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Sum capacity of the vector Gaussian broadcast channel and uplinkdownlink duality
 IEEE Trans. on Inform. Theory
, 1912
"... We characterize the sum capacity of the vector Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate fourway connection between the vector broadcast channel, the corresponding pointtopo ..."
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Cited by 175 (2 self)
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We characterize the sum capacity of the vector Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate fourway connection between the vector broadcast channel, the corresponding pointtopoint channel (where the receivers can cooperate), the multiple access channel (where the role of transmitters and receivers are reversed), and the corresponding pointtopoint channel (where the transmitters can cooperate). 1
Stochastic Power Control for Cellular Radio Systems
 IEEE Trans. Commun
, 1997
"... For wireless communication systems, iterative power control algorithms have been proposed to minimize transmitter powers while maintaining reliable communication between mobiles and base stations. To derive deterministic convergence results, these algorithms require perfect measurements of one or mo ..."
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Cited by 89 (8 self)
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For wireless communication systems, iterative power control algorithms have been proposed to minimize transmitter powers while maintaining reliable communication between mobiles and base stations. To derive deterministic convergence results, these algorithms require perfect measurements of one or more of the following parameters: (i) the mobile's signal to interference ratio (SIR) at the receiver, (ii) the interference experienced by the mobile, and (iii) the bit error rate. However, these quantities are often difficult to measure and deterministic convergence results neglect the effect of stochastic measurements. In this work, we develop distributed iterative power control algorithms that use readily available measurements. Two classes of power control algorithms are proposed. Since the measurements are random, the proposed algorithms evolve stochastically and we define the convergence in terms of the mean squared error (MSE) of the power vector from the optimal power vector that is t...
Optimal Sequences, Power Control, and User Capacity of Synchronous CDMA Systems with Linear MMSE Multiuser Receivers
 IEEE TRANS. INFORM. THEORY
, 1999
"... There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spreadspectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjuncti ..."
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Cited by 78 (5 self)
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There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spreadspectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (SCDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its qualityofservice (QoS) requirement (expressed in terms of its desired signaltointerference ratio) met. Our characterization allows us to describe the user capacity through a simple effective bandwidth characterization: Users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity.
Stability of continuoustime distributed consensus algorithms
, 2004
"... We study the stability properties of linear timevarying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibri ..."
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Cited by 51 (0 self)
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We study the stability properties of linear timevarying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the offdiagonal terms in the differential equation.
Asymptotics for steadystate tail probabilities in structured Markov queueing models
 Commun. Statist.Stoch. Mod
, 1994
"... In this paper we establish asymptotics for the basic steadystate distributions in a large class of singleserver queues. We consider the waiting time, the workload (virtual waiting time) and the steadystate queue lengths at an arbitrary time, just before an arrival and just after a departure. We s ..."
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Cited by 38 (10 self)
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In this paper we establish asymptotics for the basic steadystate distributions in a large class of singleserver queues. We consider the waiting time, the workload (virtual waiting time) and the steadystate queue lengths at an arbitrary time, just before an arrival and just after a departure. We start by establishing asymptotics for steadystate distributions of Markov chains of M/GI/1 type. Then we treat steadystate distributions in the BMAP/GI/1 queue, which has a batch Markovian arrival process (BMAP). The BMAP is equivalent to the versatile Markovian point process or Neuts (N) process; it generalizes the Markovian arrival process (MAP) by allowing batch arrivals. The MAP includes the Markovmodulated Poisson process (MMPP), the phasetype renewal process (PH) and independent superpositions of these as special cases. We also establish asymptotics for steadystate distributions in the MAP/MSP/1 queue, which has a Markovian service process (MSP). The MSP is a MAP independent of the arrival process generating service completions during the time the server is busy. In great generality (but not always), the basic steadystate distributions have asymptotically exponential tails in all these models. When they do, the asymptotic parameters of the different distributions are closely related. 1.
A necessary and sufficient condition for consensus over random networks
 IEEE Transactions on Automatic Control
, 2008
"... Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuoustime stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discre ..."
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Cited by 20 (2 self)
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Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuoustime stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discretetime case, our assumption is that the underlying graph of the system at any given time instance is derived from a random graph process, independent of other time instances. These graphs can be weighted, directed and with dependent edges. For the continuoustime case, we assume that the switching is governed by a Poisson point process and the graphs characterizing the topology of the system are independent and identically distributed over time. For both such frameworks, we present necessary and sufficient conditions for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. These easily verifiable conditions depend on the spectrum of the average weight matrix and the average Laplacian matrix for the discretetime and continuoustime cases, respectively. I.
Heavytraffic asymptotic expansions for the asymptotic decay rates
 in the BMAP/G/1 queue. Stochastic Models
, 1994
"... versatile Markovian point process, tail probabilities in queues, asymptotic decay rate, PerronFrobenius eigenvalue, asymptotic expansion, caudal characteristic curve, heavy traffic In great generality, the basic steadystate distributions in the BMAP / G /1 queue have asymptotically exponential tai ..."
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Cited by 15 (10 self)
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versatile Markovian point process, tail probabilities in queues, asymptotic decay rate, PerronFrobenius eigenvalue, asymptotic expansion, caudal characteristic curve, heavy traffic In great generality, the basic steadystate distributions in the BMAP / G /1 queue have asymptotically exponential tails. Here we develop asymptotic expansions for the asymptotic decay rates of these tail probabilities in powers of one minus the traffic intensity. The first term coincides with the decay rate of the exponential distribution arising in the standard heavytraffic limit. The coefficients of these heavytraffic expansions depend on the moments of the servicetime distribution and the derivatives of the PerronFrobenius eigenvalue δ(z) of the BMAP matrix generating function D(z) at z = 1. We give recursive formulas for the derivatives δ (k) ( 1). The asymptotic expansions provide the basis for efficiently computing the asymptotic decay rates as functions of the traffic intensity, i.e., the caudal characteristic curves. The asymptotic expansions also reveal what features of the model the asymptotic decay rates primarily depend upon. In particular, δ(z) coincides with the limiting timeaverage of the factorial cumulant generating function (the logarithm of the generating function) of the arrival counting process, and the derivatives δ (k) ( 1) coincide with the asymptotic factorial cumulants of the arrival counting process. This insight is important for admission control schemes in multiservice networks based in part on asymptotic decay rates. The interpretation helps identify appropriate statistics to compute from network traffic data in order to predict performance. 1.
Uniform Acceleration Expansions for Markov Chains with TimeVarying Rates
 Annals of Applied Probability
, 1997
"... We study uniform acceleration (UA) expansions of finitestate continuoustime Markov chains with timevarying transition rates. The UA expansions can be used to justify, evaluate, and refine the pointwise stationary approximation, which is the steadystate distribution associated with the timedepen ..."
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Cited by 14 (8 self)
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We study uniform acceleration (UA) expansions of finitestate continuoustime Markov chains with timevarying transition rates. The UA expansions can be used to justify, evaluate, and refine the pointwise stationary approximation, which is the steadystate distribution associated with the timedependent generator at the time of interest. We obtain UA approximations from these UA asymptotic expansions. We derive a timevarying analog to the uniformization representation of transition probabilities for chains with constant transition rates, and apply it to establish asymptotic results related to the UA asymptotic expansion. These asymptotic results can serve as appropriate timevarying analogs to the notions of stationary distributions and limiting distributions. We illustrate the UA approximations by doing a numerical example for the timevarying Erlang loss model. 1 Accepted for publication in the Annals of Applied Probability. AMS 1991 subject classifications. 60J27, 60K30. Keywords...
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 13 (3 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
Consensus over random networks
 IEEE Transactions on Automatic Control
, 2007
"... Abstract — We consider the decentralized consensus problem over random information networks. In such networks, the underlying graph of the network at a given time instance is random but independent of all other times. For such a framework, we present a simple necessary and sufficient criteria for as ..."
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Cited by 13 (2 self)
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Abstract — We consider the decentralized consensus problem over random information networks. In such networks, the underlying graph of the network at a given time instance is random but independent of all other times. For such a framework, we present a simple necessary and sufficient criteria for asymptotic consensus using simple ergodicity and probabilistic arguments. Finally, we investigate a special case for which the decentralized consensus algorithm converges to the average of the initial values. I.