Now showing 1 - 10 of 15
  • Placeholder Image
    Publication
    Analyses of compound TCP with Random Early Detection (RED) queue management
    (17-07-2015)
    Manjunath, Sreelakshmi
    ;
    We study the performance of Compound TCP with Random Early Detection (RED) in three different limiting regimes. In the first regime, averaging over the queue size helps to decides the probability of dropping packets. Then, we consider a model where averaging over the queue size is not performed, but the queue is modelled as an integrator. Finally, we consider a model where the threshold for dropping packets is so small that it is not possible to model the queue as an integrator. In these three regimes, we derive sufficient, as well as necessary and sufficient conditions for local stability. These conditions help to capture the dependence of protocol and network parameters on system stability. We also show that in the event of loss of local stability, the Compound TCP-RED system undergoes a Hopf bifurcation which would lead to limit cycles. Some of the analytical results are corroborated using packet-level simulations.
  • Placeholder Image
    Publication
    Analysis of TCP with an Exponential-RED (E-RED) queue management policy with two delays
    (17-07-2015)
    Prasad, Sai
    ;
    We analyze Compound TCP, the default protocol in the Windows operating system, along with an Exponential-RED (E-RED) queue policy. The E-RED queue policy specially aims for high link utilization. Our setup considers two sets of TCP flows, each having a different round-trip time, operating over a single bottleneck link. For this system, we first derive a sufficient condition for local stability. The stability condition reveals that the link gain needs to scale with the maximum round-trip time in the system. Additionally, the Compound parameter α needs to be chosen judiciously if stability is to be ensured. We then computationally show that, as parameters vary, the system can undergo a Hopf bifurcation. This bifurcation alerts us about the emergence of limit cycles, in the system dynamics, as stability is just lost. Finally, we exhibit the emergence of such limit cycles, in the queue size, via packet-level simulations. These limit cycles can result in the loss of link utilization and should be avoided.
  • Placeholder Image
    Publication
    Stability and Hopf bifurcation analysis of TCP with a RED-like queue management policy
    (01-01-2014)
    Prasad, Sai
    ;
    We analyse a non-linear fluid model of TCP coupled with a Random Early Detection (RED)-like queue management policy. We first show that the conditions for local stability, as parameters vary, will be violated via a Hopf bifurcation. Thus, a stable equilibrium would give rise to limit cycles. To identify the type of the Hopf bifurcation, and to determine the stability of the bifurcating limit cycles, we apply the theory of normal forms and the center manifold analysis. Some numerical computations accompany our theoretical work. © 2014 IEEE.
  • Placeholder Image
    Publication
    Stability and performance analysis of compound TCP with the exponential-RED and the drop-tail queue policies
    (20-06-2019)
    Prasad, Sai
    ;
    The analysis of transport protocols, along with queue management policies, forms an important aspect of performance evaluation for the Internet. In this article, we study Compound TCP (C-TCP), the default TCP in the Windows operating system, along with the Exponential-RED (E-RED) queue policy and the widely used Drop-Tail queue policy. We consider queuing delay, link utilization and the stability of the queue size as the performance metrics. We first analyse the stability properties of a nonlinear model for C-TCP coupled with the E-RED queue policy. We observe that this system, in its current form, may be difficult to stabilize as the feedback delay gets large. Further, using an exogenous and non-dimensional parameter, we show that the system loses local stability via a Hopf bifurcation, which gives rise to limit cycles. Employing Poincaré normal forms and the center manifold theory, we outline an analytical framework to characterize the type of the Hopf bifurcation and to determine the orbital stability of the emerging limit cycles. Numerical examples, stability charts and bifurcation diagrams complement our analysis. We also conduct packet-level simulations, with E-RED and Drop-Tail, in small and large buffer-sizing regimes. With large buffers, E-RED can achieve small queue sizes compared with Drop-Tail. However, it is difficult to maintain the stability of the E-RED policy as the feedback delay gets large. On the other hand, with small buffers, E-RED offers no clear advantage over the simple Drop-Tail queue policy. Our work can offer insights for the design of queue policies that can ensure low latency and stability.
  • Placeholder Image
    Publication
    Stability and Performance Analysis of Compound TCP with REM and Drop-Tail Queue Management
    (01-08-2016) ;
    Manjunath, Sreelakshmi
    ;
    Prasad, Sai
    ;
    We study Compound TCP (C-TCP), the default TCP in the Windows operating system, with Random Exponential Marking (REM) and the widely used Drop-Tail queue policy. The performance metrics we consider are stability of the queue size, queuing delay, link utilization, and packet loss. We analyze the following models: 1) a nonlinear model for C-TCP with Drop-Tail and small buffers; 2) a stochastic variant of REM along with C-TCP; and 3) the original REM proposal as a continuous-time nonlinear model with delayed feedback. We derive conditions to ensure local stability and show that variations in system parameters can induce a Hopf bifurcation, which would lead to the emergence of limit cycles. With Drop-Tail and small buffers, the Compound parameters and the buffer size both play a key role in ensuring stability. In the stochastic variant of REM, larger thresholds for marking/dropping packets can destabilize the system. With the original REM proposal, using Poincaré normal forms and the center manifold analysis, we also characterize the type of the Hopf bifurcation. This enables us to analytically verify the stability of the bifurcating limit cycles. Packet-level simulations corroborate some of the analysis. Some design guidelines to ensure stability and low latency are outlined.
  • Placeholder Image
    Publication
    Stability and Hopf bifurcation analysis of the Mackey-Glass and Lasota equations
    (01-01-2014)
    Manjunath, Sreelakshmi
    ;
    Time delays are an integral part of various physiological processes. In this paper, we analyse two models for physiological systems: the Mackey-Glass and Lasota equations. We first exhibit a sufficient condition to ensure local stability, and then outline the associated necessary and sufficient condition for stability. Using a non-dimensional bifurcation parameter, we then highlight that stability will be lost via a Hopf bifurcation. We also explicitly characterise the type of the Hopf bifurcation using Poincaré normal forms and the center manifold theory. The theoretical analysis is complemented with some numerical examples, stability charts and bifurcation diagrams. © 2014 IEEE.
  • Placeholder Image
    Publication
    Local Stability and Hopf Bifurcation Analysis for Compound TCP
    (01-12-2018)
    Ghosh, Debayani
    ;
    ;
    We conduct a local stability and Hopf bifurcation analysis for Compound transmission control protocol (TCP), with small Drop-Tail buffers, in three topologies. The first topology consists of two sets of TCP flows having different round-trip times and feeding into a core router. The second topology consists of two distinct sets of TCP flows, regulated by a single-edge router and feeding into a core router. The third topology comprises two distinct sets of TCP flows, regulated by two separate edge routers and feeding into a core router. In each case, we conduct a local stability analysis and obtain conditions on the network and protocol parameters to ensure stability. If these conditions get marginally violated, we show that the underlying systems lose local stability via a Hopf bifurcation. After exhibiting a Hopf, a key concern is to determine the asymptotic orbital stability of the bifurcating limit cycles. We then present a detailed analytical framework to address the stability of the limit cycles and the type of the Hopf bifurcation by invoking Poincaré normal forms and the center manifold theory. We finally conduct packet-level simulations to corroborate our analytical insights.
  • Placeholder Image
    Publication
    Local Hopf bifurcation analysis of logistic population dynamics models with two delays
    (01-01-2014)
    Manjunath, Sreelakshmi
    ;
    Multiple time lags can occur very naturally in the study of population dynamics. In this paper, we study two forms of the delay logistic equation with two discrete time delays. For both the models, we identify the condition for the first local Hopf bifurcation. For our analysis, we employ a non-dimensional bifurcation parameter. Using Poincaré normal forms and the center manifold theory, we also conduct the requisite analysis to determine the type of the Hopf bifurcation. This enables us to determine the asymptotic orbital stability of the bifurcating periodic solutions. The analysis is complemented with some numerical examples and bifurcation diagrams. © 2014 IEEE.
  • Placeholder Image
    Publication
    Performance analysis of compound TCP with a Proportional Integral (PI) control policy
    (17-07-2015)
    Manjunath, Sreelakshmi
    ;
    In this paper, we study the performance of Compound TCP with the classical Proportional Integral (PI) control policy implemented at routers. We first conduct a local stability analysis and derive the necessary and sufficient condition for local stability of the non-linear model of Compound with PI. We explicitly show that the system undergoes a Hopf bifurcation as it transits into instability, which would lead to the emergence of limit cycles in the queue size. We then use Poincaré normal forms and center manifold theory to provide an analytical basis to characterise the Hopf bifurcation and determine the orbital stability of the limit cycles. The analysis is complemented with numerical examples.
  • Placeholder Image
    Publication
    Local stability and Hopf bifurcation analysis of a Rate Control Protocol with two delays
    (17-07-2015)
    Abuthahir,
    ;
    There is growing interest in explicit congestion control for congestion management in future high bandwidth-delay communication networks. In the class of explicit congestion control protocols, the Rate Control Protocol (RCP) is a protocol designed to minimize flow completion time which is an important metric for the user. RCP estimates the common fair share rate for all flows by using two forms of feedback: rate mismatch and queue size. An outstanding design question for RCP is whether the feedback based on queue size is useful or not. In an effort to make progress on this question, we study the local stability and Hopf bifurcation properties of RCP with feedback based only on rate mismatch. In particular, we focus on the proportionally fair variant of RCP over a network carrying flows with two different round-trip times. We show that as parameters vary, the system may lose local stability through a Hopf bifurcation which leads to the emergence of limit cycles. Using Poincaré normal forms and the center manifold theorem, we show that the system would give rise to a super-critical Hopf bifurcation and the emerging limit cycles are asymptotically orbitally stable. The analysis is corroborated with some numerical examples and bifurcation diagrams.