Gaurav Raina

Part II: control theory for buffer sizing

This article describes how control theory has been used to address the question of how to size the buffers in core Internet routers. Control theory aims to predict whether the is stable, i.e. whether TCP flows are desynchronized. If flows are desynchronized then small buffers are sufficient [14 ]; the theory here shows that small buffers actually promote desynchronization--a virtuous circle.

Buffer sizes for large multiplexers: TCP queueing theory and instability analysis

In large multiplexers with many TCP flows, the aggregate traffic flow behaves predictably; this is a basis for the fluid model of Misra, Gong and Towsley V. Misra et al., (2000) and for a growing literature on fluid models of congestion control. In this paper we argue that different fluid models arise from different buffer-sizing regimes. We consider the large buffer regime (buffer size is bandwidth-delay product), an intermediate regime (divide the large buffer size by the square root of the number of flows), and the small buffer regime (buffer size does not depend on number of flows). Our arguments use various techniques from queueing theory. We study the behaviour of these fluid models (on a single bottleneck Kink, for a collection of identical long-lived flows). For what parameter regimes is the fluid model stable, and when it is unstable what is the size of oscillations and the impact on goodput? Our analysis uses an extension of the Poincare-Linstedt method to delay-differential equations. We find that large buffers with drop-tail have much the same performance as intermediate buffers with either drop-tail or AQM; that large buffers with RED are better at least for window sizes less than 20 packets; and that small buffers with either drop-tail or AQM are best over a wide range of window sizes, though the buffer size must be chosen carefully. This suggests that buffer sizes should be much much smaller than is currently recommended.

Local bifurcation analysis of some dual congestion control algorithms

We perform the necessary calculations to determine the stability and asymptotic forms of solutions bifurcating from steady state in a nonlinear delay differential equation with a single discrete delay. The results are used to examine the loss of local stability in a selection of congestion control algorithms employed over a single link. In particular, we analyze the fair and the delay-based dual algorithms. Explicit conditions are derived to ensure the onset of stable limit cycles as these algorithms just lose local stability. Further, we are able to quantify the effect parameters of the system have on the amplitude of the bifurcating periodic solutions.

Stability and fairness of explicit congestion control with small buffers

Rate control protocols that utilise explicit feedback from routers are able to achieve fast convergence to an equilibrium which approximates processor-sharing on a single bottleneck link, and hence such protocols allow short flows to complete quickly. For a network, however, processor-sharing is not uniquely defined but corresponds with a choice of fairness criteria, and proportional fairness has a reasonable claim to be the network generalization of processor-sharing. In this paper, we develop a variant of RCP (rate control protocol) that achieves α-fairness when buffers are small, including proportional fairness as the case α = 1. At the level of theoretical abstraction treated, our model incorporates a general network topology, and heterogeneous propagation delays. For our variant of the RCP algorithm, we establish a simple decentralized sufficient condition for local stability. An outstanding question for explicit congestion control is whether the presence of feedback based on queue size is helpful or not, given the presence of feedback based on rate mismatch. We show that, for the variant of RCP considered here, feedback based on queue size may cause the queue to be less accurately controlled. A further outstanding question for explicit congestion control is the scale of the step-change in rate that is necessary at a resource to accommodate a new flow. We show that, for the variant of RCP considered here, this can be estimated from the aggregate flow through the resource, without knowledge of individual flow rates.

Delay and loss-based transport protocols: Buffer-sizing and stability

It is generally accepted that buffers, in Internet routers, should be much smaller than the currently deployed bandwidth-delay product rule. However, as yet, there is no consensus on the optimal buffer-sizing strategy. Our focus will be on the performance, with respect to sizing buffers, of transport protocols that use queuing delay and packet loss as their feedback signals for flow and congestion control. The protocols we choose for our study are Compound, Illinois, and AFRICA.

TCP: Local stability and Hopf bifurcation

In this paper we analyze a fluid model of TCP with an approximation of drop tail using tools from control and bifurcation theory. The focus of our analysis and experiments lies in a regime where the buffer sizes are small, as recently advocated by Appenzeller, Keslassy and McKeown [G. Appenzeller, I. Keslassy, N. McKeown, Sizing router buffers, in: Proceedings of ACM SIGCOMM, 2004]. We find that to ensure local stability of TCP with drop tail it is necessary and sufficient that the arrival rate be greater than capacity by a certain factor, which does not depend on the round-trip time. This factor is found to be 1.1415. The next natural question to ask is: what if these conditions of local stability are just violated? This entails conducting a local bifurcation theoretic analysis (at the point of linear instability), from which we conclude that the corresponding nonlinear system undergoes a supercritical Hopf bifurcation. So as stability of the equilibrium is just lost, it is regained by a stable limit cycle. The analysis is complemented by simulations at the packet level performed using the Network Simulator, ns2.

Mobile payment architectures for India

Mobile payments are a new and alternative payment method. Instead of using traditional methods like cash, cheque, or credit cards, a customer can use a mobile phone to transfer money or to pay for goods and services. Mobile payments have numerous advantages over traditional payment methods. Apart from their apparent flexibility, they enable consumers who do not have easy access to banking facilities to participate readily in financial transactions. Unfortunately, existing mobile payment solutions in India are not interoperable; i.e. they only offer services for merchants registered with them and do not allow the transfer of money to, or between, users of other payment providers. This limitation reduces the widespread adoption of mobile payments. In this paper, we propose new mobile payment architectures that support interoperability. A key technical aspect of the mobile payment process is to lookup customer details, for which we propose the following three design options: (1) a central database, (2) a peer-to-peer query, or (3) a hierarchical lookup. These options are evaluated using relevant metrics such as the complexity of implementation and scalability with respect to system size. Based on our evaluation we recommend that initially the peer-to-peer design is chosen, and once the technology is more widespread, the central database option should be adopted.

Stability Analysis of a Max-Min Fair Rate Control Protocol (RCP) in a Small Buffer Regime

In this note we analyse various stability properties of a max-min fair rate control protocol (RCP) operating with small buffers. We first tackle the issue of stability for networks with arbitrary topologies. We prove that the max-min fair RCP fluid model is globally stable in the absence of propagation delays, and also derive a set of conditions for local stability when arbitrary heterogeneous propagation delays are present. The network delay stability result assumes that, at equilibrium, there is only one bottleneck link along each route. Lastly, in the simpler setting of a single link, single delay model, we investigate the impact of the loss of local stability via a Hopf bifurcation.

A generalized control method for a Tilt-rotor UAV stabilization

Unmanned Aerial Vehicles (UAVs) are currently a very interesting field of research in the modern scientific community, especially in their application to military operations. In this paper we focus on the Tilt-rotor UAV. This is a UAV capable of Vertical Take-Off and Landing (VTOL), with a rotor on each side of its airframe. Each rotor can be tilted independently to provide both lift and forward thrust to the rotor-craft. The Euler-Lagrange formulation is used to develop the model of the UAV. A key aspect in the design is the ability of the UAV to hover in one position. To that end, we design a back-stepping based proportional-derivative (PD) controller. The generalized structure of the proposed controller makes it easy to derive the equations of force and torque. Simulations demonstrate that the controller is capable of stabilizing the UAV. We also highlight its ability to track continuous trajectories.

Back-stepping control strategy for stabilization of a Tilt-rotor UAV

In todays world, the study and applications of Vertical Take-Off and Landing (VTOL) capable Unmanned Aerial Vehicles (UAVs) have increased vastly. A wide variety of UAVs are currently being employed in both civilian and military sectors. In this paper, our focus will be on the Tilt-rotor UAV. The Tilt-rotor has a rotor on each side of its airframe, tilted to provide both lift and forward thrust to the rotor-craft. We develop a model that aims to enable the Tilt-rotor UAV to hover in one specific position. Because of the under-actuated property of the Tilt-rotor, we design a back-stepping based proportional-derivative (PD) controller. The controller was able to achieve the desired objective of stabilization.