Abstract—Recent advance in scalable video coding (SVC) makes it possible for users to receive the same video with different qualities. To adopt SVC in P2P streaming, two key design questions need to be answered: 1) layer subscription: how many layers each peer should receive? 2) layer scheduling: how to deliver to peers the layers they subscribed? From the system point of view, the most efficient solution is to maximize the aggregate video quality on all peers, i.e., the social welfare. From individual peer point of view, the solution should be fair. Fairness in P2P streaming should additionally take into account peer contributions to make the solution incentive-compatible. In this paper, we first develop utility maximization models to understand the interplay between efficiency, fairness and incentive in layered P2P streaming. We show that taxation mechanisms can be devised to strike the right balance between social welfare and individual peer welfare. We then develop practical taxation-based P2P layered streaming designs, including layer subscription strategy, chunk scheduling policy, and mesh topology adaptation. Extensive trace-driven simulations show that the proposed designs can effectively drive layered P2P streaming systems to converge to the desired operating points in a distributed fashion. I.

This chapter studies the problem of decentralized resource allocation among competing users in communication networks. The growth in the scale of communication networks and the newly emerging interactions between administrative domains and end-users with different needs and quality of service requirements necessitate new approaches to the modeling and control of communication networks that recognize the difficulty of formulating and implementing centralized control protocols for resource allocation. The current research in this area has developed a range of such approaches. Central to most of these approaches is the modeling of end-users and sometimes also of service providers as self-interested agents that make decentralized and selfish decisions. This research has two important implications: (i) The modeling of communication networks consisting of multiple selfish agents requires tools from game theory. (ii) In the absence of centralized control, the interaction of multiple selfish agents may lead to suboptimal resource allocation. This chapter will survey and develop existing work focusing on the role of prices, both used as control parameters in the network and set by service providers in order to increase their revenues. We will identify the different roles that prices may play in communication networks depending on the degree of strategic interactions among users and between users and service providers, and explore their impact on network performance under different scenarios. We will also highlight how the study of large-scale communication networks raises new modelling challenges and develop the mathematical tools that are commonly used in this analysis. The chapter is organized into three sections: the first two sections correspond to two conceptually different strategic settings, one where pricing is used to achieve some socially beneficial objective, and the other where 1 2 Asuman Ozdaglar and R. Srikant prices are set by multiple service providers to maximize their revenues. The last section places the material in this chapter in the context of the broader literature, discusses some emerging applications of game theory to communication networks, and suggests a number of areas for future research.

Abstract—Economic forces behind the Internet evolution have diversified the types of ISP (Internet Service Provider) intercon-nections. In particular, settlement-free peering and paid peering proved themselves as effective means for reducing ISP costs. In this paper, we propose T4P (Transit for Peering), a new type of hybrid bilateral ISP relationships that continues the Internet trend towards more flexible interconnections at lower costs. With a T4P interconnection, one ISP compensates the other ISP for their peering by providing this other ISP with a partial-transit service. In comparison to paid peering, T4P is able to reduce the combined transit/peering costs of an ISP due to the subadditive nature of transit billing. As a cost-effective alternative to existing interconnection types, T4P expands and strengthens the connectivity of the Internet, e.g., between content and eyeball networks. After analyzing incentives of ISPs to adopt T4P, we use real traffic data from several IXPs (Internet eXchange Points) to quantify the T4P economic benefits. Our evaluation confirms the promising potential of T4P. I.

Abstract. We study an online problem that occurs when the capacities of machines are heterogeneous and all jobs are identical. Each job is asso-ciated with a subset, called feasible set, of the machines that can be used to process it. The problem involves assigning each job to a single machine in its feasible set, i.e., to find a feasible assignment. The objective is to maximize the throughput, which is the sum of the bandwidths of the jobs; and minimize the total load, which is the sum of the loads of the machines. In the online setting, the jobs arrive one-by-one and an algo-rithm must make decisions based on the current state without knowledge of future states. By contrast, in the offline setting, all the jobs with their feasible sets are known in advance to an algorithm. Let m denote the total number of machines, α denote the competitive ratio with respect to the throughput and β denote the competitive ratio with respect to the total load. In this paper, our contribution is that we propose an online al-gorithm that finds a feasible assignment with a throughput-competitive upper bound α = O( m), and a total-load-competitive upper bound β = O( m). We also show a lower bound αβ = Ω( m), of the problem in the offline setting, which implies a lower bound αβ = Ω( m), of the problem in the online setting.

We analyze several distributed, continuous time protocols for a fair allocation of bandwidths to flows in a network (or resources to agents). Our protocols converge to an allocation which is a logarithmic approximation, simultaneously, to all canonical social welfare functions (i.e. functions which are symmetric, concave, and non-decreasing). These protocols can be started in an arbitrary state. While a similar protocol was known before, it only applied to the simple bandwidth allocation problem, and its stability and convergence time was not understood. In contrast, our protocols also apply to the more general case of Leontief utilities, where each user may place a different requirement on each resource. Further, we prove that our protocols converge in polynomial time. The best convergence time we prove is), where n is the number of agents in the O(n log ncmaxamax cminamin network, cmax and cmin are the maximum and minimum capacity of the links, and amax, amin are the largest and smallest Leontief coefficients, respectively. This time is achieved by a simple MIMD (multiplicative increase, multiplicative decrease) protocol which had not been studied before in this setting. We also identify combinatorial properties of these protocols that may be useful in proving stronger convergence bounds. The final allocations by our protocols are supported by usage-sensitive dual prices which are fair in the sense that they shield light users of a resource from the impact of heavy users. Thus our protocols can also be thought of as efficient distributed schemes for computing fair prices. 1

Today, we are going to talk about Kelly, et al [1] work. The authors consider the following scenario. Let r be an index for users, and also represent the route for the r th user. Users have different preferences, utility of user r is Ur(xr) where xr is the amount of flow she has been assigned, and Ur represents her utility function which supposed to be a strictly concave, non-decreasing, differentiable function. Note that the strictly concaveness condition here is not very important because we know much about linear utility functions. Our goal is to reach to the optimum solution of the SY ST EM(U, A, c) problem bellow, where U is the vector of utility functions of users, A is the adjacency matrix, (i.e. A[j, r] = 1 ⇔ j ∈ r), and c is the capacity constraints on the edges.