Performance analysis and stochastic stability of congestion control protocols

Abstract

Abstruct-We study an Adaptive Window Protocol (AWP) witha general increase and decrease profile in the presence of window dependent random losses. We derive a steady-slate Kolmogorov equation and obtain its solution in analytic form. We obtain some stochastic ordering relations for a protocol with different bounds on window, A closed form necesary ahd sufticient stability condition using the stochastic ordering for the window process is established. Finally, we apply the general results to particular TCP versions such as New Reno TCP, Scalable TCP and Highspeed TCP. We observe that HighSpeed TCP can be used to approximate almost any kind of window behavior by varying only one design parameter. I . INTRODUCTIOYMost of the performance studies of Adaptive Window Protocols (AWP) consider specific instances of the problem (for example [3]. 121, [61 study Additive Increase Multiplicative Decrease (ATMD) protocols). However, various modifications to TCP are frequently proposed to address specific problems arising in various types of networks; recent examples include Highspeed TCF [51 and Scalable TCP C41 proposed for very high bandwidth-delay product networks. These new proposals can also be viewed in the framework of Additive Increase protocols so that now the additive increase in a round-trip time is function of the current window size (it is constant in the case of standard TCP). Performance related analysis of any such protocol has always been an important issue. It is thus desirable to have a general framework (and its solution) for performance anakysis of an AWP.The loss process seen by a TCP sender may have its origin in deliberate markingldropping owing to some active queue management (AQM) scheme employed in the network, or could be due to congestion losses or link errors, in general the rate of receiving a loss signal will depend on the window process itself (see [6] for related discussion). In this study, we consider a general state dependent loss rate. It is clear that the stability of window process of a general AWP will depend on the rate at which it receives loss signals. For example, an aggressive protocol may result in very high windows for moderate loss rates and vice versa.Stability of the window process is thus interesting to study.We address the problem of finding conditions for stability of a general AWP controlled window evolution under a general statedependent loss rate. The contributions (and organization) of this work is as follows:Section 11: We give a characterization of a general AWP and identify the various quantities that determine the performance o f such protocols. The window evolution under a general AWP is mapped to that under an AWP with a linear increase profile (like in standard TCP). Kolmogorov equations satisfied by the stationary probability measure is then derived. Section 111: Gives conditions under which two AWPs have related stationary distribution. Furthermore, we demonstrate that the window process under multiplicative decrease protocol is also related to the workload proce...

An extension of the square root law of TCP

“…Several different approaches have been used in this line of work; for example direct modeling and performance analysis [2,3], simulation [7], approximations [21] and probabilistic scaling [5,11,19,20]. In this work, we combine probabilistic scaling and performance analysis methods to analyze a class of congestion avoidance algorithms which we (following [3]) call general increase multiplicative decrease (GIMD) algorithms. As argued in [2,3,14], the recent explosion of bandwidth on the Internet raises the question whether the conservative AIMD scheme is (still) optimal.…”

“…In this work, we combine probabilistic scaling and performance analysis methods to analyze a class of congestion avoidance algorithms which we (following [3]) call general increase multiplicative decrease (GIMD) algorithms. As argued in [2,3,14], the recent explosion of bandwidth on the Internet raises the question whether the conservative AIMD scheme is (still) optimal. In particular, the multiplicative increase multiplicative decrease scheme, also called scalable TCP has been proposed; cf.…”

“…As argued and demonstrated in [3], the process {V t : t ≥ 0} can also be used directly as a continuous time model for TCP like mechanisms. From that point of view, Section 2 can be seen as an additional motivation for the models considered in [3].…”

“…From that point of view, Section 2 can be seen as an additional motivation for the models considered in [3]. The conditions in that paper allow for more general decrease mechanisms than multiplicative decrease, but do not include clumps of losses.…”

TCP and iso-stationary transformations

“…Dumas et al [8] consider the case α = 0, β > −1, and present the stationary distribution for β = 1. Altman et al [1] consider the case α < 1 and give an explicit analysis of β = 0, 1 using rather general mappings that involve both space and time transformations. Baccelli et al [3] consider a more general class of models for non-persistent flows, that includes our model for the case α = 0, β ≤ 0.…”