TO BE SUBMITTED TO IEEE/ACM TRANSACTIONS ON NETWORKING 1 Redefining Fairness in the Study of TCP-friendly Traffic Controls Dah Ming Chiu, Senior Member, IEEE Adrian Sai-Wah Tam Abstract— In best-effort networks, fairness has been used as a criterion to guide the design of traffic controls. The notion of fairness has evolved over time, from simple equality to a form of equality modulated by the user’s need (e.g. max-min and proportional fairness). However, fairness has always been defined on a per-user basis for a deterministic workload. In this paper, we argue that we must redefine the notion of fairness when we study traffic controls for the co-existence of elastic and inelastic traffics. We show that requiring inelastic flows to be friendly to TCP flows on a per-flow basis, as suggested by the TCP- friendly doctrine, does not necessarily maximize the network’s utility. Instead, inelastic flows may follow their own form of traffic control, such as admission control (without congestion control). At the aggregate level, however, we show that it still makes sense to maintain balance between elastic and inelastic traffic. In order to support our arguments, we develop a methodology for comparing different traffic controls for given different utility functions and stochastic workloads. Index Terms— congestion control, admission control, fairness, utility maximization, non-convex utility function, stochastic traffic model I. I NTRODUCTION Internet is a connectionless network. It relies on congestion control implemented in the end-systems to prevent offered load exceeding network capacity, as well as evenly allocate network resources to different users and applications. In the past, the applications (such as email, file transfer) were predominantly elastic in their bandwidth requirements. The Internet architecture served these applications well. As the Internet shifts to support increasing volume of multimedia applications, there has been continuous debate on the next generation Internet architecture. Various proposals have been made for building a multi-services network to support different types of applications, for example ATM [1], Integrated Service [2], Differentiated Service [3] and MPLS- based traffic engineering [4]. Despite such efforts, a prevalent belief is that the Internet’s connectionless service model does not need to change, as long as there is adequate provisioning of network bandwidth (see [5] for a systematic discussion of this viewpoint). What is needed instead is a relaxed end-system congestion control that co-exists with the widely used TCP congestion control. So what is a suitable alternative congestion control for multimedia applications to practice? The orthodox solution Dah Ming Chiu and Adrian Sai-Wah Tam are with the Department of Information Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong (email: {dmchiu,swtam3}@ie.cuhk.edu.hk). This work was partially supported by University Grants Committee, Hong Kong SAR under RGC grant 4232/04E (project 2150420) and AoE grant AoE/E-01/99 (project 4801312). requires all applications to share network bandwidth fairly, as existing TCP flows do. If an application needs more bandwidth than the prevailing fair share, then it should adapt its bandwidth (down) in favor of fairness. It is recognized that multimedia flows need more gradual adaptation to fair bandwidth share, so the effort of designing the alternative control is focused on a smooth transient response in bandwidth adaption. Proposals of such congestion control schemes are generally referred to as TCP-friendly congestion controls in the literature [6]–[8]. The thesis of this paper is to argue for abandoning the traditional notion of fairness in designing end-system traffic controls for different types of applications. Unlike the case with elastic traffic, the best way to deal with congestion for inelastic traffic should be some form of admission control, which is by definition unfair in the traditional sense. Furthermore, it is important to consider the stochastic nature of bandwidth allocation, rather than the allocation of bandwidth to a fixed number of flows. The fact that flows arrive at different times and have different demands for the network should also be taken into account in fair bandwidth allocation. While we argue against insisting on per-flow TCP- friendliness, our results show that in a self-regulated network, it is still sensible to apply TCP-friendliness principles at the aggregate level. In other words, it yields higher utility for both kinds of traffic to maintain a balanced allocation according to the respective demand. The methodology used to substantiate and support these arguments is to define the bandwidth allocation problem as a network utility optimization problem. There is significant prior literature on this approach which we will review. Our contribution is to extend the standard network utility maximization by considering non-concave utility functions to model inelastic flows, as well as considering both the elastic and inelastic traffic as stochastic processes. Both of these extensions have been considered recently in separate contexts [9]–[11], but we apply these extensions together to develop a methodology to evaluate different traffic controls for the co- existence of TCP and non-TCP flows. The rest of the paper are organized as follows. In section II, we briefly review the classic results on bandwidth allocation and fairness of network traffic controls. In section III, we develop our methodology for studying network fairness and discuss the validity of the TCP-friendliness approach. In section IV, we apply our approach to a homogeneous class of flows, the utility function is parametrized to model both elastic as well as inelastic flows. In section V, we apply our methodology to heterogeneous flows (both elastic and inelastic