The window distribution of multiple TCPs with random loss queues

In this paper, we consider the case of multiple ideal and persistent TCP flows (flows that are assumed to be performing idealized congestion avoidance) interacting with queue management algorithms that perform random drop-based buffer management. Our objective is to determine the stationary congestion window distribution of each of the TCP flows whenthe router port implements algorithms like RED (Random Early Detection)or ERD (Early Random Drop). We first present an analyticaltechnique to obtain the 'mean' queue occupancy and the 'mean' of the individual TCP windows. Armed with this estimate of the means, wethen derive the window distribution of each individual TCPconnection. Extensive simulation experiments indicate that, under a wide variety of operating conditions, our analytical method is quite accurate in predicting the 'mean' as well asthe distributions. The derivation of the individual distributions is based upon a numerical analysis presented which considers the case of a single TCP flow subject to variable state-dependent packet loss

Effect of Exponential Averaging on the Variability of a RED Queue

A ~ T ~ U C T- he paper analyzes how using a longer memory of the past queue occupancy in computing the average queue occupancy affects the stability and variability of a RED queue. Extensive simulation studies with both persistent and Web TCP sources are used to study the variance of the RED queue as a function of the memory of the averaging process. Our re-sults show that there is very little performance improvement (and in fact, possibly significant performance degradation) if the length of memory is increased beyond a very small value. Contrary to current practice, our re-sults show that a longer memory reduces the negative correlation typically observed among the windows of the constituent TCP flows, and hence, sug-gest the use of the instantaneous queue occupancy in practical RED queucts. I

Generalized TCP Congestion Avoidance and its Effect on Bandwidth Sharing and Variability

Abstract—To model possible suggested changes in TCP window adaptation in response to randomized feedback, such as ECN, we formulate a generalized version of the TCP congestion avoidance algorithm. We first consider multiple such generalized TCP flows sharing a bottleneck buffer under the Assured Service model and use a fixed point technique to obtain the mean window sizes and throughputs for the TCP flows. To further study how changes in the adaptation algorithm affect the variability in the throughput, we use an analytical-cum-numerical technique to derive the window distribution (and related statistics) of a single generalized flow under state-dependent randomized congestion feedback. I

Predicting Bottleneck Bandwidth Sharing by Generalized TCP Flows

The paper presents a technique for computing the individual throughputs and the average queue occupancy when multiple TCP connections share a single bottleneck buffer. The bottleneck buffer is assumed to perform congestion feedback via randomized packet marking or drops. We first present a fixed point-based analytical technique to compute the mean congestion window sizes, the mean queue occupancy and the individual throughputs when the TCP flows perform idealized congestion avoidance. We subsequently extend the technique to analyze the case where TCP flows perform generalized congestion avoidance and demonstrate the use of this technique under the Assured Service model, where each flow is assured a minimum traffic rate. Simulations are used to demonstrate the accuracy of this technique for relatively low values of packet dropping probability and a much wider range of packet marking probability

The Window Distribution of Idealized TCP Congestion Avoidance with Variable Packet Loss

This paper analyzes the stationary behavior of the TCP congestion window performing ideal congestion avoidance when the packet loss probability is not constant, but varies as a function of the window size. By neglecting the detailed window behavior during fast recovery, we are able to derive a Markov process that is then approximated by a continuous-time, continuous state-space process. The stationary distribution of this process is analyzed and derived numerically and then extrapolated to obtain the stationary distribution of the TCP window. This numerical analysis enables us to predict the behavior of the TCP congestion window when interacting with a router port performing Early Random Drop (or Random Early Detection) where the loss probability varies with the queue occupancy. Keywords---TCP, distribution, variable, loss. I. INTRODUCTION In this paper, we present a quantitative analysis of the stationary behavior of the evolution of the TCP congestion window (cwnd) ([1]) when the ..

Stationarity and existence of moments for some processes in Transport Protocols

This note establishes stationarity of a number of stochastic processes of interest in the study of Transport Protocols. For many of the processes studied in this note stationarity had been established before, but for one class the result is new. For that class, it was counterintuitive that stationarity was hard to prove. This note also explains why that class offered such stiff resistance. The stationarity is proven using Liapunov functions, without first proving tight-ness by proving boundedness of moments. After the 2006 MAMA workshop simple conditions for existence and boundedness of such moments were obtained and were added to this note.