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.

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.

This paper is principally concerned with resource allocation for connections tolerating statistical qualityof service #QoS# guarantees in a public wide-area ATM network. Our aim is to sketch a framework, based on e#ective bandwidths, for call admission schemes that are sensitivetoindividual QoS requirements and account for statistical multiplexing. We begin by describing recent results approximating the e#ective bandwidth required by heterogeneous streams sharing bu#ered links, including results for the packetized generalized processor sharing service discipline. Extensions to networks follow via the concept of decoupling bandwidths - motivated by a study of the input-output properties of queues. Based on these results we claim that networks with su#cient routing diversity will inherently satisfy nodal decoupling. We then discuss on-line methods for estimating the e#ective bandwidth of a connection. Using this type of tra#c monitoring we propose an approach to usage parameter ...

We consider large buffer asymptotics for feed-forward networks of discrete-time queues with deterministic service rate shared by multiple classes of streams subject to work conserving service policies. First we review the concept of effective bandwidths for traffic streams sharing a common buffer subject to subject to tail constraints on the workload distribution. Next, we obtain the effective bandwidth of the departure process from such a queue, proving that in fact the effective bandwidth of the output is at worst equal to that of the input, and depending on the service rate, strictly less than that of the input. We then define the notion of a decoupling bandwidth and the associated constraints, guaranteeing that asymptotics within the network are decoupled. These results provide a framework for call admission schemes which are sensitive to constraints on the tail distribution of the workload or approximate cell loss probabilities. Our results require relatively weak assumptions on both the traffic streams and service policies. We consider the problem of “optimal ” traffic shaping (via buffering) subject to a loss constraint. Finally, we discuss our results in the context of resource management for ATM networks. 1

Statistical sharing over several time-scales is a key feature of the Internet, and is likely to be an essential aspect of future ATM networks.

As a model for an ATM switch we consider the overflow frequency of a queue that is served at a constant rate and in which the arrival process is the superposition of N traffic streams. We consider an asymptotic as N !1 in which the service rate Nc and buffer size Nb also increase linearly in N . In this regime, the frequency of buffer overflow is approximately exp(\GammaN I(c; b)), where I(c; b) is given by the solution to an optimization problem posed in terms of time-dependent logarithmic moment generating functions. Experimental results for Gaussian and Markov modulated fluid source models show that this asymptotic provides a better estimate of the frequency of buffer overflow than ones based on large buffer asymptotics. ATM SWITCHES; BUFFER OVERFLOW ASYMPTOTICS; EFFECTIVE BANDWIDTHS; LARGE DEVIATIONS; MARKOV MODULATED FLUID AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60K30, SECONDARY 60F10, 60K25, 68M20, 90B10, 90B22 1. Switches handling many bursty sources In a high speed data com...

Abstract. In this paper, we undertake the first study of statistical multiplexing from the perspective of approximation algorithms. The basic issue underlying statistical multiplexing is the following: in high-speed networks, individual connections (i.e., communication sessions) are very bursty, with transmission rates that vary greatly over time. As such, the problem of packing multiple connections together on a link becomes more subtle than in the case when each connection is assumed to have a fixed demand. We consider one of the most commonly studied models in this domain: that of two communicating nodes connected by a set of parallel edges, where the rate of each connection between them is a random variable. We consider three related problems: (1) stochastic load balancing, (2) stochastic bin-packing, and (3) stochastic knapsack. In the first problem the number of links is given and we want to minimize the expected value of the maximum load. In the other two problems the link capacity and an allowed overflow probability p are given, and the objective is to assign connections to links, so that the probability that the load of a link exceeds the link capacity is at most p. In binpacking we need to assign each connection to a link using as few links as possible. In the knapsack problem each connection has a value, and we have only one link. The problem is to accept as many

Using the contraction principle, in this paper we derive a set of closure properties for sample path large deviations. These properties include sum, reduction, composition and reflection mapping. Using these properties, we show that the exponential decay rates of the steady state queue length distributions in an intree network with routing can be derived by a set of recursive equations. The solution of this set of equations is related to the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. We also prove a conditional limit theorem that illustrates how a queue builds up in an intree network.

The technology is nearly available to offer remarkably powerful new communications services: multiple streams, from multiple users, composed of different applications that require different qualities of service (QoS), all travelling over a single interconnected physical infrastructure. Society will benefit from integrated applications (video conferencing with interactive demos and shared whiteboards; computer-integrated telephony, &c.), and from increased access to information resources: access by more people, more of the time, from more places. However, as long as the laws of thermodynamics hold, the resources on which these systems are built will not be free. Efficient use of advanced networks requires a rational mechanism for allocating the scarce resources to the rapidly growing number of users and service types. Allocation in a multiple quality of service network may be the single greatest barrier to communications “anytime, anywhere”. In this paper I present a fairly general model of the problem, and, after showing that a decentralized open market will fail, I propose a mechanism for solving the problem. Historical information networks have been based on separate physical networks for each major class of service. Different wires or segments of the spectrum were used for telephony, cable and broadcast TV, telegraph, paging, data. We now appear to be in an era of dramatic change in the

We prove asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with only two queues needs special attention, as under this case, it is shown that the upper bounds and lower bounds match, thus yielding exact bounds. This result is established in this part (Part I) of the paper. The general case is much more complicated, and is treated separately in Part II of the paper [42], where tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of GPS scheduling. The proofs use sample-path large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for high-speed communication networks. 1 Int...