15446858
A new approach for asynchronous distributed rate control of elastic sessions in integrated packet networks
We develop a new class of asynchronous distributed algorithms for the explicit rate control of elastic sessions in an integrated packet network. Sessions can request for minimum guaranteed rate allocations (e.g., minimum cell rates in the ATM context), and, under this constraint, we seek to allocate the max-min fair rates to the sessions. We capture the integrated network context by permitting the link bandwidths available to elastic sessions to be stochastically time varying. The available capacity of each link is viewed as some statistic of this stochastic process [e.g., a fraction of the mean, or a large deviations-based equivalent service capacity (ESC)]. The ESC is obtained so as to satisfy an overflow probability constraint on the buffer length. For fixed available capacity at each link, we show that the vector of max-min fair rates can be computed from the root of a certain vector equation. A distributed asynchronous stochastic approximation technique is then used to develop a provably convergent distributed algorithm for obtaining the root of the equation, even when the link flows and the available capacities are obtained from on-line measurements. The switch algorithm does not require per connection monitoring, nor does it require per connection marking of control packets. A virtual buffer based approach for on-line estimation of the ESC is utilized. We also propose techniques for handling large variations in the available capacity owing to the arrivals or departures of CBR/VBR sessions. Finally, simulation results are provided to demonstrate the performance of this class of algorithms in the local and wide area network context.
5368108
A stochastic approximation approach for max-min fair adaptive rate control of ABR sessions with MCRs
The available bit rate (ABR) sessions in an ATM network share the bandwidth left over after guaranteeing service to constant bit rate (CBR) and variable bit rate (VBR) traffic. Hence the bandwidth available to ABR sessions is randomly varying. This bandwidth must be shared by the sessions in a max-min fair fashion. Our point of departure in this paper is to formulate the problem of determining the max-min fair session rates as the problem of finding the root of a certain nonlinear vector equation; the same formulation also arises with our notion of max-min fairness with positive minimum cell rates (MCRs). This formulation allows us to use a stochastic approximation algorithm for online distributed computation of the max-min fair rates. We use the well known ordinary differential equation technique to prove convergence of the algorithm in the synchronous update case. We provide simulation results using the NIST simulator to show that the algorithm is able to track the max-min fair rates for slowly varying random available link bandwidths.
15724188
Instability and performance limits of distributed simulators of feedforward queueing networks
In this article we study the performance of distributed simulation of open feedforward queueing networks, by analyzing queueing models of message flows in distributed discrete event simulators. We view each logical process in a distributed simulation as comprising a message sequencer with associated message queues, followed aby an event processor. We introduce the idealized, but analytically useful, comcept of maximum lookahead. We show that, with quite general stochatstic assumptions for message arrival and time-stamp processes, the meassage queues are unstable for conservative sequencing, and for conservative sequencing with maximum lookahead and hence for optimistic resequencing, and for any resequenceing algorithm that does not employ interprocessor flow control. Finally, we provide formulas for the throughput of distributed simulators of feedforward queueing networks.
17761375
Comparative performance analysis of versions of TCP in a local network with a lossy link
We use a stochastic model to study the throughput performance of various transport control protocol (TCP) versions (Tahoe (including its older version that we call OldTahoe), Reno, and NewReno) in the presence of random losses on a wireless link in a local network. We model the cyclic evolution of TCP, each cycle starting at the epoch at which recovery starts from the losses in the previous cycle. TCP throughput is computed as the reward rate in a certain Markov renewal-reward process. Our model allows us to study the performance implications of various protocol features, such as fast retransmit and fast recovery. We show the impact of coarse timeouts. In the local network environment the key issue is to avoid a coarse timeout after a loss occurs. We show the effect of reducing the number of duplicate acknowledgements (ACKs) for triggering a fast retransmit. A large coarse timeout granularity seriously affects the performance of TCP, and the various protocol versions differ in their ability to avoid a coarse timeout when random loss occurs; we quantify these differences. We show that, for large packet-loss probabilities, TCP-Reno performs no better, or worse, than TCP-Tahoe. TCP-NewReno is a considerable improvement over TCP-Tahoe, and reducing the fast-retransmit threshold from three to one yields a large gain in throughput; this is similar to one of the modifications in the TCP-Vegas proposal. We explain some of these observations in terms of the variation of fast-recovery probabilities with packet-loss probability. The results of our analysis compare well with a simulation that uses actual TCP code.
43715944
Performance Analysis and Scheduling of Stochastic Fork-Join Jobs in a Multicomputer System
The authors model a parallel processing system comprising several homogeneous computers interconnected by a communication network. Jobs arriving to this system have a linear fork-join structure. Each fork of the job gives rise to a random number of tasks that can be processed independently on any of the computers. Since exact analysis of fork-join models is known to be intractable, the authors resort to obtaining analytical bounds to the mean job response time of the fork-join job. For jobs with a single fork-join and, probabilistic allocation of tasks of the job to the N processors, they obtain upper and lower bounds to the mean job response time. Upper bounds are obtained using the concept of associated random variables and are found to be a good approximation to the mean job response time. A simple lower bound is obtained by neglecting queueing delays. They also find two lower bounds that include queueing delays. For multiple fork-join jobs, they study an approximation based on associated random variables. Finally, two versions of the join-the-shortest-queue (JSQ) allocation policy (i.e., JSQ by batch and JSQ by task) are studied and compared, via simulations and diffusion limits. >
208013096
New insights from a fixed point analysis of single cell IEEE 802.11 WLANs
We study a fixed point formalisation of the well known analysis of Bianchi. We provide a significant simplification and generalisation of the analysis. In this more general framework, the fixed point solution and performance measures resulting from it are studied. Uniqueness of the fixed point is established. Simple and general throughput formulas are provided. It is shown that the throughput of any flow will be bounded by the one with the smallest transmission rate. The aggregate throughput is bounded by the reciprocal of the harmonic mean of the transmission rates. In an asymptotic regime with a large number of nodes, explicit formulas for the collision probability, the aggregate attempt rate and the aggregate throughput are provided. The results from the analysis are compared with ns2 simulations, and also with an exact Markov model of the back-off process. It is shown how the saturated network analysis can be used to obtain TCP transfer throughputs in some cases.
7308298
Data streaming algorithms for accurate and efficient measurement of traffic and flow matrices
The traffic volume between origin/destination (OD) pairs in a network, known as traffic matrix, is essential for efficient network provisioning and traffic engineering. Existing approaches of estimating the traffic matrix, based on statistical inference and/or packet sampling, usually cannot achieve very high estimation accuracy. In this work, we take a brand new approach in attacking this problem. We propose a novel data streaming algorithm that can process traffic stream at very high speed (e.g., 40 Gbps) and produce traffic digests that are orders of magnitude smaller than the traffic stream. By correlating the digests collected at any OD pair using Bayesian statistics, the volume of traffic flowing between the OD pair can be accurately determined. We also establish principles and techniques for optimally combining this streaming method with sampling, when sampling is necessary due to stringent resource constraints. In addition, we propose another data streaming algorithm that estimates flow matrix, a finer-grained characterization than traffic matrix. Flow matrix is concerned with not only the total traffic between an OD pair (traffic matrix), but also how it splits into flows of various sizes. Through rigorous theoretical analysis and extensive synthetic experiments on real Internet traffic, we demonstrate that these two algorithms can produce very accurate estimation of traffic matrix and flow matrix respectively.
41636502
A Study of Spatial Clustering techniques
This paper proposes a new interleaving-based method for spatial clustering developed by combining gray codes with a new ordering technique called nu-ordering. This method is compared with two existing interleaving-based techniques and another technique called hilbert-ordering. The performance comparison is done by means of a simulation study. The results show that the choice of the technique affects the clustering performance dramatically. Among the four techniques considered, both nu-ordering and hilbert method outperformed the other two methods by more than 35%; however, with minor exceptions, the hilbert technique was the best among the four techniques evaluated.
2987975
Data streaming algorithms for efficient and accurate estimation of flow size distribution
Knowing the distribution of the sizes of traffic flows passing through a network link helps a network operator to characterize network resource usage, infer traffic demands, detect traffic anomalies, and accommodate new traffic demands through better traffic engineering. Previous work on estimating the flow size distribution has been focused on making inferences from sampled network traffic. Its accuracy is limited by the (typically) low sampling rate required to make the sampling operation affordable. In this paper we present a novel data streaming algorithm to provide much more accurate estimates of flow distribution, using a "lossy data structure" which consists of an array of counters fitted well into SRAM. For each incoming packet, our algorithm only needs to increment one underlying counter, making the algorithm fast enough even for 40 Gbps (OC-768) links. The data structure is lossy in the sense that sizes of multiple flows may collide into the same counter. Our algorithm uses Bayesian statistical methods such as Expectation Maximization to infer the most likely flow size distribution that results in the observed counter values after collision. Evaluations of this algorithm on large Internet traces obtained from several sources (including a tier-1 ISP) demonstrate that it has very high measurement accuracy (within 2%). Our algorithm not only dramatically improves the accuracy of flow distribution measurement, but also contributes to the field of data streaming by formalizing an existing methodology and applying it to the context of estimating the flow-distribution.
16229780
A Multiresolution Model of Auditory Excitation Pattern and Its Application to Objective Evaluation of Perceived Speech Quality
This paper proposes a multiresolution model of auditory excitation pattern and applies it to the problem of objective evaluation of subjective wideband speech quality. The model uses wavelet packet transform for time-frequency decomposition of the input signal. The selection of the wavelet packet tree is based on an optimality criterion formulated to minimize a cost function based on the critical band structure. The models of the different auditory phenomena are reformulated for the multiresolution framework. This includes the proposition of duration dependent outer and middle ear weighting, multiresolution spectral spreading, and multiresolution temporal smearing. As an application, the excitation pattern is used to define an objective measure of auditory distortion of a distorted speech signal compared to the undistorted one. The performance of this objective measure is evaluated with a database of various kinds of NOISEX-92 degraded wideband speech signals in predicting the subjective mean opinion score (MOS) and is compared with the fast Fourier transform (FFT)-based ITU-T PESQ P.862.2 algorithm. The proposed measure is found to achieve comparable correlation between subjective MOS and objective MOS as PESQ P.862.2, with a trend suggesting better correlation for the nonstationary degradations compared to the stationary ones. Further refinement of the measure for distortion types other than additive noise is anticipated
36050355
An efficient algorithm for solving the partial sum query problem
Abstract We address the problem: given n data values, how many partial sums must be stored so that partial sums of any other combination of these n values can be calculated in one arithmetic operation from the stored values. This problem has application in online analytical processing (OLAP) databases [Gray et al., Proc. 12th Int. Conf. Data Eng. (1996)] where it is called the partial sum aggregation query. It can also be used to generate the entire power set of n values efficiently. In this paper, we derive lower bounds for this problem, devise an efficient algorithm to solve it and show that our heuristic comes reasonably close to the lower bound.