We examine a proportional-delay model for Internet differentiated services. Under this model, an ISP can control the waiting time "spacings" between di erent classes of traffic. Specifically, the ISP tries to ensure that the average waiting time of class i traffic relative to that of class i 1 traffic is kept at a constant specified ratio. If the waiting time ratio of class i 1 to class i is greater than one, the ISP can legitimately charge users of class i traffic a higher tariff rate (compared to the rate for class i 1 traffic), since class i users consistently enjoy better performance than class i 1 users. To realize such proportional delay differentiated services, we use the time-dependent priority scheduling algorithm. We formally characterize the feasible regions in which given delay ratios can be achieved. Moreover, a set of control parameters for obtaining the desired delay ratios can be determined by an efficient iterative algorithm. We also use an adaptive control algorithm to maintain the correctness of these parameters in response to changing system load. Experiments are carried out to illustrate the short-term, medium-term and long-term relative waiting time performances for different service classes under Poisson, Pareto, MMPP and mixed traffic workloads. We also carry out experiments to evaluate the achieved end-to-end accumulative waiting times for different classes of traffic which traverse multiple hops under our service model.

Several recent price-based congestion control schemes require relatively accurate path price estimates for successful operation. The proposed addition of the two-bit Explicit Congestion Notification (ECN) field in the IP header provides routers with a mechanism for conveying price information. Recently, two proposals have emerged for probabilistic packet marking at the routers; the proposals allow receivers to estimate path price from the fraction of marked packets. In this paper we introduce an alternative deterministic marking scheme for encoding path price. Under our approach, each router quantizes the price of its outgoing link to a fixed number of bits. We then make use of the IP identification (IPid)fieldtomapdata packets to different probe types, and each probe type calculates a partial sum of the path price bits. A router deduces its marking behaviour according to the IPid and the TTL (Time To Live) field of each packet. We evaluate the performance of our algorithm in terms of its error in representing the end-toend price, and compare it to probabilistic marking. We show that based on empirical Internet traffic characteristics, our algorithm performs better when estimating path price using small blocks of packets. We also derive the probability distribution of the error for our scheme, and provide a relatively simple bound on its maximum mean-squared error.

One of the triumphs of wireline network research of the last decade has been the casting of the Internet congestion control problem within an optimization framework based on utility functions. Such an approach provides a sound understanding of the underlying stability and fairness issues, as well as a post-facto justification of TCP-like additiveincrease multiplicative-decrease (AIMD) algorithms. This paper provides a counter-example showing that the same result cannot be extended to wireless networks, at least not in a straightforward manner. The fundamental difference is that wireless networks are of a broadcast nature. There is no strict notion of a “link,” since transmissions from nearby nodes interfere with each other. Using a simple model of interference in wireless networks, a counter-example of a wireless network is presented in which the congestion control mechanism has an unstable equilibrium point at the desired fair solution. Further, ns-2 simulations of this counter-example manifest an oscillatory behavior. Surprisingly, this oscillatory behavior appears to be fairly typical in wireless networks, with most randomly chosen network examples manifesting it. This loss of stability suggests a possible need for the re-design of wireless TCP and wireless queue management to explicitly account for the wireless nature of the effects of interference.

We investigate the service differentiation, in terms of average throughput, and the performance achieved using weighted window-based congestion control in networks supporting Explicit Congestion Notification (ECN). Our results show how service differentiation, queueing delay, and average throughput are affected by the increase and decrease rules of the end-system congestion control algorithms, and how they depend on the marking algorithms operating in the routers. The end-system algorithms we investigate include WTP (Willingness-To-Pay) and MulTCP congestion control, and the packet marking algorithms include RED, virtual queue marking, and load-based marking. Our investigations consider both single and multiple link topologies, and connections with different round trip times.

For over a decade, the Nash Bargaining Solution (NBS) concept from cooperative game theory has been used in networks to share resources fairly. Due to its many appealing properties, it has recently been used for assigning bandwidth in a general topology network between applications that have linear utility functions. In this paper, we use this concept for allocating the bandwidth between applications with general concave utilities. Our framework includes in fact several other fairness criteria, such as the max--min criteria. We study the impact of concavity on the allocation and present computational methods for obtaining fair allocations in a general topology, based on a dual Lagrangian approach and on SemiDefinite Programming.

We investigate the service differentiation, in terms of average throughput, and the performance achieved using weighted window-based congestion control in networks supporting Explicit Congestion Notifica- tion (ECN). Our results show how service differentiation, qucucing delay, and average throughput are affected by the increase and decrease rules of the end-system congestion control algorithms, and how they depend on the marking algorithms operating in the routers. The end-system algorithms we investigate include algorithms that achieve an average throughput proportional to some willingness-to-pay, and the marking algorithms include RED, virtual queue marking, and load-based marking.

We develop a framework for studying the interaction of an active queue management (AQM) scheme with a generic end-user congestion-control mechanism. As the number of flows in the network increases, the queue dynamics can be accurately approximated by a simple deterministic process. In addition, we investigate the sources of queue fluctuations in a probabilistic AQM scheme interacting with responsive flows. We demonstrate that there are two distinct sources of queue fluctuations; one is the deterministic oscillations which can be predicted by the aforementioned deterministic process. The other source is the random fluctuations introduced by the probabilistic nature of the marking schemes. We discuss the relationship between these two types of fluctuations and provide insights into how to control them. Concrete examples in this framework are provided for several popular algorithms such as Random Early Detection, Random

Recently researchers have proposed active queue management (AQM) mechanisms as a means of better managing congestion at the bottlenecks inside the network. Random Early Detection (RED) mechanism has been proposed to control the average queue size at the congested routers. It has been shown that the interaction between an RED gateway and TCP connections can lead to period doubling bifurcation and chaos. In this paper we extend this model and study the interaction of the RED gateway with TCP and UDP connections, using a discrete-time model. ...

This paper deals with the problem of congestion control and packet exchange on a wireless network. The mathematical model corresponding to the real protocol is inspired by and extends a known fluid flow scheme for the control of congestion on a wired network. The necessity to introduce a specific wireless model is motivated by the presence of channel error: often this error (due to intrinsic noise or channel corruption) is not known exactly. This motivates the modification of the model by approximating parts of its structure with binary functions, whose switching point is known precisely. These new discontinuous elements, while in practice greatly simplifying the structure of the algorithm (they are endowed with a 1-bit of information), complicate the theoretical analysis of its dynamical properties. We therefore approximate them with continuous functions with limiting convergence: they thus preserve the simple shape and yield themselves to analysis as well. Given this setup, we then investigate the important issues of existence and uniqueness of the equilibrium for the dynamical system, and of local asymptotic stability. Furthermore, we show that this equilibrium solves a concave net utility optimization problem, of which the classical one for wired networks is a special case. The take away point of this work is that the scheme we propose to handle the traffic on a wireless network is not only innovative and meaningful, but has also the potential to be modified and translated into practical implementation.

Abstract — Flow control, including congestion control for data transmission, and rate control for multimedia streaming, is an important issue in information transmission in both wireline and wireless networks. Widely accepted flow control methods in wireline networks are TCP [1] for data, and TCP Friendly Rate Control (TFRC) [2] for multimedia. Kelly [3] [4] has laid down theoretical framework for TCP in wireline networks demonstrating its optimality, fairness, and stability. However, TCP and TFRC both assume that packet loss in wireline networks is primarily due to congestion, and as such, are not applicable to wireless networks in which the bulk of packet loss is due to errors at the physical layer. In this paper we first show flow control in the wireless networks can be formulated as the same concave optimization problem Kelly defined in the wireline networks. TCP and TFRC in the wireless networks pursue the optimal solution using inaccurate feedback. All existing approaches to this TCP/TFRC over wireless problem correct the inaccurate feedback by casting modifications to existing protocols, such as TCP, or infrastructure elements such as routers, thereby making them hard to deploy in practice. In this paper, we formulate the problem as another concave optimization problem with a different utility function, and propose a new class of solutions. Our approach is end-to-end, and achieves reasonable performance by adjusting the number of connections of a user according to a properly selected control law. The control law is based on only one bit of information, which can be reliably measured at the application layer. We show that the control system has a unique stable equilibrium that solves the concave optimization problem, implying scalability and optimality of the solution. We apply our results to design a practical rate control scheme for data transmission over wireless networks, and characterize its performance using NS-2 simulations and actual experiments over Verizon Wireless 1xRTT data network. Analysis and simulation results also indicate our scheme is applicable to both wireline and wireless scenarios. I.