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.

We consider from a thermodynamic viewpoint queueing systems where the workload process is assumed to have an associated large deviation principle with arbitrary scaling: there exist increasing scaling functions (a t ; v t ; t 2 R+ ) and a rate function I such that if (W t ; t 2 R+ ) denotes the workload process, then lim t!1 v \Gamma1 t log P (W t =a t ? w) = \GammaI (w) on the continuity set of I . In the case that a t = v t = t it has been argued heuristically, and recently proved in a fairly general context (for discrete time models) by Glynn and Whitt [8], that the queue-length distribution (that is, the distribution of supremum of the workload process Q = sup t0 W t ) decays exponentially: P (Q ? b) ¸ e \Gammaffib and the decay rate ffi is directly related to the rate function I . We establish conditions for a more general result to hold, where the scaling functions are not necessarily linear in t: we find that the queue-length distribution has an exponential tail only if l...

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

Variable bit-rate (VBR) compressed video traffic is expected to be a significant component of the traffic mix in integrated services networks. This traffic is hard to manage because it has strict delay and loss requirements while simultaneously exhibiting burstiness at multiple time scales. We show that burstiness over long time scales, in conjunction with resource reservation using one-shot traffic descriptors, can substantially degrade the loss rate, end-to-end delay, and statistical multiplexing gain of a connection. We use large-deviation theory to model the performance of multiple time-scale traffic and to motivate the design of renegotiated constant bit rate (RCBR) service. Sources using

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.

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...

In this paper, we develop bounds on the individual session backlog and delay distribution under the Generalized Processor Sharing (GPS) scheduling discipline . This work is motivated by, and is an extension of, Parekh and Gallager 's deterministic study of the GPS scheduling discipline with leaky-bucket token controlled sessions [15], [16]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in [18] as a source traffic characterization, we establish results that extend the deterministic study of GPS: for a single GPS server in isolation, we present statistical bounds on the distributions of backlog and delay for each session. In the network setting, we show that networks belonging to a broad class of GPS assignments, the socalled Consistent Relative Session Treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the distribution of backlog and delay for each session in a Rate Proportional Processor Sharin...

We formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. We derive network's adjustment scheme and users' decision rule and establish their optimality. Since our approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network. 1 I...

Even though ATM seems to be clearly the wave of the future, one performance analysis indicates that the combination of stringent performance requirements (e.g., 10 - 9 cell blocking probabilities), moderate-size buffers and highly bursty traffic will require that the utilization of the network be quite low. That performance analysis is based on asymptotic decay rates of steady-state distributions used to develop a concept of effective bandwidths for connection admission control. However, we have developed an exact numerical algorithm that shows that the effective-bandwidth approximation can overestimate the target small blocking probabilities by several orders of magnitude when there are many sources that are more bursty than Poisson. The bad news is that the appealing simple connection-admissioncontrol algorithm using effective bandwidths based solely on tailprobability asymptotic decay rates may actually not be as effective as many have hoped. The good news is that the statistical multiplexing gain on ATM networks may actually be higher than some have feared. For one example, thought to be realistic, our analysis indicates that the network actually can support twice as many sources as predicted by the effectivebandwidth approximation. That discrepancy occurs because for a large number of bursty sources the asymptotic constant in the tail probability exponential asymptote is extremely small. That in turn can be explained by the observation that the asymptotic constant decays exponentially in the number of sources when the sources are scaled to keep the total arrival rate fixed. We also show that the effective-bandwidth approximation is not always conservative. Specifically, for sources less bursty than Poisson, the asymptotic constant grows exponentially in the numbe...