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. 1

We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In this system sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial and time-varying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment.

We describe ways in which the transmission control protocol of the Internet may evolve to support heterogeneous applications. We show that by appropriately marking packets at overloaded resources and by charging a fixed small amount for each mark received, end-nodes are provided with the necessary information and the correct incentive to use the network efficiently.

We consider the performance of a network like the Internet handling so-called elastic traffic where the rate of flows adjusts to fill available bandwidth. Realized throughput depends both on the way bandwidth is shared and on the random nature of traffic. We assume traffic consists of point to point transfers of individual documents of finite size arriving according to a Poisson process. Notable results are that weighted sharing has limited impact on perceived quality of service and that discrimination in favour of short documents leads to considerably better performance than fair sharing. In a linear network, max-min fairness is preferable to proportional fairness under random traffic while the converse is true under the assumption of a static configuration of persistent flows. Admission control is advocated as a necessary means to maintain goodput in case of traffic overload. 1 Introduction Traffic in a multiservice network is essentially composed of individual transactions or flows...

Modern communication networks are able to respond to randomly uctuating demands and failures by adapting rates, by rerouting traffic and by reallocating resources. They are able to do this so well that, in many respects, large-scale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. This paper outlines how mathematical models are being used to address current issues concerning the stability and fairness of rate control algorithms for the Internet.

We consider a resource allocation problem where individual users wish to send data across a network to maximize their utility, and a cost is incurred at each link that depends on the total rate sent through the link. It is known that as long as users do not anticipate the effect of their actions on prices, a simple proportional pricing mechanism can maximize the sum of users' utilities minus the cost (called aggregate surplus). Continuing previous efforts to quantify the effects of selfish behavior in network pricing mechanisms, we consider the possibility that users anticipate the effect of their actions on link prices. Under the assumption that the links' marginal cost functions are convex, we establish existence of a Nash equilibrium. We show that the aggregate surplus at a Nash equilibrium is no worse than a factor of 4 # 2 - 5 times the optimal aggregate surplus; thus, the efficiency loss when users are selfish is no more than approximately 34%.

In this document we study the application of weighted proportional fairness to data flows in the Internet. We let the users set the weights of their connections in order to maximise the utility they get from the network. When combined with a pricing scheme where connections are billed by weight and time, such a system is known to maximise the total utility of the network. Our study case is a national Web cache server connected to long distance links. We propose two ways of weighting TCP connections by manipulating some parameters of the protocol and present results from simulations and prototypes. We finally discuss how proportional fairness could be used to implement an Internet with differentiated services. 1 Introduction 1.1 Fairness Fairness is among the most important properties of data flows in the Internet. Fairness implies that whenever there is congestion at a bottleneck, each flow going through that bottleneck gets a fair share of the available bandwidth. TCP flo...

Measurement-based admission control (MBAC) is an attractive mechanism to concurrently offer quality of service (QoS) to users, without requiring a priori traffic specification and on-line policing. However, several aspects of such a system need to be clearly understood in order to devise robust MBAC schemes, i.e., schemes that can match a given QoS target despite the inherent measurement uncertainty, and without the tuning of external system parameters. We study the impact of measurement uncertainty, flow arrival, departure dynamics, and of estimation memory on the performance of a generic MBAC system in a common analytical framework. We show that a certainty equivalence assumption, i.e., assuming that the measured parameters are the real ones, can grossly compromise the target performance of the system. We quantify the improvement in performance as a function of the length of the estimation window and an adjustment of the target QoS. We demonstrate the existence of a critical time scale over which the impact of admissin decisions persists. Our results yield new insights into the performance of MBAC schemes, and represent quantitative and qualitative guidelines for the design of robust schemes.

Providing quality of service in random access multi-hop wireless networks requires support from both medium access and packet scheduling algorithms. However, due to the distributed nature of ad hoc networks, nodes may not be able to determine the next packet that would be transmitted in a (hypothetical) centralized and ideal dynamic priority scheduler. In this paper, we develop two mechanisms for QoS communication in multi-hop wireless networks. First, we devise distributed priority scheduling, a technique that piggybacks the priority tag of a node’s head-of-line packet onto handshake and data packets; e.g., RTS/DATA packets in IEEE 802.11. By monitoring transmitted packets, each node maintains a scheduling table which is used to assess the node’s priority level relative to other nodes. We then incorporate this scheduling table into existing IEEE 802.11 priority back-off schemes to approximate the idealized schedule. Second, we observe that congestion, link errors, and the random nature of medium access prohibit an exact realization of the ideal schedule. Consequently, we devise a scheduling scheme termed multi-hop coordination so that downstream nodes can increase a packet’s relative priority to make up for excessive delays incurred upstream. We next develop a simple analytical model to quantitatively explore these two mechanisms. In the former case, we study the impact of the probability of overhearing another packet’s priority index on the scheme’s ability to achieve the ideal schedule. In the latter case, we explore the role of multi-hop coordination in increasing the probability that a packet satisfies its end-to-end QoS target. Finally, we perform a set of ns-2 simulations to study the scheme’s performance under more realistic conditions. 1.

In this paper, we consider the use of an application-layer performance measure --- the utility --- in the context of bandwidth allocation for an available bit rate service. Our bandwidth allocation scheme can be viewed as a generalization of traditional available bit rate service; our scheme is equivalent to bandwidth max-min allocation when the utility of all applications are equal. The goal of our allocation scheme is to provide good application-layer service to a wide diversity of applications sharing available bandwidth. We achieve this goal while also supporting changes in utility over time, tolerating some inaccuracy in utility function specification, and addressing the issue of circumvention through pricing. Keywords---Utility functions, available bit rate. I. INTRODUCTION A N important class of distributed applications are those that can adapt their resource usage based on feedback from the network. These applications are robust against variability in network performance an...