Absfruct- The emerging high-speed networks, notably the ATM-based Broadband ISDN, are expected to integrate through statistical multiplexing large numbers of traffic sources having a broad range of burstiness characteristics. A prime instrument for controlling congestion in the network is admission control, which limits calls and guarantees a grade of service determined by delay and loss probability in the multiplexer. We show, for general Markovian traffic sources, that it is possible to assign a notional effective bandwidth to each source which is an explicitly identi-fied, 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 which is directly obtained from the source characteristics and the admission criterion, and for several sources it is simply additive. We consider both fluid and point process models and obtain parallel results. 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. Also, the bandwidth-reducing properties of the Leaky Bucket regulator are exhibited numerically. For a source model of video teleconferencing due to Heyman et al. with a large number of states, the effective bandwidth is easily computed. The equivalent bandwidth is bounded by the peak and mean source rates, and is monotonic and concave with respect to a parameter of the admission criterion. Coupling of state transitions of two related asynchronous sources always increases their effective bandwidth. 1.

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We show the existence of effective bandwidths for multiclass Markov fluids and other types of sources that are used to model ATM traffic. More precisely,we show that when such sources share a buffer with deterministic service rate, a constraint on the tail of the buffer occupancy distribution is a linear constraint on the number of sources. That is, for a small loss probability one can assume that each source transmits at a fixed rate called its effective bandwidth. When traffic parameters are known, effective bandwidths can be calculated and may be used to obtain a circuit-switched style call acceptance and routing algorithm for ATM networks. The important feature of the effective bandwidth of a source is that it is a characteristic of that source and the acceptable loss probability only.Thus, the effective bandwidth of a source does not depend on the number of sources sharing the buffer nor on the model parameters of other types of sources sharing the buffer.

Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate `. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and minimum envelope rate with respect to `. Based on these two new notions of traffic characterization, we develop a set of rules for network operations such as superposition, input-output relation of a single queue, and routing. Specifically, we show that (i) the MER of a superposition process is less than or equal to the sum of the MER of each process, (ii) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, (iii) the MER of a departure process from a stable queue is less than or equal to that of the input process (iv) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to ` under a further assumption of independence. These rules provide a natural way to analyze feedforward networks with multiple classes of customers. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the FCFS policy. Moreover, when restricting to the family of two-state Markov modulated arrival processes, the notion of MER with respect to ` is shown to be

Abstract-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 requiring 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 approx-imations; however, admission decisions based on this work are expected to be less overly conservative than decisions based on alternative approaches. I.

This paper presents a personal view of work to date on effective bandwidths, emphasising the unifying role of the concept: as a summary of the statistical characteristics of sources over different time and space scales; in bounds, limits and approximations for various models of multiplexing under quality of service constraints; and as the basis for simple and robust tariffing and connection acceptance control mechanisms for poorly characterized traffic. The framework assumes only stationarity of sources, and illustrative examples include periodic streams, fractional Brownian input, policed and shaped sources, and deterministic multiplexing.

The algorithms described in this thesis are designed to schedule cells in a very high-speed, parallel, input-queued crossbar switch. We present several novel scheduling algorithms that we have devised, each aims to match the set of inputs of an input-queued switch to the set of outputs more efficiently, fairly and quickly than existing techniques. In Chapter 2 we present the simplest and fastest of these algorithms: SLIP --- a parallel algorithm that uses rotating priority ("round-robin") arbitration. SLIP is simple: it is readily implemented in hardware and can operate at high speed. SLIP has high performance: for uniform i.i.d. Bernoulli arrivals, SLIP is stable for any admissible load, because the arbiters tend to desynchronize. We present analytical results to model this behavior. However, SLIP is not always stable and is not always monotonic: adding more traffic can actually make the algorithm operate more efficiently. We present an approximate analytical model of this behavior. SLIP prevents starvation: all contending inputs are eventually served. We present simulation results, indicating SLIP's performance. We argue that SLIP can be readily implemented for a 32x32 switch on a single chip. In Chapter 3 we present i-SLIP, an iterative algorithm that improves upon SLIP by converging on a maximal size match. The performance of i-SLIP improves with up to log 2 N iterations. We show that although it has a longer running time than SLIP, an i-SLIP scheduler is little more complex to implement. In Chapter 4 we describe maximum or maximal weight matching algorithms based on the occupancy of queues, or waiting times of cells. These algorithms are stabl...

We analyse the queue Q L at a multiplexer with L inputs. We obtain a large deviation result, namely that under very general conditions lim L!1 L \Gamma1 log P[Q L ? Lb] = \GammaI (b) provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. This provides an improvement on the usual effective bandwidth approximation P[Q L ? b] e \Gammaffib , replacing it with P[Q L ? b] e \GammaLI(b=L) . The difference I(b) \Gamma ffi b determines the economies of scale which are to be obtained in large multiplexers. If the limit = \Gamma lim t!1 t t (ffi) exists (here t is the finite time cumulant of the workload process) then lim b!1 (I(b) \Gamma ffi b) = . We apply this idea to a number of examples of arrivals processes: heterogeneous superpositions, Gaussian processes, Markovian additive processes and Poisson processes. We obtain expressions for in these cases. is zero for independent arrivals, but positive for arrivals with positive correlations. Thus economies of scale are obtainable for highly bursty traffic expected in ATM multiplexing.

This paper, together with [1] and [2], opens a new window for the study of queueing performance in a richer, heterogeneous input environment. It offers a unique way to understand the effect of second- and higher-order input statistics on queues, and develops new concepts of traffic measurement, network control and resource allocation for high speed networks in the frequency domain. The technique developed in this paper applies to the analysis of queue response to the individual effects of input power spectrum, bispectrum, trispectrum, and input rate steady state distribution. Our study provides clear evidence that of the four input statistics, the input power spectrum is most essential to queueing analysis. Furthermore, input power in the lowfrequency band has a dominant impact on queueing performance, whereas high-frequency power to a large extent can be neglected. The research reported here was supported by NSF under grant NCR-9015757 and by Texas Advanced Research Program under gr...

In networks that support Quality of Service (QoS), an admission control algorithm determines whether or not a new traffic flow can be admitted to the network such that all users will receive their required performance. Such an algorithm is a key component of future multi-service networks as it determines the extent to which network resources are utilized and whether the promised QoS parameters are actually delivered. Our goals in this paper are threefold. First, we describe and classify a broad set of proposed admission control algorithms. Second, we evaluate the accuracy of these algorithms via experiments using both on-off sources and long traces of compressed video; we compare the admissible regions and QoS parameters predicted by our implementations of the algorithms with those obtained from trace-driven simulations. Finally, we identify the key aspects of an admission control algorithm necessary for achieving a high degree of accuracy and hence a high statistical multiplexing gain...