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25
Effective bandwidths with priorities
 IEEE/ACM Transactions on Networking
, 1998
"... Abstract — The notion of effective bandwidths has provided a useful practical framework for connection admission control and capacity planning in highspeed communication networks. The associated admissible set with a single linear boundary makes it possible to apply stochasticlossnetwork (general ..."
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Cited by 51 (1 self)
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Abstract — The notion of effective bandwidths has provided a useful practical framework for connection admission control and capacity planning in highspeed communication networks. The associated admissible set with a single linear boundary makes it possible to apply stochasticlossnetwork (generalizedErlang) models for capacity planning. In this paper we consider the case of network nodes that use a priorityservice discipline to support multiple classes of service, and we wish to determine an appropriate notion of effective bandwidths. Just as was done previously for the firstin firstout discipline, we use largebuffer asymptotics (large deviations principles) for workload tail probabilities as a theoretical basis. We let each priority class have its own buffer and its own constraint on the probability of buffer overflow. Unfortunately, however, this leads to a constraint for each priority class. Moreover, the largebuffer asymptotic theory with priority classes does not produce an admissible set with linear boundaries, but we show that it nearly does and that a natural bound on the admissible set does have this property. We propose it as an approximation for priority classes. Then there is one linear constraint for each priority class. This linearadmissibleset structure implies a new notion of effective bandwidths, where a given connection is associated with multiple effective bandwidths: one for the priority level of the given connection and one for each lower priority level. This structure can be used regardless of whether the individual effective bandwidths are determined by largebuffer asymptotics or by some other method. 1
AN INTRODUCTION TO NUMERICAL TRANSFORM INVERSION AND ITS APPLICATION TO PROBABILITY MODELS
, 1999
"... ..."
On the Laguerre method for numerically inverting Laplace transforms
 INFORMS Journal on Computing
, 1996
"... The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 TricomiWidder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coeff ..."
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Cited by 42 (7 self)
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The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 TricomiWidder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coefficients of a generating function constructed from the Laplace transform using a bilinear transformation. We present a new variant of the Laguerre method based on: (1) using our previously developed variant of the Fourierseries method to calculate the coefficients of the Laguerre generating function, (2) developing systematic methods for scaling, and (3) using Wynn’s ɛalgorithm to accelerate convergence of the Laguerre series when the Laguerre coefficients do not converge to zero geometrically fast. These contributions significantly expand the class of transforms that can be effectively inverted by the Laguerre method. We provide insight into the slow convergence of the Laguerre coefficients as well as propose a remedy. Before acceleration, the rate of convergence can often be determined from the Laplace transform by applying Darboux’s theorem. Even when the Laguerre coefficients converge to zero geometrically fast, it can be difficult to calculate the desired functions for large arguments because of roundoff errors. We solve this problem by calculating very small Laguerre coefficients with low relative error through appropriate scaling. We also develop another acceleration technique for the case in which the Laguerre coefficients converge to zero geometrically fast. We illustrate the effectiveness of our algorithm through numerical examples. Subject classifications: Mathematics, functions: Laplace transforms. Probability, distributions: calculation by transform inversion. Queues, algorithms: Laplace transform inversion.
Efficiently providing multiple grades of service with protection against overloads in shared resources
 AT&T Technical Journal
, 1995
"... Field of the Invention The invention relates to efficiently providing multiple grades of service, including protection against overloads, for multiple customers sharing limited resources, wherein "efficiently providing " includes (i) determining when a prospective new customer can ..."
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Cited by 28 (11 self)
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Field of the Invention The invention relates to efficiently providing multiple grades of service, including protection against overloads, for multiple customers sharing limited resources, wherein &quot;efficiently providing &quot; includes (i) determining when a prospective new customer can be admitted with a desired grade of service, (ii) determining how to adjust capacity in face of changing customer demand and (iii) determining how to respond to resource failure. Background of the Invention 1. ResourceSharing Problems The setting involves one or more resources, each containing multiple resource units which provide service to multiple customers. Each customer is a source of a stream of requests. Each customer request requires a number of units from each resource, which may be zero, one or greater than one, and may be different for different customers, but which is the same for different requests of the same customer. If all requirements can be met upon arrival of a new request, then the new request is admitted, and all required resource units are held throughout the request holding time. Otherwise, the request is not admitted, and is said to be blocked.
Prioritized Resource Allocation for Stressed Networks
 IEEE/ACM Transactions on Networking
, 2001
"... AbstractOverloads that occur during times of network stress result in blocked access to all users, independent of importance. These overloads can occur because of degraded resource availability or abnormally high demand. Public broadband networks must dynamically recognize some multimedia connectio ..."
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Cited by 25 (12 self)
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AbstractOverloads that occur during times of network stress result in blocked access to all users, independent of importance. These overloads can occur because of degraded resource availability or abnormally high demand. Public broadband networks must dynamically recognize some multimedia connections as having greater importance than others and allocate resources accordingly. A new approach to connection admission control is proposed that uses an upper limit policy to optimize the admission of connections based on the weighted sum of blocking across traffic classes. This results in a simple algorithm suitable for multimedia and packet networks. This work is also the first to demonstrate that the use of an upper limit policy is superior to traditional approaches of adding extra capacity or partitioning capacity, both in terms of the amount of resources required and sensitivity to load variations. An upper limit policy can also be deployed much faster when a large overload occurs from a disaster event. I.
An inversion algorithm to compute blocking probabilities in loss networks with statedependent rates
 IEEE/ACM Trans. Networking
, 1995
"... Abstract — We extend our recently developed algorithm for computing (exact) steadystate blocking probabilities for each class in productform loss networks to cover general statedependent arrival and service rates. This generalization allows us to consider, for the first time, a wide variety of bu ..."
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Cited by 20 (7 self)
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Abstract — We extend our recently developed algorithm for computing (exact) steadystate blocking probabilities for each class in productform loss networks to cover general statedependent arrival and service rates. This generalization allows us to consider, for the first time, a wide variety of buffered and unbuffered resourcesharing models with nonPoisson traffic, as may arise with overflows in the context of alternative routing. As before, we consider noncompletesharing policies involving upperlimit and guaranteedminimum bounds for the different classes, but here we consider both bounds simultaneously. These bounds are important for providing different grades of service with protection against overloads by other classes. Our algorithm is based on numerically inverting the generating function of the normalization constant, which we derive here. Major features of the algorithm are: dimension reduction by elimination of nonbinding resources and by conditional decomposition based on special structure, an effective scaling algorithm to control errors in the inversion, efficient treatment of multiple classes with identical parameters and truncation of large sums. We show that the computational complexity of our inversion approach is usually significantly lower than the alternative recursive approach. 1
Loss networks and Markov random fields
 Journal of Applied Probability
, 1999
"... This paper examines the connection between loss networks without controls and Markov random field theory. The approach taken yields insight into the structure and computation of network equilibrium distributions, and into the nature of spatial dependence in networks. In addition, it provides further ..."
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Cited by 20 (4 self)
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This paper examines the connection between loss networks without controls and Markov random field theory. The approach taken yields insight into the structure and computation of network equilibrium distributions, and into the nature of spatial dependence in networks. In addition, it provides further insight into some commonly used approximations, enables the development of more refined approximations, and permits the derivation of some asymptotically exact results. 1
Calculating Normalization Constants of Closed Queueing Networks by Numerically Inverting Their Generating Functions
 J. ACM
, 1995
"... A new algorithm is developed for calculating normalization constants (partition functions) and moments of productform steadystate distributions of closed queueing networks and related models. The essential idea is to numerically invert the generating function of the normalization constant and rela ..."
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Cited by 12 (7 self)
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A new algorithm is developed for calculating normalization constants (partition functions) and moments of productform steadystate distributions of closed queueing networks and related models. The essential idea is to numerically invert the generating function of the normalization constant and related generating functions appearing in expressions for the moments. It is known that the generating function of the normalization constant often has a remarkably simple form, but numerical inversion evidently has not been considered before. For pdimensional transforms, as occur with queueing networks having p closed chains, the algorithm recursively performs p onedimensional inversions. The required computation grows exponentially in the dimension, but the dimension can often be reduced by exploiting conditional decomposition based on special structure. For large populations, the inversion algorithm is made more efficient by computing large sums using Euler summation. The inversion algorithm also has a very low storage requirement. A key ingredient in the inversion algorithm is scaling. An effective static scaling is developed for multichain closed queueing networks with only singleserver and (optionally) infiniteserver queues. An important feature of the inversion algorithm is a selfcontained accuracy check, which allows the results to be verified in the absence of alternative algorithms. Key words and phrases: performance analysis, closed queueing networks, productform model, normalization constant, partition function, generating function, numerical transform inversion, scaling, dimension reduction, Euler summation. 1.
An Analysis of the Effects of Mobility on Bandwidth Allocation Strategies in MultiClass Cellular Wireless Networks
, 2001
"... In this paper we present a multicell analytic model for multiclass cellular networks. We investigate the effects subscriber mobility has on bandwidth control strategies when the network supports multiple classes of subscribers having different bandwidth requirements. We introduce control strategie ..."
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Cited by 8 (0 self)
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In this paper we present a multicell analytic model for multiclass cellular networks. We investigate the effects subscriber mobility has on bandwidth control strategies when the network supports multiple classes of subscribers having different bandwidth requirements. We introduce control strategies from nonmobile networks and examine them in a mobile environment. The expressions for call blocking using these control strategies have product form solutions. This allows us to develop a multicell, multiclass, model by generalizing on the Erlang fixed point approximation using generalized multirate, multiclass, Erlang loss formulas for each class of traffic. We produce expressions for originating calls lost, handoff calls lost, forcedtermination, and mean channel occupancy for each class of traffic in each cell for different control strategies. The multicell analytic model allows us to investigate the effects of asymmetric loads and mobility patterns in the network. The analytic results are supported by simulation. Keywords Cellular networks, multiclass, mobility, bandwidth sharing I.
ResourceSharing Models with StateDependent Arrivals of Batches
 Computations with Markov Chains
, 1995
"... We recently developed a new algorithm for calculating the blocking probability of each class in resourcesharing models with upper limit and guaranteed minimum sharing policies as well as the standard completesharing policy. These models may have multiple resources and multiple classes, with each c ..."
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Cited by 5 (3 self)
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We recently developed a new algorithm for calculating the blocking probability of each class in resourcesharing models with upper limit and guaranteed minimum sharing policies as well as the standard completesharing policy. These models may have multiple resources and multiple classes, with each class requiring multiple units from each resource. These models may also have statedependent arrival and service rates. Our new algorithm is based on calculating normalization constants appearing in the productform steadystate distributions by numerically inverting their generating functions. In the present paper we provide the basis for extending the algorithm to resourcesharing models with batch arrival processes. The batch sizes are mutually independent random variables with distributions depending on the class. We show that the steadystate distribution of the resourcesharing model has a product form for both completebatch blocking and partialbatch blocking, and we derive the generating functions of the normalization constants for partialbatch blocking. We primarily focus on the BernoulliPoissonPascal (BPP) special case in which the batches have linear statedependent arrival rates, which includes finitesource inputs and Poisson inputs for the batches as special cases. With