thedifference between the total amount that they arewilling to pay and the actual amount that they dopay at the market price [22]. As depicted in Figure 1,

consumer surplus is greatly improved with a lowertransit price.

Therefore, the spot market achieves higher efficiencyand improves social welfare. The underlying reason isthat in the conventional transit market, elastic trafficis priced together with inelastic traffic that has highercosts to serve. By pricing the elastic traffic separatelywith spot transit that has no SLAs, tier-1 ISPs are ableto adopt a lower price, which in turns attracts evenmore demand and increases profit.

The demand increase with spot transit can be ex-plained by at least two factors: competition with peer-ing and transit reselling. The low price and on-demandfeature of spot transit can make it more appealing thanpeering or paid peering, considering the performancebenefits and network reachability provided by the tier-1 backbone. Further, small ISPs usually find it difficultto purchase transit directly from tier-1 ISPs due to theminimum committed data rate requirement, and relyon transit resellers instead. With spot transit, tier-1 ISPsare able to collect additional profits from these smallISPs by bypassing the transit resellers in the middle.In all, we expect that spot transit compliments thetraditional transit business of a tier-1 ISP.

3 MODELIn this section, we introduce the theoretical model forour analysis of the optimal pricing, and the benefits ofspot transit.

3.1 Spot transit marketWe consider a spot transit market with multiple tier-1 ISPs. This corresponds to an oligopoly scenario.Numerous game models can be adopted [22] and eachconsiders specific competition scenarios. Our objectiveis to study spot transit under a general model thatcaptures the key aspects of the market. For the appli-cability of results and ease of exposition, we choose tofocus on a representative tier-1 ISP, with the residualdemand that is not met by other competitors in themarket. Residual demand is a common concept inmicroeconomics in studying the pricing problem fora firm operating in a competitive market [24], [39].

Though residual demand does not model the fulldynamic interactions between ISPs, it accounts forthe availability of substitutes and switching costs. Italso allows a faithful empirical verification, since thereal-world price and demand data collected reflectthe effect of competition. The same approach is alsoadopted in [39].

3.2 DemandOne of the challenges of conducting economic analysisin networking is the lack of a good model for the resid-ual demand, or simply demand, in general. Not muchpublic information is known about the Internet transitmarket in particular for business reasons. Here we

Fig. 2. Weekly and monthly aggregated traffic at NIX,an Internet exchange in Czech Republic [26].

blend theory with practice, and use classical demandmodels from economics with empirical justificationsbased on real traffic data. We believe such an approachnot only makes the analysis tractable, but also theresults practically relevant.

3.2.1 A model for billable demand

We define spot transit demand D as the actual billableamount of bandwidth, i.e. the 95-percentile demand.Other pricing schemes, such as volume pricing, canbe studied in a similar way. The aggregated traffic ofa tier-1 ISP often exhibits a diurnal pattern with highpredictability [13], [30]. For example Figure 2 plotsthe aggregated traffic at the Neutral Internet eXchange(NIX) in Czech Republic [26]. The diurnal pattern isclearly visible in both weekly and monthly scales. Nat-urally, one can thus employ statistical methods overtraffic time series to estimate the billable demand, witha small error that arises from the inherent randomnessof demand.

Inspired by this observation, we adopt the classicalapproach in economics [31] to model the uncertaintyof billable demand in an additive fashion. Specifically,

D(p, ✏) = d(p) + ✏, (1)

following [23]. Here, p is the spot transit price in$/Mbps, d(p) is the price-dependent demand func-tion that models the billable demand (more details inSec. 3.2.2), and ✏ is a random variable defined over[A, B] to model the inherent demand uncertainty. Thusrandomness in demand is price independent. That is,the shape of the demand curve is independent of theprice, while the mean and variance of the demanddistribution are affected by the price. We provideempirical justifications for our demand model usingreal-world traffic data in Sec. 5.2.

3.2.2 Demand function d(p) and elasticity

Many demand functions d(p) are valid in economicanalysis. Instead of choosing some specific functionsto work with, our analysis assumes a general demandfunction. We only require that d(p) is a continuous,twice differentiable, decreasing, and convex function,

i.e. d

0(p) < 0, d

00(p) � 0. Monotonicity and convexity

are general characteristics of the demand-price inter-action. These assumptions are quite reasonable andcommonly accepted in the literature.

A useful concept related to demand is its elasticity.Elasticity measures the responsiveness of demand to achange in price, and is defined at a price point p as

�(p) = �p · d0(p)

d(p)

. (2)

We can observe that

�

0(p) � 0 (3)

since d

0(p) < 0 and d

00(p) � 0, i.e. elasticity is non-

decreasing in p.Next we show two canonical demand functions that

satisfy our assumptions.Iso-elastic demand. The iso-elastic demand, or con-

stant elasticity demand, is a well-known demandfunction derived from the alpha-fair utility function[24], [39], which is often used to model Internet useractivity. As the name suggests, elasticity is constant forevery price point.

d(p) = v · p�↵, v > 0, ↵ > 1. (4)

v can be interpreted as the base demand that controlsthe magnitude of demand. �(p) = ↵, where ↵ denotesthe constant elasticity: a higher value represents higherelasticity. As discussed above, demand here is theresidual demand, and high elasticity can also indicatethat the market is more competitive, and substitutesare readily available.

Linear demand. The simple linear function of de-mand is also popular [22]:

d(p) = v � ↵p, v > 0, ↵ > 0. (5)

Here v is the base demand. Elasticity of linear demandis �(p) =

↵pv�↵p . In contrast to iso-elastic demand,

now elasticity decreases in price. Thus it captures thephenomena that sometimes, demand is less sensitiveto a price change when the price is already low (recall(3)).

3.3 Surplus, profit, and social welfareTo comprehensively study the economical benefits ofspot transit we consider three metrics, namely con-sumer surplus, provider profit, and social welfare. As wehave seen from Figure 1, consumer surplus, or simplysurplus is the utility gain obtained by customers dueto the purchase of Internet transit. Specifically,

S(p) =

Z 1

p(x � p)d(x)dx. (6)

In other words, the surplus equals the amount cus-tomers are willing to pay, minus the actual cost ofpurchase at p. It is evident that S(p) increases as p

decreases, i.e. a price reduction is always beneficial forcustomers.

Next we characterize provider profit as a function ofthe spot transit price p. We consider the scenario wherethe tier-1 ISP allocates a fixed portion of the unusedbackbone bandwidth to offer spot transit services. Thisamount is defined as the capacity of spot transit C, andcan be safely used without affecting the ISP’s regularbusiness. A proper choice of C can be determined bythe ISP profiling its network utilization.

The notion of capacity here is not a rigid resourceconstraint. Since demand is inherently random andboth the spot and regular transit traffic share the samebackbone, nothing prevents the spot traffic from break-ing through the capacity C and using the capacityreserved for regular transit. Such a demand overflowscenario may negatively affect the regular transit trafficand thus the ISP’s revenue. To model the revenue loss,a penalty of m > 0 in $/Mbps is incurred wheneverdemand exceeds the capacity, i.e. D(p, ✏) > C. Anequivalent interpretation is to treat it as modeling thesurplus loss of the regular transit customers due tooverflow. m > p

C , where p

C denotes the price at whichd(p) = C. Thus, the penalty is large enough so that atthe optimal operating point, the expected demand issmaller than C.

We let f(·) denote the probability density functionof the demand uncertainty ✏ defined over [A, B]. Inpractice ✏ can often be approximated by a Gaussianrandom variable. To make sure that positive demandis possible, we require B < C which holds naturallysince the randomness is small in magnitude comparedto capacity. These assumptions will also be verifiedusing real traffic traces in Sec. 5.2.

We can now formally define the spot transit profit.If demand does not exceed the capacity, then profit issimply (p � r)D(p, ✏), where r > 0 is the unit cost ofspot transit. Otherwise the profit consists of a positivecomponent from serving the spot transit and a neg-ative component representing the demand overflowloss, and is written as (p � r)D(p, ✏) � m(D(p, ✏) � C).The profit function, R(p, ✏) can then be expressed as

R(p, ✏) =

⇢(p � r)(d(p) + ✏), ✏ C � d(p)

(p � r � m)(d(p) + ✏) + mC, ✏ > C � d(p)

The expected profit is:

E[R(p)] =

(p � r)d(p) � m

Z B

C�d(p)(d(p) � C + u)f(u)du (7)

Define �(p) = (p�r)d(p), and ⇤(p) = m

R BC�d(p)(d(p)�

C + u)f(u)du. �(p) represents the risk-free profit whendemand is deterministic. ⇤(p) is the loss function at anaverage cost of m when demand overflow happens.The overall expected profit is the difference betweenthe two.

E[R(p)] = �(p) � ⇤(p), (8)

Finally, the social welfare of a market is defined asthe sum of consumer surplus and provider profit. For

the spot transit market, its social welfare (p) is

(p) = S(p) + E[R(p)]. (9)

4 AN ECONOMIC ANALYSIS

In this section, we present our analysis on the optimalpricing of spot transit for profit maximization, as wellas the resulting profit, surplus and social welfare, totheoretically demonstrate its benefits.

4.1 Pricing for profit maximizationWith spot transit, the very first question we needto answer is, how do we price it? Our ISP needsto determine a price to maximize its expected profitwith the presence of demand uncertainty, taking intoaccount the risk of demand overflow and its monetaryimpact. The profit maximization problem can then beformulated:

max

pE[R(p)] (10)

s.t. (7)

For efficient price determination, the optimizationproblem must have an efficient solution algorithm. Themost useful criterion for this property is convexity:minimizing a convex function, or equivalently maxi-mizing a concave function over a convex constraint set.However, we show that this condition is not satisfiedfor our problem.

Consider the first-order derivative of E[R(p)], whichcan be obtained by applying the Leibniz integral rule:

E

0[R(p)] = d(p)+ d

0(p)

�p � r � m · Pr

�✏ > C � d(p)

��.

(11)It can be observed that the term in (·) is positive anddecreasing in p, and thus the term �(·)d0(p) is decreas-ing in p. However, d(p) + p · d0(p) is not monotonicallyincreasing or decreasing. Therefore, E[R(p)] is neitherconvex nor concave in p.

Luckily, we can still prove that the first-order op-timality condition E

0[R(p)] = 0 is a necessary and

sufficient condition for the optimization (10), with avery mild assumption of quasiconcavity.

Definition 1: A function g(x) is (strict) quasicon-cave if and only g

0(x)(x

0 � x) > 0 whenever g(x

0) >

g(x) (p.934, [22]).That is, a quasiconcave function is either decreasing,

increasing, or there exists x

⇤ such that g is decreasingfor x < x

⇤ and increasing for x > x

⇤. Thus, quasicon-cavity is a generalization and relaxation of concavity. Ifa function is not monotone, quasiconcavity guaranteesthat it has a unique global maximum. In other words,it alleviates the burden of considering the second-order condition by ensuring that the sufficient first-order condition is necessary even without the strongconcavity assumption [6], [22].

Lemma 1: E[R(p)] as in (7) is quasiconcave with thegeneral demand function d(p).

The proof can be found in Appendix A.Therefore, we can efficiently solve the optimal pric-

ing problem by setting the first-order derivative ofE[R(p)] to zero.

Theorem 1: Optimal price p

⇤ of the profit maxi-mization problem (10) is determined uniquely as thesolution to the first-order condition, i.e.

p

⇤= r + m · Pr

�✏ > C � d(p

⇤)

�� d(p

⇤)

d

0(p

⇤)

. (12)

For example, the optimal price of iso-elastic demand(4) satisfies

p

⇤=

↵

↵ � 1

�r + m · Pr

�✏ > C � v(p

⇤)

�↵��

. (13)

The optimal price of linear demand (5) satisfies

2p

⇤= r + m · Pr

�✏ > C � v + ↵p

⇤�+

v

↵

. (14)

Several interesting and economically satisfying ob-servations can be made from Theorem 1. First, theoptimal price p

⇤ increases with the provision cost r,which is straightforward. Second, p

⇤ also increaseswith the overflow penalty m. Third, p

⇤ increases with� d(p⇤)

d0(p⇤) , which equals p⇤

�(p⇤) from (2). That is, the ISPcan set a high price if demand elasticity is low dueto weak market competition or the uniqueness of itsservice, and vice versa. Finally, we can see that p

⇤> p

0,where p

0 is the profit maximizing price without de-mand uncertainty (m = 0). It shows that with demanduncertainty, a tier-1 ISP needs to charge a higher pricein order to cover the damage of demand overflow.

Having solved the pricing problem, we now wouldlike to study the price advantage of spot transit, i.e.whether, or when it can be offered at a cheaper pricethan regular transit. To address this question, we needto first understand the regular transit price, whichis set prior to the introduction of spot transit. Fora rational tier-1 ISP, we can interpret p̄ as the profitmaximizing price for the aggregated traffic demand¯

d(p) when it is solely served by the regular transit,which amounts to the following:

p̄ = arg max (p � r̄)

¯

d(p), (15)

where r̄ is the provision cost of regular transit. Noticethat although regular and spot transit share the sameinfrastructure cost, r̄ > r because spot transit doesnot have any QoS support or financial overhead ofcontract negotiation. Since ¯

d(p) includes both inelasticand elastic traffic demand, its elasticity is smaller,i.e. �̄(p) < �(p) for any p. Then we can prove thefollowing.

Theorem 2: p

⇤< p̄, i.e. the spot transit price is

less than the regular transit price, if the following issatisfied:

r r̄ � m

�1 � �(p

⇤)

�1�

✓

2

✓

2+ (C � d(p

⇤) � µ)

2, (16)

where µ and ✓ are the mean and standard deviationof ✏, respectively.

The proof is in Appendix B. Theorem 2 confirmsthe intuition that spot transit is cheaper than regulartransit as long as the cost difference between themis large enough. The condition (16) is sufficient butnot necessary. It is easy to satisfy, since r < r̄ al-ways holds and

�1 � �(p

⇤)

�1�1 is small in practice.

The term ✓2

✓2+(C�d(p⇤)�µ)2 bounds the tail probabilityPr(✏ > C � d(p

⇤)), and is also small given the demand

randomness ✏, i.e. its standard deviation ✓ is small.Therefore, theoretically, spot transit can be offered at adiscount in most of the cases with a general demandfunction.

We wish to emphasize that this result depends onlyon two defining characteristics of elastic traffic thatspot transit serves, i.e. low cost (16) and high elasticity�(p) > �̄(p). As will be shown soon in Sec. 4.2, theyalso guarantee the economical efficiency gains of spottransit. This demonstrates the generality of our resultsthat does not depend on the specific forms the demandfunction may take.

4.2 Surplus, profit, and social welfareNow we turn to analyzing the efficiency of the spottransit market. We seek to answer the question: atthe optimal price p

⇤, can spot transit improve surplus,profit, and eventually social welfare?

Without loss of generality, we assume that p

⇤< p̄

holds. First, as discussed in Sec. 3.3, surplus increaseswhen price decreases, and the following follows fromTheorem 2.

Lemma 2: S(p

⇤) > S(p̄).

That is, spot transit improves surplus for elastic trafficgiven its price advantage. Thus it is beneficial forcustomers.

Next from the provider’s perspective, we wish toknow whether spot transit is more attractive thanregular transit for elastic traffic. That is, whether theoptimal profit is larger than that using regular transit.Without spot transit, the expected profit that could becollected from elastic traffic at the regular transit pricep̄ is:

E[R(p̄)] = (p̄ � r̄)d(p̄), (17)

where d(p̄) is the demand that would occur at p̄.Lemma 3: E[R(p

⇤)] > E[R(p̄)].

The proof is in Appendix C. This lemma confirmsthat the spot transit market is not only beneficial forcustomers, but also profitable for ISPs, as long as it canbe offered at a lower price than the regular transit.The reason of the profitability is that since elastictraffic is more price sensitive, a price reduction canpotentially attract more demand and the end resultis a net profit increase despite the negative impact ofdemand overflow on regular transit.

Combining Lemma 2 and 3 we have

1. �(p⇤) > 1 because price reduction is only possible to gen-erate positive gains if demand increases at least proportionally inresponse.

Theorem 3: �(p

⇤) > �(p̄). Spot transit improves

social welfare by improving consumer surplus and ISPprofit.

Therefore, we have theoretically proved that spottransit is more efficient than the conventional marketfor elastic traffic, taking into account demand uncer-tainty and the overflow loss. Both ISPs and transitcustomers have clear incentives to participate in thisnew market. Given the flexibility in purchasing, spottransit represents an economically viable and attrac-tive market solution for Internet transit, especially forelastic traffic. Our analysis is valid for general demandfunctions, and can be expected to hold in most realisticcases.

5 EVALUATION

In this section, we present an empirical evaluationof spot transit based on real-world operational traf-fic information we collected from 6 representativeInternet eXchange Points (IXPs) located in America,Europe, and Asia. One significant hurdle of networkeconomic analysis is the lack of empirical data. ISPs,especially tier-1 ISPs, are reluctant to share their trafficdata publicly. A few European ISPs serving academicinstitutions do publish their traffic statistics online.Their size, traffic volume, and characteristics, however,do not faithfully reflect those of the tier-1 ISPs.

We use the traffic statistics of large IXPs to representthe tier-1 ISP traffic. IXPs are physical infrastructurefacilities through which ISPs peer with each other.They are located in key hub locations around theworld, and serve a significant portion of the Internettraffic [18]. A large IXP typically has over one hundredmember ISPs, and interconnecting hundreds of Gb/scommercial, academic, and residential traffic. Thus thescale and traffic characteristics are similar to those ofa tier-1 ISP.

Though IXPs solely serve peering traffic, empiricallyit has been verified that peering and transit trafficshare similar temporal patterns with respect to peaktimes, peak-to-valley ratios, etc. [35]. Essentially, bothare driven by the same end-user behavior, and it isintuitive that they are statistically similar. Thus, webelieve the first-order estimation of transit traffic usingpeering traffic of IXPs is appropriate as a startingpoint of our performance evaluation. In the following,we use the IXP traffic to represent the regular transitdemand ¯

d(p̄) at the regular transit price for tier-1 ISPs.

5.1 Dataset descriptionIXP data is more accessible since many publish theiraggregate traffic statistics online. Usually the incom-ing and outgoing traffic time series are reported andupdated every 5 minutes. We manually inspect thewebpages of large IXPs [4], and handpick 6 representa-tive ones across the globe that publish traffic statisticsusing the standard mrtg/rrdtool visualization tool

IXP Acronym Country # of members Peak (Gbps) Average (Gbps) Error mean µ Error s.d. ✓London IX [20] LINX (LN) U.K. 407 1200 797.1 -15.9278 174.8157Moscow IX [25] MSKIX (MSK) Russia 353 688.5 416 2.2313 115.0810

Neutral IX (Prague) [26] NIX (N) Czech Republic 54 217.8 129.6 -1.2458 30.2338New York International IX [27] NYIIX (NY) U.S. 128 205.9 157.7 3.9486 26.0743

Spain IX [34] ESPANIX (ES) Spain 58 198 172.5 -1.0476 22.3824Hong Kong IX [15] HKIX (HK) China 168 180 119.8 1.7689 22.0919

TABLE 1IXPs studied and statistics of their traffic and week-ahead prediction errors.

[5] with a reasonable time granularity2. We crawl thewebsites of these IXPs to collect the weekly aggregatedtraffic statistics images. All the data is collected in 2012and is more recent than the dataset in [35]. Table 1 listsall the IXPs we studied in this paper.

Traffic data is published as png images using mrtg,and is not readily available in numerical forms. Wefollow the approach of [35] to use an optical characterrecognition (OCR) program to read the png imagesand output the numeric array containing the traffictime series. Each IXP uses a slightly different mrtgconfiguration, including the size, bit depth, and colorrepresentation. Thus, we modified the software pro-vided by [35] to handle each IXP’s png image individ-ually. The raw image files, the numeric data, and thesoftware for converting png images are available in[3]. The basic traffic information is shown in Table 1.

5.2 Demand model validationAs a first step, we conduct an empirical validation ofour demand model stated in Sec. 3.2.1. Recall from (1)that we model the 95-percentile demand as the sumof the demand function d(p) and a random variable ✏

to model the uncertainty. Since the aggregated traffichas a clear diurnal pattern, an intuitive justification ofthis model can be provided if the ISP can accuratelyestimate its 95-th percentile demand based on thetraffic time series, with a small error term to accountfor the unpredictable dynamics that corresponds to ✏

[7], [30].We assume that the tier-1 ISP of interest uses the

most recent history to estimate/predict the futuredemand time series, the simplest regression method[7]. Once the entire time series can be predicted, its95-percentile can be readily obtained. More complexalgorithms can yield more accurate prediction for alonger time window [30], which is beyond the focusof this paper. Thus, if the prediction window size is T ,the future demand at time t is Dt = Dt�T .

We run this week-ahead prediction on all 6 IXPs.Figures 3 and 4 show the week-ahead (T = 7 days)prediction result of LINX and NIX traffic for an exam-ple. We can observe that simple week-ahead predictionbased on the most recent history is fairly accurate.Figures 5 and 6 show the Q-Q plots of the prediction

2. Some large IXPs, such as Deutscher IX, Amsterdam IX, andJPNAP only publish daily and/or yearly traffic stats that are toocoarse to analyze.

Week 1 Week 2

400

600

800

1000

1200

1400

Dem

and

(Gbp

s)

Original dataPredicted

Fig. 3. Week-ahead pre-diction of the LINX traffic.

Week 1 Week 20

50

100

150

200

250

300

Dem

and

(Gbp

s)

Original dataPredicted

Fig. 4. Week-ahead pre-diction of the NIX traffic.

−5 0 5−300−200−100

0100200300

Standard Normal Quantiles

Pred

ictio

n Er

ror Q

uant

iles

Fig. 5. Q-Q plot of week-ahead prediction error onthe LINX trace.

−5 0 5−100

−50

0

50

100

Standard Normal Quantiles

Pred

ictio

n Er

ror Q

uant

iles

Fig. 6. Q-Q plot of week-ahead prediction error onthe NIX trace.

errors. They lie closely on a linear line, suggesting thatthe error term ✏ behaves much like a Gaussian randomvariable.

The error mean µ and standard deviation ✓ for theweek-ahead prediction on all 6 IXPs are shown inTable 1. The mean is close to zero and the standarddeviation is small compared to the predicted data.Since the demand series can be accurately predictedwith a small error, the 95-percentile demand can bereadily calculated with the same error statistics. Thisvalidates our demand model.

Note that although the IXP data contains both elasticand inelastic traffic, essentially our demand model isbased upon the observation that demand of a tier-1ISP is highly predictable due to multiplexing, whichis valid for both traffic types. We use the 95-percentiletraffic from the IXP data to represent the aggregatedregular transit demand ¯

d(p̄) at the regular price p̄. Weadjust � 2 [0.2, 0.7] to obtain elastic traffic out of theaggregated, where � denotes the relative proportion ofelastic traffic. µ and ✓ then scales linearly with �.

The validation result also suggests that ✏ can bemodeled as a Gaussian random variable. Thus we letA = µ�3✓ and B = µ+3✓ so that it contains more than99% of the probability mass and results in reasonablygood numerical accuracy and approximation [31]. Thespot transit capacity C is set to (0.4 + �) times the

aggregated regular transit demand ¯

d(p̄) throughoutthe evaluation. For a backbone with peak utilization of50%, the underutilized capacity equals ¯

d(p̄). 50%–110%of this underutilized capacity is thus safe to be usedfor spot transit. We believe such setting represents atypical operating environment of spot transit. One canreadily verify that B < C holds as assumed in Sec. 3.3.

Note that we have used the simplest predictionalgorithm, and the result is therefore only a lowerbound. With more complex algorithms one can obtainmore accurate prediction for a longer time window[30], which is beyond the focus of this paper. Theprediction techniques and the line of reasoning applyto both elastic and inelastic traffic. We emphasize thatour demand uncertainty model is dependent only onthe observation that demand at a tier-1 ISP is highlypredictable.

5.3 Obtaining cost and demand parameters fromdataAfter validating the model, the next key step is toobtain cost and demand parameters in our model. Ouranalysis in Sec. 4 is applicable to general demand func-tions. In the evaluation we use two common demandfunctions, iso-elastic and linear demand as in Sec. 3.2.2.To derive model parameters for them, we use the Q22011 median GigE transit price in New York, London,and Hong Kong published in [37] as the regular transitprice p̄ in America, Europe, and Asia. Table 2 lists theprice data.

First, to obtain the cost of regular transit r̄, sincenow we know the regular transit demand ¯

d(p̄) andp̄, assuming ISPs are rational and profit-maximizing,from (22) we can obtain

r̄ = p̄

✓1 � 1

↵̄

◆(18)

for iso-elastic demand with (4), and

r̄ = p̄ �¯

d(p̄)

↵̄

(19)

for linear demand with (5). Studies have shown thatthe more elastic residential Internet traffic has an elas-ticity of around 2.7 for cable and DSL [8]. We thusassume the demand elasticity ↵̄ = 2 in (18) for aggre-gated traffic, i.e. dr̄ = 0.5p̄. Since r̄ is invariant acrosstwo demand models, we can substitute r̄ into (19) toobtain ↵̄ for linear demand in different continents.

To obtain demand parameters, we first multiply � 2[0.2, 0.7] to ¯

d(p̄) to calculate the elastic traffic demandat the regular price d(p̄) from the IXP dataset. Thenfrom (4) and (5) we know that as long as the demandsensitivity parameter ↵ is known we can obtain thebase demand

v = d(p̄) · p̄↵ (20)

for iso-elastic demand and

v = d(p̄) + ↵p̄ (21)

Location Price p̄ ($USD/Mbps)London 7.5

New York 7Hong Kong 22

TABLE 2The regular transit prices in major Internet exchange

locations [37].

for linear demand. The entire elastic demand curved(p) can then be obtained. We use a range of valuesfor � > 1 to control the relative elasticity of spot transitversus regular transit, in order to evaluate the effect ofelasticity on the benefits of spot transit. For iso-elasticdemand, ↵ corresponds directly to elasticity, and ↵ =

�↵̄ so that spot transit is � more sensitive. For lineardemand, since ↵ also affects the demand magnitude,we have to first scale it down by �, i.e. ↵ = � · �↵̄.

We stress that the purpose of evaluation is to verifythe analysis in Sec. 4 and gain insights on the potentialof spot transit in a realistic setting. We do not claimthe numerical accuracy of the results obtained here fortier-1 ISPs. The exact pricing and monetary benefitsheavily depend on various factors and can only becalculated on a case-by-case basis.

5.4 Overall benefitsFirst and foremost, we evaluate the overall benefits ofspot transit with typical parameter setting. For bothdemand models, we set � = 1.25, r = 0.5r̄, andm = p̄ so that elastic traffic, i.e. spot transit demand,is 1.25 times more sensitive than regular transit, costis half of the regular cost, and overflow penalty isequal to regular price. � = [0.2, 0.7], and the capacityC = (0.4+�)

¯

d(p̄). For a backbone with peak utilizationof 50%, the underutilized capacity equals ¯

d(p̄). 50%-110% of this underutilized capacity is thus safe to beused for spot transit. We believe such setting repre-sents a typical operating environment of spot transit.Figures 7-16 show the evaluation results of all 6 IXPsfor both demand models.

Figures 7 and 10 plot the normalized spot transitprice p⇤

p̄ for both demand models. Observe that spottransit is offered at a discount, ranging from more than30% to 15%. This demonstrates the price advantage ofspot transit. Price increases with �, suggesting that asrelative proportion of elastic traffic increases, demandoverflow probability increases since cost, penalty, andelasticity does not change with � here. Figures 8 and11 show the profit improvement of spot transit. We cansee that spot transit significantly improves tier-1 ISP’sprofit, by 80%-130% with iso-elastic demand, and by63%-65% with linear demand. Same observation canbe made in terms of consumer surplus as shown inFigures 14 and 16. Spot transit improves surplus by10%-40% with iso-elastic demand, and by 120%-200%with linear demand. Since price increases with �, theimprovement decreases as a result.

0.2 0.3 0.4 0.5 0.6 0.70.6

0.7

0.8

0.9

Proportion of elastic traffic

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 7. Optimal spot price with iso-elastic demand.

0.2 0.3 0.4 0.5 0.6 0.70.7

0.9

1.1

1.3

1.5

Proportion of elastic traffic

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 8. Profit improvement with iso-elastic demand.

0.2 0.3 0.4 0.5 0.6 0.7

0.2

0.4

0.6

0.8

Proportion of elastic traffic

Surp

lus i

mpr

ovem

ent

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 9. Surplus improvement with iso-elastic demand.

0.2 0.3 0.4 0.5 0.6 0.70.82

0.84

0.86

0.88

0.9

Proportion of elastic traffic

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 10. Optimal spot price with lineardemand.

0.2 0.3 0.4 0.5 0.6 0.70.63

0.64

0.65

0.66

Proportion of elastic traffic

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 11. Profit improvement with lin-ear demand.

0.2 0.3 0.4 0.5 0.6 0.71

1.2

1.4

1.6

1.8

2

Proportion of elastic traffic

Surp

lus i

mpr

ovem

ent

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 12. Surplus improvement withlinear demand.

0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

2

2.5

Proportion of elastic traffic

$USD

(Mill

ion)

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 13. Profit gain of spottransit with iso-elastic de-mand.

0.2 0.3 0.4 0.5 0.6 0.70

2

4

6

Proportion of elastic traffic

$USD

(Mill

ion)

Fig. 14. Surplus gain ofspot transit with iso-elasticdemand.

0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

2

Proportion of elastic traffic

$USD

(Mill

ion)

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 15. Profit gain of spottransit with linear demand.

0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

2

2.5

Proportion of elastic traffic

$USD

(Mill

ion)

Fig. 16. Surplus gain ofspot transit with linear de-mand.

One may wonder at this point, what is the exactdollar amount of spot transit’s benefits? Figures 13 and16 plot the absolute profit and surplus gain for iso-elastic demand, and Figures 14 and 15 plot the abso-lute gains for linear demand, respectively. The profitgain stands more than $1 million for large IXPs likeLINX, and in the order of hundreds of thousands of

dollars for smaller ones like NIX, NYIIX and ESPANIXfor both models. The absolute surplus gain dependsmore on the shape of demand curve, and is moresalient with iso-elastic demand that allows price to goto infinity. Again the gain is in the order of milliondollars for large IXPs, and hundreds of thousands ofdollars for smaller ones. Thus, our evaluation not onlyconfirms the qualitative analysis in Sec. 4.2, but alsoquantitatively shows that spot transit offers significantfinancial incentives with more than $1 million dollarsof gains possible (monthly) for both tier-1 ISPs andtransit customers, depending on the size of the ISP.

Another interesting observation from the results isthat, the smallest IXP, HKIX, enjoys more dramaticperformance improvement than others despite its rel-atively small scale, especially in terms of consumersurplus. The reason is that the regular transit price inAsia and other more remote areas of Internet is muchhigher than other regions, resulting in a much largerprofit margin in $/Mbps for tier-1 ISPs. Thus, withthe same price discount, its profit and surplus gainsare more profound than bigger IXPs in major cities ofEurope and America. This illustrates that spot transitis potentially more attractive in “remote” regions ofInternet where regular transit is much more expensive.

5.5 Pricing analysis

Now we the effect of various parameters on spot tran-sit pricing. We choose to present results with iso-elasticdemand since both models lead to similar conclusions.

0.1 0.3 0.5 0.7 0.9

0.65

0.7

0.75

Relative spot transit cost

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 17. The effect of r on spot pricewith iso-elastic demand.

0.5 0.7 0.9 1.1 1.3 1.50.62

0.63

0.64

0.65

0.66

0.67

Relative overflow penalty

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 18. The effect of m on spot pricewith iso-elastic demand.

1.2 1.4 1.6 1.8 20.6

0.65

0.7

0.75

Relative elasticity (gamma)

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 19. The effect of � on spot pricewith iso-elastic demand.

Figures 17-19 show how spot transit price is affectedby cost r, penalty m, and elasticity ↵, respectively. Wevary the relative cost r/r̄ between 0.1 and 0.9 withm = p̄ and � = 1.25, relative penalty m/p̄ between0.5 and 1.5 with r = 0.5r̄ and � = 1.25, and relativeelasticity � between 1.1 and 2 with r = 0.5r̄ andm = p̄. Other parameter settings remain the same asin the previous section. We observe that spot priceincreases with all of the three factors, as expectedfrom Theorem 1. Price is less sensitive to penaltym compared to cost and elasticity, since penalty isonly imposed on the overflown portion of demand.Also from Figure 17 we can see that when r � 0.4r̄,r̄ � r 0.6r̄ = 0.3p̄ < 0.5m(1 � 1

2⇤1.25 ) = 0.3p̄, spottransit price is still offered at more than 15% discount.This confirms our discussion of Theorem 2 in Sec. 4.1that even when the condition r r̄�0.5m(1��(p

⇤)

�1)

is not satisfied, i.e. when the cost difference is notlarge, spot transit can still be much cheaper thanregular transit, and improves the overall efficiency ofthe market as proved in Theorem 3.

5.6 Sensitivity analysisWe have studied how cost r, penalty m, and elasticity↵ affect spot transit pricing. In this section, we analyzehow these model parameters affect the profit andsurplus improvement of spot transit.

First we vary r and m individually as we did inthe previous section, and plot the profit and surplusimprovement with iso-elastic demand in Figures 20-23. Observe that as cost r and penalty m increase,both profit and surplus drop which is intuitive tounderstand. Spot transit is able to provide positiveimprovement even when r = 0.9r̄ or m = 1.5p̄. Resultsof linear demand are similar and not presented.

We then vary elasticity ↵ by varying � between 1.1and 2. Figures 24-25 show the corresponding profitand surplus improvement. We can see that although alarger ↵ increases spot transit prices, it also increasesthe profit and surplus gains at the same time, whichis in sharp contrary to the results of cost and penalty.The reason for the discrepancy is that increasing ↵

does not change cost and penalty of spot transit, andas a result the profit margin is actually increased due

0.1 0.3 0.5 0.7 0.90

1

2

3

Relative spot transit cost

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 20. Profit improve-ment vs. r with iso-elasticdemand.

0.1 0.3 0.5 0.7 0.90.2

0.3

0.4

0.5

0.6

0.7

Relative spot transit cost

Surp

lus i

mpr

ovem

ent

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 21. Surplus improve-ment vs. r with iso-elasticdemand.

0.5 0.7 0.9 1.1 1.3 1.51.3

1.35

1.4

1.45

Relative overflow penalty

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 22. Profit improve-ment vs. m with iso-elasticdemand.

0.5 0.7 0.9 1.1 1.3 1.50.3

0.4

0.5

0.6

Relative overflow penaltySu

rplu

s im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 23. Surplus improve-ment vs. m with iso-elasticdemand.

to the price increase. From the numerical result wealso observe that demand at p

⇤ also increases despitethe price increase because the elasticity now is larger.The overall effect of increased elasticity therefore ispositive, in spite of slightly increased revenue loss dueto demand overflow either.

1.2 1.4 1.6 1.8 21

1.5

2

2.5

Relative elasticity (gamma)

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 24. Profit improve-ment vs. � with iso-elasticdemand.

1.2 1.4 1.6 1.8 20.2

0.4

0.6

0.8

1

Relative elasticity (gamma)

Surp

lus i

mpr

ovem

ent

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 25. Surplus improve-ment vs. � with iso-elasticdemand.

Finally, we study a worst-case scenario, where all thethree parameters are deliberately chosen to represent

the worst operating environment with high cost, highpenalty, and low elasticity for spot transit. Specifically,we let r = 0.9r̄, m = 1.5p̄, and � = 1.1, and plotthe spot transit price, profit and surplus improvementwith varying � in Figures 26-31. In other words, thesefigures represent the minimum improvement over arange of parameter values.

0.2 0.3 0.4 0.5 0.6 0.70.8

0.85

0.9

0.95

1

Relative spot transit cost

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 26. Worst-case pricewith iso-elastic demand.

0.2 0.3 0.4 0.5 0.6 0.70.9

0.92

0.94

0.96

Proportion of elastic traffic

Nor

mal

ized

spot

pric

e

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 27. Worst-case pricewith linear demand.

We can see that with the worst combination ofparameters, spot transit is still slightly cheaper thanregular transit for both demand models. The profitimprovement stands above 10%, and the surplus im-provement is 5% with iso-elastic demand and morethan 60% with linear demand. The results cleardemonstrates that the advantage of spot transit isrobust against a wide range of parameter values, andspot transit can be expected to provide significantgains in a typical operating environment.

0.2 0.3 0.4 0.5 0.6 0.70.125

0.13

0.135

0.14

0.145

0.15

Proportion of elastic traffic

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 28. Worst-caseprofit improvement withiso-elastic demand.

0.2 0.3 0.4 0.5 0.6 0.70

0.05

0.1

0.15

0.2

0.25

Proportion of elastic traffic

Surp

lus i

mpr

ovem

ent

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 29. Worst-case sur-plus improvement with iso-elastic demand.

0.2 0.3 0.4 0.5 0.6 0.70.142

0.144

0.146

0.148

Proportion of elastic traffic

Prof

it im

prov

emen

t

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 30. Worst-case profitimprovement with lineardemand.

0.2 0.3 0.4 0.5 0.6 0.7

0.7

0.8

0.9

1

Proportion of elastic traffic

Surp

lus i

mpr

ovem

ent

LINXMSKIXNIXNYIIXESPANIXHKIX

Fig. 31. Worst-case sur-plus improvement with lin-ear demand.

6 DISCUSSION OF FEASIBILITY

We have compellingly demonstrated, through boththeoretical analysis and empirical evaluation based

on real-world traffic and price data, that spot transitprovides significant financial benefits to tier-1 ISPs andtransit customers. However, profitability alone doesnot guarantee the feasibility of spot transit. In thissection, we examine some practical aspects that webelieve are important to the establishment of such anew transit settlement market.

6.1 Market infrastructureIn the spot transit market, customers can purchaseand utilize spot transit on-demand from tier-1 ISPs.This requires a physically connected infrastructureamongst all customers and the ISP. We believe thisseemingly daunting task has, to a large extent, beensolved by the proliferation of network exchange fa-cilities, such as Internet Exchange Points (IXP) andNetwork Access Points (NAP), across the world. Theyhost hundreds of ISPs each already, including tier-1 ISPs [4]. Though IXPs carry mostly peering trafficfor now, the infrastructure can certainly be utilized tosupport spot transit with little additional cost. Such apublic infrastructure enables tier-1 ISPs to support anycustomers present in the IXP, and customers to flexiblyswitch between spot transit providers. By supportingspot transit IXPs also diversify and expand its businessline.

In case the tier-1 ISP or the transit customer is notpresent in an IXP, it is highly likely that a private linkexists between the two for carrying regular transit.Spot transit can then be provided over the existingprivate link. Even in the extremely rare case that a newlink has to be set up, such a one-time cost is expectedto be rather insignificant compared to the long-termbenefits of spot transit.

6.2 Inter-domain routing, service differentiation,and billingThe introduction of spot transit traffic does not posetechnical challenges or complications for inter-domainrouting of BGP (Border Gateway Protocol). Though itshares the same network backbone with regular transittraffic, spot transit traffic can be easily identified andmanaged by a designated AS (Autonomous System)number acquired by the tier-1 ISP. The ISP advertisesroutes with the designated AS number when it sup-ports spot transit, and stops doing so when it doesnot wish to carry spot transit due to say insufficientcapacity or other considerations.

To make sure spot transit traffic does not negativelyimpact regular traffic, ISPs may wish to impose servicedifferentiation, e.g. bandwidth limit. In fact ISPs havebeen practicing service differentiation for many yearsand there is little additional difficulty in managingspot transit traffic. For example, an ISP can rely ondifferentiated services (DiffServ) commonly used toprovide to provide different QoS. It recognizes spottransit traffic by the designated AS number, and clas-sify it by setting the DSCP (differentiated services code

point) bits in the IP header of packets to have a lowerpriority than regular transit traffic. The ISP then cancompute and limit the total bandwidth used by spottransit packets. Or it may use priority queueing basedon the DSCP bits so that packets of spot transit trafficwill only be forwarded by the routers when there is nopacket from regular transit traffic in the egress port.

Billing is also straightforward by tracking trafficdestined to the designated AS number. No contractis required and only the used amount of bandwidth isbilled based on 95-th percentile billing or any othersuitable method. The spot transit bill can easily becombined with the regular transit bill if the customeruses both from the same tier-1 ISP.

6.3 Market cannibalizationOne may be concerned that the tier-1 ISP’s regulartransit business would be negatively impacted by of-fering spot transit customers, resulting in the so-calledmarket cannibalization [2]. We have already shownthat, the spot transit profit is significantly larger thanthe profit collected from serving the elastic traffic withregular transit due to an increase of demand as aresult of price reduction. The demand increase doesnot necessarily translate to a decrease of regular transitdemand. In fact we do not expect spot transit to besuitable for the relatively inelastic traffic which findsregular transit with SLAs more reliable.

The demand increase with spot transit can be ex-plained by at least two factors: competition with peer-ing and transit reselling. The low price and on-demandfeature of spot transit can make it more appealing thanpeering or paid peering, considering the performancebenefits and network reachability provided by the tier-1 backbone. An ISP that relies mostly on (paid) peeringfor cost reasons can utilize spot transit for a portion ofits elastic traffic with much better reachability. Further,small ISPs usually find it difficult to purchase transitdirectly from tier-1 ISPs due to the minimum com-mitted data rate requirement. They purchase transitfrom medium size ISPs that buy transit at bulk andresell to these small customers. With spot transit, tier-1 ISPs are able to collect additional profits from smallISPs by bypassing the transit resellers in the middle.In all, we expect that spot transit compliments ratherthan cannibalizes the traditional transit business of atier-1 ISP.

7 RELATED WORK

An extensive literature exists on the Internet transitmarket in both networking and economics. Two as-pects are particularly related to our work: optimal pric-ing design, and novel market approaches for Internettransit.

Internet broadband access pricing generally is de-signed and computed to optimize revenue, social wel-fare, or performance. [29] argues that the predominant

flat-rate pricing structure for selling retail Internetaccess encourages waste and is incompatible withservice differentiation. [17], [32] study the benefits ofusage-based pricing and argue that, with price differ-entiation, one can use resources more efficiently. [10],[28] study Paris Metro Pricing in which service dif-ferentiation and congestion control are autonomouslyachieved by charging different prices for differentservice tiers that share the same infrastructure. Time isanother dimension to unbundle connectivity. Hande etal. [14] characterize the economic loss due to the ISP’sinability or unwillingness to price broadband accessbased on time of day. Jiang et al. [16] study the optimaltime-dependent prices for an ISP selling broadband ac-cess based on solving optimization offline with trafficestimates.

Our work is different in that we study pricing ofspot transit, a new market for Internet transit. [21]proposes a Shapley value based cooperative settlementbetween content, transit, and eyeball ISPs. The focus ison performance and optimality of the Internet ecosys-tem with selfish ISPs through fair and efficient profitsharing. [38] proposes a clean-slate market structureand routing protocol for exchange of Internet paths.[9], [35], [39] are more related to our work. [39] stud-ies tiered pricing based on packet destinations androuting costs for selling Internet transit. It is shownthat a few tiers is enough to capture the optimal profitgain for a tier-1 ISP. From the customer’s perspective,[35] proposes to use Tuangou (group buying), and[9] innovates T4P (transit for peering) that providespartial transit to peering partners, to reduce transitcosts.

Spot transit is orthogonal to these novel settlementschemes, and compliments them in that tiered pricing,Tuangou, and T4P can be readily applied in spot tran-sit market just like they are used in the regular transitmarket. The benefits of spot transit, as mentioned,depend on the very characteristics of elastic trafficinstead of the specifics of settlement details. We usea simple model derived from [23], [31] where demandrandomness is modeled additively. The technical dis-tinction is clear: we use a general demand function andanalyze the profit and surplus improvement, while[23], [31] only study pricing based on a linear demandfunction.

8 CONCLUDING REMARKSIn this paper, we advocate to create a spot transitmarket, where under-utilized backbone capacity isoffered at discounted to serve elastic traffic, and transitcustomers can purchase transit on-demand. We sys-tematically studied the pricing and economical bene-fits of spot transit. Through both theoretical analysisand empirical evaluation with real-world price andtraffic data, we demonstrated that significant profitand surplus improvement can be generally expectedfrom the spot transit market. The gains are also robust

for a wide range of parameter settings. Given thepotential economical benefits, we believe spot transitwill encourage many entities to engage in this newmarket.

We conclude the paper by pointing out some in-teresting open problems with the introduction of spottransit. For example, how can the tier-1 ISP use smarttraffic engineering algorithms to provide better perfor-mance isolation between the regular and spot transittraffic? How do we quantify the effect of spot transiton novel settlement schemes such as paid peering?How would it change the Internet AS level topology,and the entire ecosystem? Lastly, it is also interestingto study other pricing strategies for the spot market,such as derivative following, regret-based pricing, etc.from microeconomics, and compare their effectiveness.

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Hong Xu received the B.E. degree from theDepartment of Information Engineering, TheChinese University of Hong Kong, in 2007,and the M.A.Sc. and Ph.D. degrees fromthe Department of Electrical and ComputerEngineering, University of Toronto. He joinedthe Department of Computer Science, CityUniversity of Hong Kong in August 2013,where he is currently an assistant professor.His research interests include data centernetworking, cloud computing, network eco-

nomics, and wireless networking. He is a member of ACM and IEEE.

Baochun Li received the B.E. degree fromthe Department of Computer Science andTechnology, Tsinghua University, China, in1995 and the M.S. and Ph.D. degrees fromthe Department of Computer Science, Univer-sity of Illinois at Urbana-Champaign, Urbana,in 1997 and 2000.

Since 2000, he has been with the Depart-ment of Electrical and Computer Engineer-ing at the University of Toronto, where heis currently a Professor. He holds the Nortel

Networks Junior Chair in Network Architecture and Services fromOctober 2003 to June 2005, and the Bell Canada Endowed Chair inComputer Engineering since August 2005. His research interests in-clude large-scale distributed systems, cloud computing, peer-to-peernetworks, applications of network coding, and wireless networks.

Dr. Li was the recipient of the IEEE Communications SocietyLeonard G. Abraham Award in the Field of Communications Systemsin 2000. In 2009, he was a recipient of the Multimedia Communica-tions Best Paper Award from the IEEE Communications Society, anda recipient of the University of Toronto McLean Award. He is a seniormember of IEEE and IEEE Computer Society and a member of ACM.