Internet and graphs are very much related. The graphical structure of internet has been studied extensively to provide efficient solutions to routing and other problems. But most of these studies assume a central authority which controls and manages the internet. In the recent years game theoretic models have been proposed which do not require a central authority and the users are assumed to be routing their flows selfishly. The existence of Nash Equilibria, congestion and the amount of inefficiency caused by this selfish routing is a major concern in this field. A type of paradox in the selfish routing networks, Braess' Paradox, first discovered by Braess, is a major contributor to inefficiency. Several pricing mechanisms have also been provided which give a game theoretical model between users(consumers) and ISPs ( Internet Service Providers or sellers) for the internet. We propose a novel pricing mechanism, based on real world Internet network architecture, which reduces the severity of Braess' Paradox in selfish routing game theoretic networks. It's a pricing mechanism between combinatorial users and ISPs. We prove that Nash equilibria exists in this network and provide bounds on inefficiency . We use graphical properties of internet to prove our result. Several interesting extensions and future work have also been discussed.
Hayrapetyan et. al @cite_10 analyze among similar lines as us but for their cost function they assume a constant term for the per unit flow price charged by ISPs but in the real world scenario generally the per unit charge decreases if the flow required by the user increases i.e. ISPs provide concession for more flow. Our model captures this. They have not done any analysis of the effect of Braess' Paradox in their network, too. We show that in our model the severity of Braess' Paradox is reduced.
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We consider a network where each user is charged a fixed price per unit of bandwidth used, but where there is no congestion-dependent pricing. However, the transmission rate of each user is assumed to be a function of network congestion (like TCP), and the price per unit bandwidth. We are interested in answering the following question: how should the network choose the price to maximize its overall revenue? To obtain a tractable solution, we consider a single link accessed by many users where the capacity is increased in proportion to the number of users. We show the following result: as the number of users increases, the optimal price per unit bandwidth charged by the service provider may increase or decrease depending upon the bandwidth of the link. However, for all values of the link capacity, the service provider's revenue per unit bandwidth increases and the overall performance of each user (measured in terms of a function of its throughput, the network congestion and the cost incurred by the user for bandwidth usage) improves. Since the revenue per unit bandwidth increases, it provides an incentive for the service provider to increase the available bandwidth in proportion to the number of users. Usage-based pricing of offered traffic to a data network can be an effective technique for congestion control. To gain insight into the benefits usage-based pricing offers, the authors propose and study a simple model in which many users wish to transmit packets to a single-server queue. Based on the announced price per packet and the available quality of service (QoS) (e.g., mean delay), each user independently decides whether or not to transmit. Given statistical assumptions about the incoming traffic streams and the QoS as a function of offered load, the equilibrium relationship between price and QoS is determined by a fixed-point equation. The relationships among price, QoS, revenue, and server capacity are illustrated numerically, assuming a particular type of random user population. These examples indicate that adjusting the price to maximize revenue results in an efficient use of service capacity with an associated small mean delay. In this paper, we present a combined study of price competition and traffic control in a congested network. We study a model in which service providers own the routes in a network and set prices to maximize their profits, while users choose the amount of flow to send and the routing of the flow according to Wardrop's principle. When utility functions of users are concave and have concave first derivatives, we characterize a tight bound of 2-3 on efficiency in pure strategy equilibria of the price competition game. We obtain the same bound under the assumption that there is no fixed latency cost, i.e., the latency of a link at zero flow is equal to zero. These bounds are tight even when the numbers of routes and service providers are arbitrarily large. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008 Network congestion is a fundamental problem facing Internet users today. A network where users are selfish, and thus reluctant to defer to other users, may result in the famous "tragedy of the commons", where, in the absence of controls, a shared resource is overconsumed by individuals who consider only their personal costs and not the cost to society as a whole. In terms of the Internet, the "tragedy" could be viewed as congestive collapse, resulting from overconsumption of the shared network resource. It is important to distinguish congestion pricing from other forms of network pricing. Charging network users for the congestion they cause can lead to more efficient network utilization by forcing them to take social costs into account. In a congestion-pricing framework, the congestion charge would replace usage and QoS charges. Users would pay their ISPs a subscription charge to cover fixed costs and a congestion charge only when appropriate. This pricing scheme is feasible because, in the absence of congestion, the marginal cost of a network link is practically zero. Congestion pricing can also benefit network operators. By indicating the level of congestion and the user tolerance of it in their networks, congestion pricing can inform operators about when to re-provision and increase network capacity. Data traffic demand over the Internet is increasing rapidly, and it is changing the pricing model between Internet service providers (ISPs), content providers (CPs) and end users. One recent pricing proposal is sponsored data plan, i.e., when accessing contents from a particular CP, end users do not need to pay for that volume of traffic consumed, but the CP will sponsor for this data consumption. In this paper, our goal is to understand the rationale behind this new pricing model, as well as its impacts to the wireless data market, in particular, who will benefit and who will be hurt from this scheme. We build a two-class service model to analyze the consumers' traffic demand under the sponsored data plan with consideration of QoS. We use a two-stage Stackelberg game to characterize the interaction between CPs and the ISP and reveal a number of important findings. Our conclusions include: 1) When the ISP's capacity is sufficient, the sponsored data plan benefits consumers and CPs in the short run, but the ISP does not have incentives to further improve its service in the long run. 2) When ISP's capacity is insufficient, the ISP and end users may achieve a win- win trade, while the ISP and CPs always compete for the revenue. 3) The sponsored data plan may enlarge the un- balance in revenue distribution between different CPs; CPs with higher unit income and poorer technology support are more likely to prefer the sponsored data plan. The paper addresses the issue of providing Quality of Service (QoS) guarantees in the Internet. After a brief discussion of Internet traffic characteristics, we consider the possibility of performing multiplexing with predictable performance for stream and elastic traffic using open–loop and closed–loop control, respectively. QoS depends essentially on providing sufficient capacity to handle expected demand. We argue that flow awareness is additionally necessary to ensure that traffic is directed over routes with available capacity and to avoid congestion collapse in case of overload. Proposed flow–aware controls allow simple volume–based charging and the development of an economic model similar to that of the telephone network. This paper investigates pricing of Internet connectivity services in the context of a monopoly ISP selling broadband access to consumers. We first study the optimal combination of flat-rate and usage-based access price components for maximization of ISP revenue, subject to a capacity constraint on the data-rate demand. Next, we consider time-varying consumer utilities for broadband data rates that can result in uneven demand for data-rate over time. Practical considerations limit the viability of altering prices over time to smoothen out the demanded data-rate. Despite such constraints on pricing, our analysis reveals that the ISP can retain the revenue by setting a low usage fee and dropping packets of consumer demanded data that exceed capacity. Regulatory attention on ISP congestion management discourages such technical" practices and promotes economics based approaches. We characterize the loss in ISP revenue from an economics based approach. Regulatory requirements further impose limitations on price discrimination across consumers, and we derive the revenue loss to the ISP from such restrictions. We then develop partial recovery of revenue loss through non-linear pricing that does not explicitly discriminate across consumers. While determination of the access price is ultimately based on additional considerations beyond the scope of this paper, the analysis here can serve as a benchmark to structure access price in broadband access networks. As Internet traffic grows exponentially due to the pervasive Internet accesses via mobile devices and increasing adoptions of cloud-based applications, broadband providers start to shift from flat-rate to usage-based pricing, which has gained support from regulators such as the FCC. We consider generic congestion-prone network services and study usage-based pricing of service providers under market competition. Based on a novel model that captures users' preferences over price and congestion alternatives, we derive the induced congestion and market share of the service providers under a market equilibrium and design algorithms to calculate them. By analyzing different market structures, we reveal how users' value on usage and sensitivity to congestion influence the optimal price, revenue, and competition of service providers, as well as the social welfare. We also obtain the conditions under which monopolistic providers have strong incentives to implement service differentiation via Paris Metro Pricing and whether regulators should encourage such practices. As Internet traffic grows exponentially due to the pervasive Internet accesses via mobile devices and increasing adoptions of cloud-based applications, broadband providers start to shift from flat-rate to usage-based pricing, which has gained support from regulators such as the FCC. We consider generic congestion-prone network services, including cloud services, and study the pay-as-you-go type of usage-based pricing of service providers under market competition. Based on a novel model that captures users' preferences over usage price and congestion alternatives, we derive the induced congestion and market share of the service providers under a market equilibrium and design algorithms to calculate them. By analyzing different market structures, we reveal how users' value on usage and sensitivity to congestion influence the optimal price, revenue, and competition of service providers, as well as the social welfare. We also obtain the conditions under which monopolistic providers have strong incentives to implement service differentiation via Paris Metro Pricing and whether regulators should encourage such practices. This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max-min fairness of rates emerges as a limiting special case; more generally, the charges users are prepared to pay influence their allocated rates. In the preferred version of the model, a user chooses the charge per unit time that the user will pay; thereafter the user's rate is determined by the network according to a proportional fairness criterion applied to the rate per unit charge. A system optimum is achieved when users' choices of charges and the network's choice of allocated rates are in equilibrium. We study the efficiency implications of competition among profit-maximizing service providers in communication networks. Service providers set prices for transmission of flows through their (sub)network. The central question is whether the presence of prices will help or hinder network performance. We investigate this question by considering the difference between users' willingness to pay and delay costs as the efficiency metric. Previous work has demonstrated that in networks consisting of parallel links, efficiency losses from competition are bounded. Nevertheless, parallel-link networks are special, and in most networks, traffic has to simultaneously traverse links (or subnetworks) operated by independent service providers. The simplest network topology allowing this feature is the parallel-serial structure, which we study in this paper. In contrast to existing results, we show that in the presence of serial links, the efficiency loss relative to the social optimum can be arbitrarily large. The reason for this degradation of performance is the double marginalization problem, whereby each serial provider charges high prices not taking into account the effect of this strategy on the profits of other providers along the same path. Nevertheless, when there are no delay costs without transmission (i.e., latencies at zero are equal to zero), irrespective of the number of serial and parallel providers, the efficiency of strong oligopoly equilibria can be bounded by 1 2, where strong oligopoly equilibria are equilibria in which each provider plays a strict best response and all of the traffic is transmitted. However, even with strong oligopoly equilibria, inefficiency can be arbitrarily large when the assumption of no delay costs without transmission is relaxed. We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of the social cost of a flow at equilibrium over the cost when centralized coordination among users is allowed. We study bottleneck congestion games where the social cost is determined by the worst congestion on any resource. In the literature, bottleneck games assume player utility costs determined by the worst congested resource in their strategy. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the number of resources. In order to obtain smaller price of anarchy we introduce exponential bottleneck games, where the utility costs of the players are exponential functions of their congestions. In particular, the delay function for any resource r is MCr, where Cr denotes the number of players that use r, and M is an integer constant. We find that exponential bottleneck games are very efficient and give the following bound on the price of anarchy: O(log |R|), where R is the set of resources. This price of anarchy is tight, since we demonstrate a game with price of anarchy Ω(log |R|). We obtain our tight bounds by using two novel proof techniques: transformation, which we use to convert arbitrary games to simpler games, and expansion, which we use to bound the price of anarchy in a simpler game. The available bandwidth (avail-bw) in a network path is of major importance in congestion control, streaming applications, quality-of-service verification, server selection, and overlay networks. We describe an end-to-end methodology, called self-loading periodic streams (SLoPS), for measuring avail-bw. The basic idea in SLoPS is that the one-way delays of a periodic packet stream show an increasing trend when the stream's rate is higher than the avail-bw. We have implemented SLoPS in a tool called pathload. The accuracy of the tool has been evaluated with both simulations and experiments over real-world Internet paths. Pathload is nonintrusive, meaning that it does not cause significant increases in the network utilization, delays, or losses. We used pathload to evaluate the variability ("dynamics") of the avail-bw in Internet paths. The avail-bw becomes significantly more variable in heavily utilized paths, as well as in paths with limited capacity (probably due to a lower degree of statistical multiplexing). We finally examine the relation between avail-bw and TCP throughput. A persistent TCP connection can be used to measure roughly the avail-bw in a path, but TCP saturates the path and increases significantly the path delays and jitter. THE CAPABILITIES AND EFFICIENT OPERATION OF SEVERAL TYPES OF TRANSPORTATION SYSTEMS ARE STUDIED. FOR HIGHWAY TRAFFIC THE MAIN EMPHASIS IS ON CONGESTION AND ITS CONSEQUENCES. QUEUING MODELS ARE USED TO DETERMINE FLUCTUATIONS IN WAITING TIME FOR TWO CASES, THE FLOW OF CARS THROUGH AN INTERSECTION AND THE PASSING OF SLOWER CARS BY FASTER CARS ON A TWO-LANE HIGHWAY. THE RESULTS OF THESE STUDIES ARE INCORPORATED INTO A NON-LINEAR MODEL OF HIGHWAY TRAFFIC BEHAVIOR ON A ROAD NETWORK. THE CAPACITIES ARE EXPRESSED BY THE RELATIONSHIP BETWEEN TRAFFIC FLOWS ON ALL ROUTES AND THE COSTS ENCOUNTERED ON EACH AS A RESULT OF THESE FLOWS. HIGHWAY TRAFFIC DEMANDS ARE THE RESULT OF A GREAT MANY INDIVIDUAL DECISIONS ABOUT DESTINATION, ROUTES, AND PREFERRED SPEEDS. THE ANALOGY BETWEEN HIGHWAY TRAFFIC EQUILIBRIUM AND THE MARKET RESPONSE MODELS USED BY ECONOMISTS IS GIVEN. IF THE INDIVIDUALLY INCURRED COST OF TRANSPORTATION IS REGARDED AS THE "PRICE" IN THE TRANSPORTATION "MARKET," THE ECONOMIST'S DEMAND CURVE BECOMES APPLICABLE. FOR A SINGLE ROAD IT GIVES THE FLOW OF TRAFFIC DEMANDED FOR ANY GIVEN COST ENCOUNTERED ON THAT ROAD. GENERALLY, THE HIGHER THE COST, THE SMALLER THE FLOW. CONSIDERING A ROAD NETWORK THE DEMAND FUNCTION GIVES THE FLOWS ON EACH ROUTE IN RESPONSE TO A SET OF TRANSPORTATION COSTS ALONG THESE ROUTES. EQUILIBRIUM EXISTS IF THE FLOWS ON ALL ROADS RESULTING FROM THESE COSTS ARE THE SAME AS THE FLOWS THAT PRODUCE THESE SAME COSTS. THIS CONCEPT IS APPLIED TO A STUDY OF TRAFFIC EQUILIBRIUM AND USE OF THE ANALYSIS IN THE PREDICTION OF TRAFFIC FLOWS IS DISCUSSED. THE ANALYSIS OF DEMAND AND OF EQUILIBRIUM RECOGNIZES THAT FREEDOM OF CHOICE IS PART OF THE SERVICE RENDERED BY THE ROAD NETWORK. TOLLS FROM THE USERS OF CONGESTED ROADS AT RATES THAT WOULD MEASURE THE COST TO OTHERS CAUSED BY THE AVERAGE ROAD USER WOULD ENCOURAGE BETTER USE OF THE HIGHWAY SYSTEM. THERE ARE OBSERVATIONS ON HOW CLOSELY MAXIMUM EFFICIENCY CAN BE APPROACHED BY PROPER CHOICE OF RATES ON PRESENT TOLL ROADS AND BY OTHER WAYS OF PENALIZING ADDITIONS TO TRAFFIC CONGESTION. BECAUSE OF THE NONLINEAR RELATIONSHIP BETWEEN USE AND COST, SUCH PRICING DOES NOT NECESSARILY PRODUCE REVENUES EQUAL TO THE TOTAL COST OF OPERATING AND FINANCING THE INDIVIDUAL FACILITY. SOME OBSERVATIONS ON THE QUESTION OF CRITERIA FOR EXTENSIONS OR IMPROVEMENTS OF THE NETWORK TO RELIEVE CONGESTION ARE GIVEN. AUTHOR We use the tools from game theory to understand the impacts of the inherent congestion pricing schemes in TCP Vegas as well as the problems of parameter setting of TCP Vegas on its performance. It is shown how these inherent pricing schemes result in a rate control equilibrium state that is a Nash equilibrium which is also a global optimum of the all-Vegas networks. On the other hand, if the TCP Vegas’ users are assumed to be selfish in terms of setting their desired number of backlogged packets in the buffers along their paths, then the network as a whole, in certain circumstances, would operate very inefficiently. This poses a serious threat to the possible deployment of Vegas-based TCP (such as FAST TCP) in the future Internet. We address whether local ISPs should be allowed to charge content providers, who derive advertising revenue, for the right to access end-users. We compare two-sided pricing where such charges are allowed to one-sided pricing where they are prohibited. By deriving provider equilibrium actions (prices and investments), we determine which regime is welfare-superior as a function of a few key parameters. We find that two-sided pricing is more favorable when the ratio between parameters characterizing advertising rates and end-user price sensitivity is either low or high. This paper studies economic utilities and quality of service (QoS) in a two-sided non-neutral market where Internet service providers (ISPs) charge content providers (CPs) for the content delivery. We propose new models that involve a CP, an ISP, end users and advertisers. The CP may have either a subscription revenue model (charging end users) or an advertisement revenue model (charging advertisers). We formulate the interactions between the ISP and the CP as a noncooperative game for the former and an optimization problem for the latter. Our analysis shows that the revenue model of the CP plays a significant role in a non-neutral Internet. With the subscription model, both the ISP and the CP receive better (or worse) utilities as well as QoS in the presence of the side payment at the same time. With the advertisement model, the side payment impedes the CP from investing on its contents. We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. Unlike telephone operators, which pay termination fees to reach the users of another network, Internet Content Providers (CPs) do not pay the Internet Service Providers (ISPs) of users they reach. While the consequent cross subsidization to CPs has nurtured content innovations at the edge of the Internet, it reduces the investment incentives for the access ISPs to expand capacity. As potential charges for terminating CPs' traffic are criticized under the net neutrality debate, we propose to allow CPs to voluntarily subsidize the usagebased fees induced by their content traffic for end-users. We model the regulated subsidization competition among CPs under a neutral network and show how deregulation of subsidization could increase an access ISP's utilization and revenue, strengthening its investment incentives. Although the competition might harm certain CPs, we find that the main cause comes from high access prices rather than the existence of subsidization. Our results suggest that subsidization competition will increase the competitiveness and welfare of the Internet content market; however, regulators might need to regulate access prices if the access ISP market is not competitive enough. We envision that subsidization competition could become a viable model for the future Internet.