Anwar Elwalid

Effective bandwidth of general Markovian traffic sources and admission control of high speed networks

A prime instrument for controlling congestion in a high-speed network is admission control, which limits calls and guarantees a grade of service determined by delay and loss probability in the multiplexer. It is shown that for general Markovian traffic sources it is possible to assign a notional effective bandwidth to each source that is an explicitly identified, simply computed quantity with provably correct properties in the natural asymptotic regime of small loss probabilities. It is the maximal real eigenvalue of a matrix that is directly obtained from the source characteristics and the admission criterion, and for several sources it is simply additive. Both fluid and point process models are considered. Numerical results show that the acceptance set for heterogeneous classes of sources is closely approximated and conservatively bounded by the set obtained from the effective bandwidth approximation. The bandwidth-reducing properties of the leaky bucket regulator are exhibited numerically. >

MATE: MPLS adaptive traffic engineering

Destination-based forwarding in traditional IP routers has not been able to take full advantage of multiple paths that frequently exist in Internet service provider networks. As a result, the networks may not operate efficiently, especially when the traffic patterns are dynamic. This paper describes a multipath adaptive traffic engineering mechanism, called MATE, which is targeted for switched networks such as multiprotocol label switching (MPLS) networks. The main goal of MATE is to avoid network congestion by adaptively balancing the load among multiple paths based on measurement and analysis of path congestion. MATE adopts a minimalist approach in that intermediate nodes are not required to perform traffic engineering or measurements besides normal packet forwarding. Moreover MATE does not impose any particular scheduling, buffer management, or a priori traffic characterization on the nodes. This paper presents an analytical model, derives a class of MATE algorithms, and proves their convergence. Several practical design techniques to implement MATE are described. Simulation results are provided to illustrate the efficacy of MATE under various network scenarios.

A new approach for allocating buffers and bandwidth to heterogeneous, regulated traffic in an ATM node

A new approach to determining the admissibility of variable bit rate (VBR) traffic in buffered digital networks is developed. In this approach all traffic presented to the network is assumed to have been subjected to leaky-bucket regulation, and extremal, periodic, on-off regulated traffic is considered; the analysis is based on fluid models. Each regulated traffic stream is allocated bandwidth and buffer resources which are independent of other traffic. Bandwidth and buffer allocations are traded off in a manner optimal for an adversarial situation involving minimal knowledge of other traffic. This leads to a single-resource statistical-multiplexing problem which is solved using techniques previously used for unbuffered traffic. VBR traffic is found to be divisible into two classes, one for which statistical multiplexing is effective and one for which statistical multiplexing is ineffective in the sense that accepting small losses provides no advantage over lossless performance. The boundary of the set of admissible traffic sources is examined, and is found to be sufficiently linear that an effective bandwidth can be meaningfully assigned to each VBR source, so long as only statistically-multiplexable sources are considered, or only nonstatistically-multiplexable sources are considered. If these two types of sources are intermixed, then nonlinear interactions occur and fewer sources can be admitted than a linear theory would predict. A qualitative characterization of the nonlinearities is presented. The complete analysis involves conservative approximations; however, admission decisions based on this work are expected to be less overly conservative than decisions based on alternative approaches. >

Fundamental bounds and approximations for ATM multiplexers with applications to video teleconferencing

The main contributions of this paper are two-fold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing systems capacity as determined by the number of admissible sources for given cell-loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on large deviations theory. The main assumption is that the sources are Markovian and time-reversible. Our approximation to the steady-state buffer distribution is called Chenoff-dominant eigenvalue since one parameter is obtained from Chernoffs theorem and the other is the systems dominant eigenvalue. Fast, effective techniques are given for their computation. In our application we process the output of variable bit rate coders to obtain DAR(1) source models which, while of high dimension, require only knowledge of the mean, variance, and correlation. We require cell-loss probability not to exceed 10/sup -6/, trunk bandwidth ranges from 45 to 150 Mb/s, buffer sizes are such that maximum delays range from 1 to 60 ms, and the number of coder-sources ranges from 15 to 150. Even for the largest systems, the time for analysis is a fraction of a second, while each simulation takes many hours. Thus, the real-time administration of admission control based on our analytic techniques is feasible. >

The importance of long-range dependence of VBR video traffic in ATM traffic engineering: myths and realities

There has been a growing concern about the potential impact of long-term correlations (second-order statistic) in variable-bit-rate (VBR) video traffic on ATM buffer dimensioning. Previous studies have shown that video traffic exhibits long-range dependence (LRD) (Hurst parameter large than 0.5). We investigate the practical implications of LRD in the context of realistic ATM traffic engineering by studying ATM multiplexers of VBR video sources over a range of desirable cell loss rates and buffer sizes (maximum delays). Using results based on large deviations theory, we introduce the notion of Critical Time Scale (CTS). For a given buffer size, link capacity, and the marginal distribution of frame size, the CTS of a VBR video source is defined as the number of frame correlations that contribute to the cell loss rate. In other words, second-order behavior at the time scale beyond the CTS does not significantly affect the network performance. We show that whether the video source model is Markov or has LRD, its CTS is finite, attains a small value for small buffer, and is a non-decreasing function of buffer size. Numerical results show that (i) even in the presence of LRD, long-term correlations do not have significant impact on the cell loss rate; and (ii) short-term correlations have dominant effect on cell loss rate, and therefore, well-designed Markov traffic models are effective for predicting Quality of Service (QOS) of LRD VBR video traffic. Therefore, we conclude that it is unnecessary to capture the long-term correlations of a real-time VBR video source under realistic ATM buffer dimensioning scenarios as far as the cell loss rates and maximum buffer delays are concerned.

Analysis and design of rate-based congestion control of high speed networks, I: stochastic fluid models, access regulation

The paper gives models and analytic techniques for addressing critical issues of the Broadband Integrated Services Digital Network which will use the Asynchronous Transfer Mode. The traffic is expected to be highly bursty and variable at the source and consequently a key issue is admission control. We study a 4-parameter device called a regulator which acts as a policing device as well as a traffic shaper. The device is a generalized leaky bucket with a data buffer, a token buffer supplied by a constant-rate token stream, and a peak rate controller; the outputs of the device are streams of priority and marked cells. The composite system comprising of the source and the regulator is represented in a stochastic fluid model since fluid flow has been found to have properties well matched to the ATM environment, and the Markov Modulated Fluid Source allows bursty characteristics to be accurately modelled. A complete procedure based on spectral expansions for calculating the systems stationary state distribution is given. It is shown that with proper design the regulator effectively controls a three-way trade-off between throughput, delay and burstiness. Numerical results reveal that performance is sensitive to source characteristics such as the squared coefficient of variation of burst and silent periods. The second part of the paper characterizes the output of the regulator. The distributions of the time periods spent in the various states by the output process are calculated exactly. From this an approximate Markovian characterization is obtained. The output streams of priority and marked cells are coupled to capture their correlations. For the simple case of two-state on-off sources, the approximate Markovian characterization of the regulators output rate processes is explicitly given and it is distinguished by the property that all moments are identical to those of the actual processes. With this characterization an original goal of analyzing a composite system of access regulation and statistical multiplexing is separated, decomposed and thereby made tractable.

Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes

Generalized processor sharing (GPS) is the basis for the packet scheduler of choice in IP routers and ATM switches of the future. The currently accepted approach for the design of GPS schedulers is based on deterministic QoS guarantees, which, it is generally accepted, is overly conservative and leads to limitations on capacity. We develop a framework for GPS scheduling which is based on statistical QoS guarantees and statistical multiplexing. We give the design of GPS weights which maximize the coverage of operating points, and also the design of the connection admission control (CAC). The general framework is end-to-end, with two heterogeneous QoS classes coexisting with a third, best effort class. Each QoS class has a specified delay bound together with a bound on the probability of its violation. An important objective is to maximize the bandwidth available to best effort traffic, while just satisfying the guarantees of the QoS classes. To this end, we consider output regulated GPS scheduling, which limits each connections share of the bandwidth to a designed value. The sources are subject to standard dual leaky bucket regulation. For the design of the GPS weights we give procedures based on two key concepts, the realizable set and the critical weights. The realizable set is the union of all admissible sets of connections of both classes over all weights. One of the main contributions is a pragmatic design process by which most of the realizable set is realized by only two critical weights. The numerical results show that there are substantial capacity gains from statistical multiplexing.

Analysis, approximations and admission control of a multi-service multiplexing system with priorities

We consider an ATM system with an architecture which is designed to accommodate users with very different quality of service requirements. Sources which belong to a high priority class share a FCFS buffer, which has priority access to the trunk. A low priority class of sources have a separate FCFS buffer, which receives the residual bandwidth, if any. By administering admission control the service guarantees for both classes may be satisfied. The sources are bursty and stochastic fluid models are used to handle burst-scale congestion effects. We develop simple, fast and robust analytic approximations for the queue distributions in the two buffers. We calculate the admissible set by using our analytic approximations and find that it is reasonably accurate and a conservative approximation to the correct set. The key element in our analysis is a characterization of the output of the high priority buffer as another Markov-modulated fluid source. A refinement to the now well known effective bandwidth approximation is used to calculate buffer content distributions.

Fluid models for the analysis and design of statistical multiplexing with loss priorities on multiple classes of bursty traffic

The authors give the complete solution for a stochastic fluid model of statistical multiplexing with loss priorities in asynchronous transfer mode (ATM)-based broadband ISDN. In this model each Markov modulated fluid source generates priority and marked cell streams which are bursty, mutually correlated, and periodic during bursts. The output of many such sources is buffered and multiplexed for transmission. The loss priority is implemented by selectively discarding marked cells when the buffer content exceeds a threshold level. The equilibrium state distribution exhibits jumps, a feature not existent in prior fluid models. The computational complexity for two-state sources is dominated by a single system of linear equations of dimension equal to twice the number of sources, in particular, the complexity is independent of buffer size. The complete delay distribution for each traffic class is obtained. Numerical results are given. The analysis is generalized to several priority classes of traffic.<<ETX>>

Statistical multiplexing with loss priorities in rate-based congestion control of high-speed networks

Statistical multiplexing with loss priorities is a central element in ATM-based B-ISDN. Cell priorities arise from the marking schemes employed by the access regulators to identify excess cells, which are dropped during periods of congestion, Also, in real time applications, such as hierarchically coded voice and video, cells are assigned priorities which correspond to their importance to service quality, so that when congestion occurs only the least important are dropped. The authors present a stochastic fluid model of statistical multiplexing with loss priorities. Each Markov modulated fluid source generates streams of different priorities. The burstiness of each stream and the correlation between the priority streams are captured in the mode. The loss priority is implemented by selectively discarding cells of certain priority classes when the buffer content exceeds a corresponding threshold. To handle high dimensional source models, the authors develop an algebraic theory for the efficient computation of the spectrum of the statistical multiplexing system, which generalizes previous results for on-off sources. It is shown that to obtain the solution of the statistical multiplexing problem with J priority classes, J different 1-class problems need to be solved, together with a system of linear equations which describe the behavior of the stationary distribution at the thresholds. The numerical results demonstrate the manner in which i) the threshold level controls the tradeoff between delay of higher priority cells and the loss probability of lower priority cells, and ii) the buffer size controls the loss probability of higher priority cells. >