Impact of QoS on Internet User Welfare

Transcription

1 Impact of QoS on Internet User Welfare Galina Schwartz, Nikhil Shetty, and Jean Walrand Department of Electrical Engineering and Computer Sciences (EECS), University of California Berkeley, Cory Hall, Berkeley, CA , USA. {schwartz, nikhils, Abstract. In this paper, we investigate the welfare eects of transition from a single-service class to two-service classes in the Internet. We consider an ISP who oers network access to a xed user base, consisting of users who dier in their quality requirements and willingness to pay for the access. We model user-isp interactions as a game in which the ISP makes capacity and pricing decisions to maximize his prots and the users only decide which service to buy, if any. Our model provides robust pricing for networks with single- and two-service classes. Our results indicate that transition to multiple service classes is socially desirable, but could be blocked due to the unfavorable distributional consequences that it inicts on the existing network users. To facilitate the transition, we propose a simple regulatory tool that alleviates the political economic constraints and thus makes the transition feasible. 1 Introduction In today's Internet, despite the technological possibility of providing dierentiated services 1, no such services are actually oered by the ISPs. We outline ve main reasons for the persistence of this situation. First, ISPs claim that the demand is uncertain and hence the risks involved render such a QoS provision unprotable 2. Therefore, ISPs lack incentives to explore oering QoS. Second, there is a lack of coordination between the ISPs in QoS provision. It is possible that each ISP would individually like to oer QoS. But, the provision of QoS depends on all ISPs on a path between two users, not just on a single ISP. Lack of coordination between the ISPs and conicts about dividing the QoS revenue between the involved ISPs preclude them from oering QoS [4]. Third, QoS provision appears to be an inferior investment relative to plain capacity expansion. For e.g. [5] asserts that over-engineering the current network by investing in capacity is more protable than investing in provision of multiple service classes while [6] concludes that the upfront costs might be too high and call for very simple QoS mechanisms. 1 For the sake of brevity, we use the term QoS to refer to such dierentiated services. 2 Indeed, this profound uncertainty posits considerable diculties for estimating demand [13].

2 Fourth, the current threat of network neutrality regulations hampers ISPs' incentives for QoS. Indeed, in the current regime, the ISPs are at their best behavior, i.e., they suer from self-imposed constraints [79]. These constraints preclude them from investing into developing QoS. Indeed, in the existing political climate, such investments are subject to regulatory uncertainty. For example, if an ISP evaluates the NPV (net present value) of its project to provide a specic QoS product, a positive probability of imposition of a neutral regime clearly reduces the project's NPV relative to the situation where the threat of regulation is not present. It is likely that these self-imposed constraints also create disincentives to invest in capacity expansion. Lastly, fth, the existing QoS pricing research [10,11] indicates the diculties of robust pricing of QoS. The idea of utilizing DiServ to provide multiple service classes by pricing them dierently was around for a while [12]. Still, recent research attempts [10] suggest that the only socially optimal capacity division allocates zero capacity share for non-premium services. This paper mostly focuses on the fth reason, but also suggests a connection to the third and fourth. We make the following contributions to the literature. First, we develop robust pricing for a single ISP providing two service classes. Second, we investigate the political economic considerations that may constrain the feasibility of transition from the current network (where QoS is not provided) to the network with QoS provision. Third, we propose a simple regulatory tool that permits to alleviate the political economic constraints and make the transition feasible. In this paper, we develop a model that permits robust pricing of dierentiated services, based on the network architecture similar to the Paris Metro proposal (PMP) [12]. Other closely related papers modeling PMP are [13,14]. Although the authors in [13] include capacity choice in the description of the game, they assume zero capacity costs, and mostly focus on a subgame in which capacities are xed. While [13] assumes zero costs of capacity, in [14], capacity is costly, with capacity costs increasing and convex. On one hand, [13] demonstrates that monopolistic ISP will indeed provide two service classes, and suggest that the lack of QoS provision on the Internet could be a consequence of competition among the ISPs. On the other hand, [14] nds that, in equilibrium, the two competitors have dierent prices and congestion levels, with the most expensive one being the least congested. Both, [13, 14] focus on ISP competition, with network access provided by duopolists. They do not study the eects of ISP choices on user welfare. We assume that capacity is costly, and provide full analysis of capacity choice and its division and its consequences for user welfare, but we do it for a monopolistic ISP. Our model is extendable to multiple ISPs, and our preliminary results [15] indicate that ISP competition does not necessarily preclude QoS provision. In this paper, we also connect the ongoing network neutrality debate with ISPs' incentives to invest into QoS provision. We argue that the threat of neutrality regulations hampers ISPs' incentives for QoS and hence denies society the higher welfare eects associated with multiple service classes. In our related work [16], we explore an inexpensive regulatory tool that simplies the division

3 of capacity and alleviates investment disincentives of ISPs by establishing property rights over a small fraction of their capacity. This tool facilitates the social planner to reduce the harmful eects of transition to multiple service classes and enables the deployment of QoS and development of novel applications. 2 Model We start with a simple model, in which a single ISP (a monopolist) oers connectivity to a user base of xed size, and we let N (which we assume to be large) be the total number of users. First, the ISP chooses his capacity C > 0 that he builds at a constant unit cost τ > 0. Investment in capacity is irreversible. Second, once the capacity is sunk, the ISP makes a pricing decision after which each user decides whether to adopt the service. The ISP's objective is to maximize his prot Π total which equals his revenue net of his expense on capacity: Π total = max {pz τc}, C,p where Z is the number of users who adopt the service, and p is the ISP access price for users. If the ISP oers multiple service classes and allocates a capacity C i > 0 for the provision of service i at a price p i > 0, his objective becomes: Π total = max C i,p i { } p i Z i τc, where C = i C i and Z i is the number of users who adopt service i. We assume that, on average, each user sends an identical unit amount of trac. We dene the quality of service q observed by users as q = 1 Z/C, if Z users are multiplexed in capacity C. This denition of quality reects the common perception about service quality. As Z decreases and capacity remains the same, the quality of service improves, i.e., as the capacity per user increases, the quality increases as well. Further, we assume that each user in the user base is characterized by his type θ, which is a random variable uniformly distributed in [0, 1]. To characterize the user demand, we make the following assumptions. For a user with type θ, the lowest acceptable service quality is q = θ; and his highest aordable price is p = θ. Thus, a user buys a service only if this service is acceptable and aordable, i.e., p < θ q. (See [17] for a related discussion of this model.) For a user of type θ, if the quality of service q θ, his surplus is the dierence between the price and his willingness to pay (which is θ itself). Thus, for the user with type θ, the surplus U θ is given by { U θ = (θ p)i(q θ), where 1 if y 0 I(y) = 0 if y < 0. (1) θ represents the quality of the application that a user is interested in. Thus, in our model, user adoption is determined by the availability of the most quality intensive application that his type θ utilizes. Indeed, if a user adopts the network i

4 service for only, he gains no extra surplus from the fact that the actual network quality permits him to use streaming video (which he does not utilize). Compare this to the user demand in [18]. In general, for a distribution g(θ) of user types θ [0, 1], the aggregate user surplus becomes U total = 1 0 U θg(θ)ndθ, and with our assumption of uniformly distributed user types, we have U total = 1 0 U θndθ. Let c denote capacity per user in the user base (c = C/N) and let z denote the fraction of users adopting the service of quality q (z = Z/N). Then, Z/C = z/c and from our denition of service quality: q = 1 z/c. Let also Π = Π total N and U = U total N, where Π is the prot and U is the surplus per user in the base. Thus, the ISP objective and user surplus become: Π = max {pz τc} and 1 U = U θ dθ. (2) c,p 0 Per user in the base, the social surplus S is the sum of user surplus and provider prot, i.e., S = U +Π. Below, we analyze the ISP's optimal choices for scenarios where the ISP provides (i) a single service, and (ii) two dierent services, possibly in the presence of a regulator who constrains the ISP. 3 Analysis 3.1 Single Service Class In this section, we assume that the ISP provides only a single service class. This means that his entire capacity is oered at a single price p. To start, we let ISP capacity be xed at C and solve the problem of optimal pricing. Once capacity is sunk, the ISP's objective is to maximize his revenue R (per user in the base): R(c) = max p pz. From (1), a user with type θ will adopt the access (service) if and only if p < θ q, where q = 1 z/c, with z being the fraction of users who adopt the service. Clearly, the service is aordable to all users with type θ > p. As more users adopt the service, z increases and q decreases until it becomes equal to the user type at some critical value of θ. Let users with types θ (θ, θ] adopt the service. Then, we obtain (see [19]) θ = p and θ = p + c 1 + c, and z = c (1 p). (3) 1 + c Using (3), we express the revenue as R(c, p) = pz = c p(1 p). (4) 1 + c To nd the optimal price (which corresponds to maximum ISP revenue), we dierentiate (4) w.r.t. p and obtain p = 1/2. Thus, for any c, the revenue is maximized at p c = 1/2, and R(c) = 4(1+c). Henceforth, we will use the superscript to designate the values that correspond to the ISP's optimal choice in the single service class case. Next, we use the expression for R(c) to simplify the ISP objective to Π = max c τc, which leads to (see [19]): c 4(1+c)

5 c = 1 2 τ 1 and p = 1/2; θ = 1 2 and θ = 1 2 +c 1+c. Notice that, c is positive for τ [0, 0.25] only. The optimal values Π, U and S are derived in the [19]. 3.2 Two Service Classes (Divided Capacity) Next, we assume that the ISP divides his capacity C = cn into two parts and provides two services. Let C l = c l N and C h = c h N be the capacities utilized for each service (l and h respectively), and p l and p h be the prices charged for the respective services; we assume p l < p h. Further, let z l and z h be the fraction of users who adopt the respective services l and h. From our denition of service quality (Section 2), q i = 1 z i /c i, where c i = C i /N, i = l, h and i c i = c. Let x denote the capacity fraction allocated to the provision of service h. Then, c h = xc and c l = (1 x)c, (5) and the ISP objective can be written as Π = Π total /N = max c,x,ph,p l ( i=l,h p iz i τc). From (5), one can easily switch between the use of (c l, c h ) and (c, x) as choice variables. In fact, the expressions in terms of c l and c h easily transform to the ones in terms of c and x. Although we will express the ISP's objective in terms of c and x, to simplify the presentation we express the equations in c l and c h. Theorem 1. For any xed c and x, in the ISP optimum, p l (c, x) = 1 2 c h c l 2[(1+c l )(1+c h )c l +c h ], p h = p l+c l θ l = p l, θl = θ h = p h, θ h = p h+c h 1+c l (6) 1+c h, (7) where users with θ (θ l, θ l ] and θ (θ h, θ h ] adopt service l and h respectively. For proof, see [19]. From Theorem 1, we have θ h > θ l, which implies that service h, that has a higher price (p l < p h ) has higher quality (q l < q h ) too. Henceforth, we will denote the ISP's optimal choices in two service classes by. Corollary 1. For any xed c and x in the ISP optimum, we have p l (c, x) < 1 2 and p h(c, x) > 1 2. (8) For proof, see [19]. From (1) and Corollary 1, we deduce that in the case of a transition from a single service class to two service classes, all existing users who adopt service l gain surplus while those who adopt service h lose surplus. From Theorem 1 (using (6) and (7)), we derive the maximum revenue R(c, x) R(c, x) = [(1 + c h )c l + c h ] 2 4 [(1 + c l )(1 + c h )c l + c h ] (1 + c h ). (9) Expression (9) is too cumbersome to carry out investigation analytically. Hence, we use MATLAB R to obtain the solution numerically, for results see [19].

6 3.3 Network Regulations In the absence of regulation, from Section 3.2, the ISP objective could be written as a function of c and x as follows: Π = max c,x Π(c, x) = max c,x {R(c, x) τc}. We will say that the network is regulated when x is chosen by an outside party (regulator). We assume that the regulator's choice variable is x, i.e., the regulator only aects the ISP by constraining him from dedicating more than a fraction x of the entire capacity to service h. Then, the regulated ISP's prot maximization can be expressed as Π = max c,p l,p h {p l z l + p h z h τc} where c l (1 x)c and c h xc. We consider three regulatory scenarios. Regulator 1 (a social planner) maximizes social surplus (sum of aggregate user surplus and ISP prot), regulator 2 maximizes user surplus and regulator 3 maximizes the surplus of the users served under a single service class (i.e., users with type θ (θ, θ ]). For the regulators 1-3, the respective objectives S 1, S 2 and S 3 are: S 1 = max x {U + Π} and S 2 = max U and S 3 = max U x x θ (θ, θ ], (10) where U is dened in (2). Let x 1, x 2, x 3 be the values of x chosen by the regulators 1-3 respectively. From (10), it is intuitive that: x 3 < x 2 < x 1 < x. The case of a single service class is identical to the imposition of x = 0. We do not consider explicit regulations in the case of single service class, but we believe that the lack of QoS provision by ISPs in the current Internet reects the tacit presence of such a regulatory threat. The ongoing network neutrality debate reects that the threat is indeed real. We argue that this regulatory threat makes the ISPs to act as if the constraint x 0 is imposed [7]. This threat could be one of the reasons why QoS is not provided currently. 4 Results Fig. 1(a) depicts the surplus gain of the single class users (users with type θ (θ, θ ]). From Fig. 1(a), in the absence of regulation or with regulator 1, the transition to two service classes results in aggregate surplus loss for these users. Although, with regulator 2, these users do gain surplus, this might be insucient to make the transition politically feasible, especially if the percentage of losing single service class users is high. We suggest that users who lose surplus from transition are likely to resist the change. Hence, when this fraction of users is high, these users may block such a transition. To assure feasibility, the regulator may need to reduce the fraction of such losing users. We use regulator 3 to show that it is possible to keep the fraction of users with surplus loss under 10%. Fig. 1(b) depicts the percentage of existing single service users whose surplus decreases after the transition to two service classes. This fraction should be taken into account and kept suciently low by the regulator to assure that these users do not block the transition. This is exactly the reason why we consider

7 regulator 3. Indeed, with the unregulated ISP and regulator 1, more than 50% of single service class users lose from the transition to two service classes. But, for regulator 3, the percentage of losing users is at most 10%. For regulator 2, the percentage of users with surplus loss from transition to two service classes is 40% at τ = 0.1. But, as τ decreases, this fraction decreases and reaches 10% at τ = To sum up, regulator 3 makes the transition to two service classes politically viable and this transition is socially desirable (despite the fact that only a limited fraction of capacity is allocated to service h) Unregulated ISP Regulator Regulator 2 Regulator Unregulated ISP Regulator 1 Regulator 2 Regulator Fraction reserved for basic service (1 x) (a) Percent Surplus Change for Existing Single Class users (τ = 0.02) Cost of Capacity (τ) (b) Percentage of Single Class users with loss of surplus Fig. 1. Comparison of Regulatory Regimes 5 Discussion and Conclusion We make the following contributions to the literature. First, we develop robust pricing for the network with two service classes. Second, we investigate the political economic considerations that may constrain the feasibility of transition from the current network (where QoS is not provided) to the network with QoS provision. Third, we propose a simple regulatory tool that permits to alleviate the political economic constraints and make the transition feasible. Specically, from our analysis, the transition to two service classes is socially desirable, but it could be blocked due to unfavorable distributional consequences that the transition inicts on some fraction of current network users. We introduce a regulator (regulator 3), whose objective is to maximize the surplus of the existing users. We show that with this regulator, at any unit cost of capacity

8 at most 10% of these users will experience surplus loss by the transition to two service classes. Regulator 3 reaches this outcome via the imposition of a ceiling on the fraction of installed capacity that the ISPs are allowed to allocate to the provision of QoS services. References [1] Gupta, A., Jukic, B., Li, M., Stahl, D.O., Whinston, A.B.: Estimating Internet Users' Demand Characteristics. Computational Economics 17(2-3) (2001) [2] Varian, H.R.: The Demand for Bandwidth: Evidence from the INDEX Project. (2001) [3] Altmann, J., Rupp, B., Varaiya, P.: Eects of Pricing on Internet User Behavior. Netnomics 3(1) (2001) 6784 [4] He, L., Walrand, J.: Pricing and Revenue Sharing Strategies for Internet Service Providers. Proc. IEEE INFOCOM (March 2005) [5] Odlyzko, A.: The Economics of the Internet: Utility, Utilization, Pricing, and Quality of Service. Technical report (1999) [6] Crowcroft, J., Hand, S., Mortier, R., Roscoe, T., Wareld, A.: QoS's Downfall: At the Bottom, or Not at All! In: RIPQoS '03: Proc. ACM SIGCOMM workshop on Revisiting IP QoS, New York, NY, USA, ACM (2003) [7] Felten, E.: Nuts and Bolts of Network Neutrality. Working Paper, itpolicy.princeton.edu/pub/neutrality.pdf (2006) [8] Yoo, C.S.: Network Neutrality and the Economics of Congestion. Georgetown Law Journal 94 (June 2006) [9] Sidak, J.G.: A Consumer-Welfare Approach to Network Neutrality Regulation of the Internet. SSRN elibrary [10] Stahl, D.O., Dai, R., Whinston, A.B.: An Economic Analysis of Multiple Internet QoS Channels. (2003) [11] He, L., Walrand, J.: Pricing Dierentiated Internet Services. Proc. IEEE INFO- COM (March 2005) [12] Odlyzko, A.: Paris Metro Pricing for the Internet. In: EC '99: Proc. of the 1st ACM conference on Electronic commerce, ACM (1999) [13] Gibbens, R., Mason, R., Steinberg, R.: Internet Service Classes under Competition. 18(12) (December 2000) [14] de Montmarin, M.D.M.: A Result Similar to the Odlyzko's 'Paris Metro Pricing'. Applied Economics 38 (2006) [15] Schwartz, G., Shetty, N., Walrand, J.: Impact of QoS on Internet User Welfare: Eect of ISP Competition. In preparation, SSW-MultiQOS.pdf (2008) [16] Schwartz, G., Shetty, N., Walrand, J.: Network Neutrality: Avoiding the Extremes. In: Forty-sixth Annual Allerton Conference. (2008) [17] Walrand, J.: 3. In: Economic Models of Communication Networks. Springer (2008) 5787 [18] Hermalin, B.E., Katz, M.L.: The Economics of Product-Line Restrictions With an Application to the Network Neutrality Debate. (July 2006) [19] Schwartz, G., Shetty, N., Walrand, J.: Modeling the Impact of QoS on Internet User Welfare and ISP Incentives. Working Paper, ~nikhils/ssw-qos.pdf (2008)