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74
Effective Bandwidths for Multiclass Markov Fluids and Other ATM Sources
, 1993
"... 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 l ..."
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Cited by 236 (17 self)
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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 circuitswitched 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.
Notes on Effective Bandwidths
, 1996
"... 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 unde ..."
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Cited by 157 (4 self)
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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.
Buffer Overflow Asymptotics For A Buffer Handling Many Traffic Sources
 Journal of Applied Probability
, 1995
"... 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 ..."
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Cited by 79 (0 self)
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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 timedependent 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...
Resource Management in WideArea ATM Networks using Effective Bandwidths
 IEEE J. SELECT. AREAS COMMUN
, 1995
"... This paper is principally concerned with resource allocation for connections tolerating statistical qualityof service (QoS) guarantees in a public widearea ATM network. Our aim is to sketch a framework, based on effective bandwidths, for call admission schemes that are sensitivetoindividual QoS r ..."
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Cited by 71 (3 self)
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This paper is principally concerned with resource allocation for connections tolerating statistical qualityof service (QoS) guarantees in a public widearea ATM network. Our aim is to sketch a framework, based on effective bandwidths, for call admission schemes that are sensitivetoindividual QoS requirements and account for statistical multiplexing. We begin by describing recent results approximating the effective bandwidth required by heterogeneous streams sharing buffered 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 inputoutput properties of queues. Based on these results we claim that networks with sufficient routing diversity will inherently satisfy nodal decoupling. We then discuss online methods for estimating the effective bandwidth of a connection. Using this type of traffic monitoring we propose an approach to usage parameter ...
Allocating Bandwidth for Bursty Connections
 SIAM J. Comput
, 1997
"... 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 highspeed networks, individual connections (i.e., communication sessions) are very bursty, wit ..."
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Cited by 66 (0 self)
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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 highspeed 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 binpacking, 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
Decoupling bandwidths for networks: A decomposition approach to resource management for networks
 In Proceedings of INFOCOM’94, IEEE
, 1994
"... We consider large buffer asymptotics for feedforward networks of discretetime 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 su ..."
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Cited by 63 (3 self)
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We consider large buffer asymptotics for feedforward networks of discretetime 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
Charging and Accounting for Bursty Connections
 Internet Economics
, 1996
"... Statistical sharing over several timescales is a key feature of the Internet, and is likely to be an essential aspect of future ATM networks. ..."
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Cited by 60 (5 self)
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Statistical sharing over several timescales is a key feature of the Internet, and is likely to be an essential aspect of future ATM networks.
Sample Path Large Deviations and Intree Networks
 Queueing Systems
, 1994
"... 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 distri ..."
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Cited by 43 (8 self)
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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.
Effective Bandwidths for Stationary Sources
, 1995
"... At a buffered switch in an ATM (asynchronous transfer mode) network it is important to know what combinations of different types of traffic can be carried simultaneously without risking more than a very small probability of overflowing the buffer. We show that a simple and serviceable measure of eff ..."
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Cited by 38 (7 self)
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At a buffered switch in an ATM (asynchronous transfer mode) network it is important to know what combinations of different types of traffic can be carried simultaneously without risking more than a very small probability of overflowing the buffer. We show that a simple and serviceable measure of effective bandwidths may be computed for stationary traffic sources. For large buffers the effective bandwidth of a source is a function only of its mean rate, index of dispersion and the size of the buffer. Keywords: communications, effective bandwidths, large deviations, stationary processes 1 Effective bandwidths The traffic in an ATM network is packaged in cells and carried over links between switches in the network. Traffic sources are bursty and so for periods of time cells may arrive at a switch faster than they can be switched to output links. For this reason, switches are buffered and the problem is to know how much total total traffic can be carried while keeping the probability of b...
On the relevance of time scales in performance oriented traffic characterizations
 In IEEE INFOCOM’96
, 1996
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