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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 187 (14 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.
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 60 (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 ...
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 40 (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 Bandwidth in High Speed Digital Networks
 IEEE Journal on Selected Areas in Communications
, 1999
"... The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theor ..."
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Cited by 18 (5 self)
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The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. This includes (i) identification of the appropriate energy function, entropy function and effective bandwidth function of a source, (ii) the calculus of the effective bandwidth functions, (iii) bandwidth allocation and buffer management, (iv) traffic descriptors, and (v) envelope processes and conjugate processes for fast simulations and bounds.
Computable Exponential Bounds for Intree Networks with Routing
 Proc. INFOCOM'95
, 1995
"... In this paper, we re ne the calculus proposed in [5, 8, 9]. The new calculus, including network operations for multiplexing, inputoutput relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular ..."
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Cited by 9 (1 self)
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In this paper, we re ne the calculus proposed in [5, 8, 9]. The new calculus, including network operations for multiplexing, inputoutput relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above by the sum of a constant and an Erlang random variable. The decay rate of the Erlang random variable is not greater than ( in some cases equal to) the decay rate of the tail distribution of the stationary queue length. The number of stages of the Erlang random variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper bounds are derived.