Abstract not found

This paper studies a simple strategy, proposed independently by Gallager [1] and Katevenis [2], for fairly allocating link capacity in a point-to-point packet network with virtual circuit routing. Each link offers its packet transmission slots to its user sessions by polling them in round-robin order. In addition, window flow control is used to prevent excessive packet queues at the network nodes. As the window size increases, the session throughput rates are shown to approach limits that are perfectly fair in the max-min sense. That is, the smallest session rate in the network is as large as possible and, subject to that constraint, the second-smallest session rate is as large as possible, etc. If each session has periodic input (perhaps with jitter) or has such heavy demand that packets are always waiting to enter the network, then a finite window size suffices to produce perfectly fair throughput rates. The round-robin method is considerably simpler than earlier strategies for achieving global fairness. The fair session rates are not explicitly computed, and the only overhead communication is that required for the window acknowledgments. The main drawback is that large windows are needed to achieve even approximately fair throughputs in some (hopefully rare) situations, and large windows permit large cross-network delays. Fortunately, the round-robin method offers other throughput guarantees that, while falling short of perfect fairness, do apply even for sessions with small windows. Such sessions are promised reasonable bounds on their cross-network packet delay as well.

This report is a contributed chapter to the Handbook of Theoretical Computer Science (North-Holland, 1990). Its aim is to describe the main mathematical methods and applications in the average-case analysis of algorithms and data structures. It comprises two parts: First, we present basic combinatorial enumerations based on symbolic methods and asymptotic methods with emphasis on complex analysis techniques (such as singularity analysis, saddle point, Mellin transforms). Next, we show how to apply these general methods to the analysis of sorting, searching, tree data structures, hashing, and dynamic algorithms. The emphasis is on algorithms for which exact "analytic models" can be derived.

Abstract—An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finite-state channels, hidden Markov models, identifiability, Kalman filter, maximum-likelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.

Abstract not found

We address the problem of characterising the security of a program against unauthorised information flows. Classical approaches are based on non-interference models which depend ultimately on the notion of process equivalence. In these models confidentiality is an absolute property stating the absence of any illegal information flow. We present a model in which the notion of non-interference is approximated in the sense that it allows for some exactly quantified leakage of information. This is characterised via a notion of process similarity which replaces the indistinguishability of processes by a quantitative measure of their behavioural difference. Such a quantity is related to the number of statistical tests needed to distinguish two behaviours. We also present two semantics-based analyses of approximate non-interference and we show that one is a correct abstraction of the other.

This paper analyzes a class of games of incomplete information where each agent has

General characterizations of valid confidence sets and tests in problems which involve locally almost unidentified (LAU) parameters are provided and applied to several econometric models. Two types of inference problems are studied: (1) inference about parameters which are not identifiable on certain subsets of the parameter space, and (2) inference about parameter transformations with singularities (discontinuities). When a LAU parameter or parametric function has an unbounded range, it is shown under general regularity conditions that any valid confidence set with level 1 \Gamma ff for this parameter should be unbounded with probability close to 1 \Gamma ff in the neighborhood of nonidentification subsets and should as well have a non-zero probability of being unbounded under any distribution compatible with the model: no valid confidence set which is bounded with probability one does exist. These properties hold even if "identifying restrictions" are imposed. Similar results also ob...

The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time--dependent systems in which randomness plays a role. In this paper, we are concerned with Fokker--Planck equations for which the drift term is given by the gradient of a potential. For a broad class of potentials, we construct a time--discrete, iterative variational scheme whose solutions converge to the solution of the Fokker--Planck equation. The major novelty of this iterative scheme is that the time step is governed by the Wasserstein metric on probability measures. This formulation enables us to reveal an appealing, and previously unexplored, relationship between the Fokker--Planck equation and the associated free energy functional. Namely, we demonstrate that the dynamics may be regarded as a gradient flux, or a steepest descent, for the free energy wi...

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section Ž n. and time series Ž T. observations. The limit theory allows for both sequential limits, wherein T� � followed by n��, and joint limits where T, n�� simultaneously; and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence of long-run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parameterized in terms of the matrix regression coefficient of the long-run average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.