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106
Capacity of Fading Channels with Channel Side Information
, 1997
"... We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencyselective fadi ..."
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Cited by 397 (23 self)
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We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencyselective fading channels. Inverting the channel results in a large capacity penalty in severe fading.
CDMA Uplink Power Control as a Noncooperative Game
, 2002
"... We present a gametheoretic treatment of distributed power control in CDMA wireless systems. ..."
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Cited by 115 (22 self)
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We present a gametheoretic treatment of distributed power control in CDMA wireless systems.
Source Time Scale and Optimal Buffer/Bandwidth Tradeoff for Heterogeneous Regulated Traffic in a Network Node
, 1996
"... In this paper, we study the problem of resource allocation and control for an ATM node with regulated traffic. Both guaranteed lossless service and statistical service with small loss probability are considered. We investigate the relationship between source characteristics and the buffer/bandwidt ..."
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Cited by 61 (3 self)
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In this paper, we study the problem of resource allocation and control for an ATM node with regulated traffic. Both guaranteed lossless service and statistical service with small loss probability are considered. We investigate the relationship between source characteristics and the buffer/bandwidth tradeoff under both services. Our contributions are the following. For guaranteed lossless service, we find that the optimal resource allocation scheme suggests a time scale separation of sources sharing an ATM node with finite bandwidth and buffer space, with the optimal buffer/bandwidth tradeoff determined by the sources' time scale. For statistical service with a small loss probability, we present a new approach for estimating the loss probability in a shared buffer multiplexor with the so called "extremal" onoff, periodic sources. Under this approach, the optimal resource allocation for statistical service is achieved by maximizing both the benefits of buffering sharing and ba...
Efficiencydriven heavytraffic approximations for manyserver queues with abandonments
 Management Science
, 2004
"... Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in ..."
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Cited by 43 (28 self)
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Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in the presence of substantial customer abandonment, callcenter servicelevel agreements (SLA’s) can be met in the ED regime, where the arrival rate exceeds the maximum possible service rate. Mathematically, the ED regime is defined by letting the arrival rate and the number of servers increase together so that the probability of abandonment approaches a positive limit. To obtain the ED regime, it suffices to let the arrival rate and the number of servers increase with the traffic intensity ρ held fixed with ρ> 1 (so that the arrival rate exceeds the maximum possible service rate). Even though the probability of delay necessarily approaches 1 in the ED regime, the ED regime can be realistic because, due to the abandonments, the delays need not be excessively large. This paper establishes ED manyserver heavytraffic limits and develops associated approximations for performance measures in the M/M/s/r + M model, having a Poisson arrival process, exponential service times, s servers, r extra waiting spaces and exponential abandon times (the final +M). In the ED regime, essentially the same limiting behavior occurs when the abandonment rate α approaches 0 as when the number of servers s approaches ∞; indeed, it suffices to assume that s/α → ∞. The ED approximations are shown to be useful by comparing them to exact numerical results for the M/M/s/r + M model obtained using an algorithm developed in Whitt (2003), which exploits numerical transform inversion.
Threshold autoregression with a unit root
 Econometrica
, 2001
"... This paper develops an asymptotic theory of inference for an unrestricted tworegime threshold autoregressive Ž TAR. model with an autoregressive unit root. We find that the asymptotic null distribution of Wald tests for a threshold are nonstandard and different from the stationary case, and suggest ..."
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Cited by 34 (1 self)
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This paper develops an asymptotic theory of inference for an unrestricted tworegime threshold autoregressive Ž TAR. model with an autoregressive unit root. We find that the asymptotic null distribution of Wald tests for a threshold are nonstandard and different from the stationary case, and suggest basing inference on a bootstrap approximation. We also study the asymptotic null distributions of tests for an autoregressive unit root, and find that they are nonstandard and dependent on the presence of a threshold effect. We propose both asymptotic and bootstrapbased tests. These tests and distribution theory allow for the joint consideration of nonlinearity Ž thresholds. and nonstationary Žunit roots.. Our limit theory is based on a new set of tools that combine unit root asymptotics with empirical process methods. We work with a particular twoparameter empirical process that converges weakly to a twoparameter Brownian motion. Our limit distributions involve stochastic integrals with respect to this twoparameter process. This theory is entirely new and may find applications in other contexts. We illustrate the methods with an application to the U.S. monthly unemployment rate. We find strong evidence of a threshold effect. The point estimates suggest that the threshold effect is in the shortrun dynamics, rather than in the dominate root. While the conventional ADF test for a unit root is insignificant, our TAR unit root tests are arguably significant. The evidence is quite strong that the unemployment rate is not a unit root process, and there is considerable evidence that the series is a stationary TAR process.
Forecasting Multifractal Volatility
 Journal of Econometrics
"... This paper develops analytical methods to forecast the distribution of future returns for a new continuoustime process, the Poisson multifractal. The process captures the thick tails, volatility persistence, and moment scaling exhibited by many nancial time series. It can be interpreted as a stocha ..."
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Cited by 29 (4 self)
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This paper develops analytical methods to forecast the distribution of future returns for a new continuoustime process, the Poisson multifractal. The process captures the thick tails, volatility persistence, and moment scaling exhibited by many nancial time series. It can be interpreted as a stochastic volatility model with multiple frequencies and a Markov latent state. We assume for simplicity that the forecaster knows the true generating process with certainty but only observes past returns. The challenge in this environment is long memory and the corresponding innite dimension of the state space. We introduce a discretized version of the model that has a nite state space and an analytical solution to the conditioning problem. As the grid step size goes to zero, the discretized model weakly converges to the continuoustime process, implying the consistency of the density forecasts. JEL Classication: C22; C53; F31 Keywords: Forecasting; Long memory; Multiple frequencies; Stoch...
Continued Fraction Algorithms, Functional Operators, and Structure Constants
, 1996
"... Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2dimensional generalization. This paper surveys the main properties of functional operators,  transfer operat ..."
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Cited by 28 (4 self)
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Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2dimensional generalization. This paper surveys the main properties of functional operators,  transfer operators  due to Ruelle and Mayer (also following Lévy, Kuzmin, Wirsing, Hensley, and others) that describe precisely the dynamics of the continued fraction transformation. Spectral characteristics of transfer operators are shown to have many consequences, like the normal law for logarithms of continuants associated to the basic continued fraction algorithm and a purely analytic estimation of the average number of steps of the Euclidean algorithm. Transfer operators also lead to a complete analysis of the "Hakmem" algorithm for comparing two rational numbers via partial continued fraction expansions and of the "digital tree" algorithm for completely sorting n real numbers by means of ...
Validity of heavy traffic steadystate approximations in open queueing networks
, 2006
"... We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavytraffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic ..."
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Cited by 28 (4 self)
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We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavytraffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic intensity approaches unity. However, barring simple instances, it is still not known whether the stationary distribution of RBM provides a valid approximation for the steadystate of the original network. In this paper we resolve this open problem by proving that the rescaled stationary distribution of the GJN converges to the stationary distribution of the RBM, thus validating a socalled “interchangeoflimits” for this class of networks. Our method of proof involves a combination of Lyapunov function techniques, strong approximations and tail probability bounds that yield tightness of the sequence of stationary distributions of the GJN.
Mellin Transforms and Asymptotics: The Mergesort Recurrence, Acta Informatica
, 1994
"... Abstract. Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divideandconquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard topdown recursive mergesort algorithm, in the average case, as wel ..."
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Cited by 27 (5 self)
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Abstract. Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divideandconquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard topdown recursive mergesort algorithm, in the average case, as well as in the worst and best cases. It also derives the variance and shows that the cost of mergesort has a Gaussian limiting distribution. The approach is applicable to a number of divideandconquer recurrences. Many algorithms are based on a recursive divideandconquer strategy of splitting a problem into two subproblems of equal or almost equal size, separately solving the subproblems, and then knitting their solutions together to find the solution to the original problem. Accordingly, their complexity is expressed by recurrences of the usual divideandconquer form where the initial condition,f, , and the ‘‘knitting costs”, e,, depend on the problem being studied. Typical examples are mergesort, heapsort, Karatsuba’s multiprecision multiplication, discrete Fourier transforms, binomial queues, sorting networks, etc. It is relatively easy to determine general orders of growth for solutions to these recurrences as explained in standard texts, see the “master theorem ” of [6, p. 621. However, a precise asymptotic analysis is often appreciably more delicate. At a more detailed level, divideandconquer recurrences tend to have solutions that involve periodicities, many of which are of a fractal nature. It is our purpose here to discuss the analysis of such periodicity phenomena while focussing on the analysis of the standard topdown recursive mergesort algorithm. For example, as we shall soon see, the average cost of running mergesort on n keys satisfies u (n) = n lg n + nB (lg n) + 0 (n),
Scheduling a multiclass queue with many exponential servers: Asymptotic optimality in heavytraffic,” The Annals of Applied Probability
, 2004
"... We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, line ..."
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Cited by 26 (8 self)
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We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavytraffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n ≈ r + β √ r for some scalar β. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.)