Generating beta random rate variables from probabilistic estimates of fireline production times

An extension of probabilistic PERT/CPM is proposed as a framework for soliciting expert opinion to characterize random variables for stochastic treatment in simulation models. By eliciting minimum, modal, ninetieth percentile, and maximum estimates, the distribution of variables with probability density functions of beta form can be explicitly characterized without relying on the traditional, but empirically unverified, assumption of a standard deviation equal to one-sixth of the range. This practical and inexpensive technique is illustrated by application to a wildfire protection planning problem – estimating the time required to produce a given length of fireline by different firefighting resources under diverse conditions. The estimated production times are an essential input to a planning model of initial attack on wildland fires used by the California Department of Forestry and Fire Protection, and provide that agency with useful rules-of-thumb for use in firefighter training.     

Fine Densities for Excessive Measures and the Revuz Correspondence

Suppose that U is the resolvent of a Borel right process on a Lusin space X. If is a U-excessive measure on X then we show by analytical methods that for every U-excessive measure with the Radon–Nikodym derivative d/d possesses a finely continuous version. (Fitzsimmons and Fitzsimmons and Getoor gave a probabilistic approach for this result.) We extend essentially a technique initiated by Mokobodzki and deepened by Feyel. The result allows us to establish a Revuz type formula involving the fine versions, and to study the Revuz correspondence between the -finite measures charging no set that is both -polar and -negligible (U being the potential component of ) and the strongly supermedian kernels on X. This is an analytic version of a result of Azéma, Fitzsimmons and Dellacherie, Maisonneuve and Meyer, in terms of additive functionals or homogeneous random measures. Finally we give an application to the context of the semi-Dirichlet forms, covering a recent result of Fitzsimmons.     

A new derivation of Frisch's algorithm for calculating vertex-pair connectivity

In this paper we give a new and conceptually simple version of Frisch's algorithm for calculating the vertex connectivity of a graph. We show how this algorithm is obtained immediately from the Ford and Fulkerson labelling algorithm by using a 2-ply scanning step. Data structures are introduced which lead to efficiencies in execution, and the final algorithm is presented in a go-to-less notation.This work was supported in part by U.S. Army Research Office, Durham under contract DA HC04 69 C 0012, and NSF Grant GJ-965.     

Queues with Equally Heavy Sojourn Time and Service Requirement Distributions

For the G/G/1 queue with First-Come First-Served, it is well known that the tail of the sojourn time distribution is heavier than the tail of the service requirement distribution when the latter has a regularly varying tail. In contrast, for the M/G/1 queue with Processor Sharing, Zwart and Boxma [26] showed that under the same assumptions on the service requirement distribution, the two tails are equally heavy. By means of a probabilistic analysis we provide a new insightful proof of this result, allowing for the slightly weaker assumption of service requirement distributions with a tail of intermediate regular variation. The new approach allows us to also establish the tail equivalence for two other service disciplines: Foreground–Background Processor Sharing and Shortest Remaining Processing Time. The method can also be applied to more complicated models, for which no explicit formulas exist for (transforms of) the sojourn time distribution. One such model is the M/G/1 Processor Sharing queue with service that is subject to random interruptions. The latter model is of particular interest for the performance analysis of communication networks.     

Characterizing matchings as the intersection of matroids

This paper deals with the problem of representing the matching independence system in a graph as the intersection of finitely many matroids. After characterizing the graphs for which the matching independence system is the intersection of two matroids, we study the function (G), which is the minimum number of matroids that need to be intersected in order to obtain the set of matchings on a graph G, and examine the maximal value, (n), for graphs with n vertices. We describe an integer programming formulation for deciding whether (G)k. Using combinatorial arguments, we prove that (n)(log logn). On the other hand, we establish that (n)O(logn/ log logn). Finally, we prove that (n)=4 for n=5,,12, and sketch a proof of (n)=5 for n=13,14,15.An earlier version appears as an extended abstract in the Proceedings of COMB01 [5]. Supported by the Gerhard-Hess-Forschungs-Förderpreis (WE 1462) of the German Science Foundation (DFG) awarded to R. Weismantel.     

Backward doubly stochastic differential equations and systems of quasilinear SPDEs

Summary We introduce a new class of backward stochastic differential equations, which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential equations, thus extending the Feynman-Kac formula for linear SPDE's.The research of this author was partially supported by DRET under contract 901636/A000/DRET/DS/SRThe research of this author was supported by a grant from the French Ministère de la Recherche et de la Technologie, which is gratefully acknowledged     

Ruin Probabilities for Large Claims in Delayed Renewal Risk Model

This paper investigates ruin probabilities (x) in the delayed renewal risk model, where x is the initial capital of an insurance company. Under the assumption that the claim size is heavy-tailed, we aim at a tail equivalence relationship of (x) as x . The result we obtain in this paper is surprisingly the same as the previous classical results.This work was supported by National Science Foundation of China (No. 10071081).     

On the variance of the number of pivot steps required by the simplex algorithm

The article provides an asymptotic probabilistic analysis of the variance of the number of pivot steps required by phase II of the shadow vertex algorithm — a parametric variant of the simplex algorithm, which has been proposed by Borgwardt [1]. The analysis is done for data which satisfy a rotationally invariant distribution law in then-dimensional unit ball.     

Chapter 1 Introduction: Extensions and new developments in DEA

The extensions, new developments and new interpretations for DEA covered in this paper include: (1) new measures of efficiency, (2) new models and (3) new ways of implementing established models with new results and interpretations presented that include treatments of congestion, returns-to-scale and mix and technical inefficiencies and measures of efficiency that can be used to reflect all pertinent properties. Previously used models, such as those used to identify allocative inefficiencies, are extended by means of assurance region approaches which are less demanding in their information requirements and underlying assumptions. New opportunities for research are identified in each section of this chapter. Sources of further developments and possible sources for further help are also suggested with references supplied to other papers that appear in this volume and which are summarily described in this introductory chapter.     

N = 4 Superconformal Algebra in Curved Space and Pseudo-Hyper-Kähler Geometry

We construct the representation of the small N=4 superconformal algebra in curved space under the minimal interaction assumption. We find that the structure relations of the algebra are satisfied within our assumption in the background of the metric of a pseudo-hyper-Kähler manifold.     

Evolving System Architectures for Multimedia Network Design

This paper discusses implementation issues concerning a telecommunications planning system for networks with hypothetical multimedia stochastic traffic. Stochasticity of the traffic and probabilistic statements about service commitment are captured by a chance-constrained stochastic programming formulation of the complex network dimensioning and traffic management problem treated in our previous work. Our approach involves a hierarchy of design objectives associated with the respective network layers. These are met by constituting a set of models – the Integrated Network Design System (INDS) – with common data, solvers and a graphical user interface (GUI) operating under the interactive control of the network planner.     

Contributions to the theory of stochastic programming

Two stochastic programming decision models are presented. In the first one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be infinite in which case stochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.This work was supported in part by the Institute of Economic Planning, Budapest.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands, under the title Programming under probabilistic constraints and programming under constraints involving conditional expectations.     

Probabilistisch kompakte L-unscharfe Mengen

In the case of completely distributive lattices (L,) we establish a probabilistic version of Alexander's subbase lemma and of Tychonoff's theorem for L-fuzzy sets. As an application we obtain that probabilistic topologies induced by compact ordinary topologies are also compact; i.e. ordinary compactness is consistent with probabilistic compactness. Regarding the validity of these results a counterexample shows that the complete distributivity of (L,) cannot be replaced by a weaker distributivity condition.     

Stochastic PDEs Driven by Nonlinear Noise and Backward Doubly SDEs

We study a new kind of backward doubly stochastic differential equations, where the nonlinear noise term is given by Itô–Kunita's stochastic integral. This allows us to give a probabilistic interpretation of classical and Sobolev's solutions of semilinear parabolic stochastic partial differential equations driven by a nonlinear space-time noise.     

Chapter 13 Satisficing DEA models under chance constraints

DEA (Data Envelopment Analysis) models and concepts are formulated here in terms of the P-Models of Chance Constrained Programming, which are then modified to contact the satisficing concepts of H.A. Simon. Satisficing is thereby added as a third category to the efficiency/inefficiency dichotomies that have heretofore prevailed in DEA. Formulations include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. Attention is also devoted to situations in which variations in inputs and outputs are related through a common random variable. Extensions include new developments in goal programming with deterministic equivalents for the corresponding satisficing models under chance constraints.     

Partly convex programming and zermelo's navigation problems

Mathematical programs, that become convex programs after freezing some variables, are termed partly convex. For such programs we give saddle-point conditions that are both necessary and sufficient that a feasible point be globally optimal. The conditions require cooperation of the feasible point tested for optimality, an assumption implied by lower semicontinuity of the feasible set mapping. The characterizations are simplified if certain point-to-set mappings satisfy a sandwich condition.The tools of parametric optimization and basic point-to-set topology are used in formulating both optimality conditions and numerical methods. In particular, we solve a large class of Zermelo's navigation problems and establish global optimality of the numerical solutions.Research partly supported by NSERC of Canada.     

G-networks: a unifying model for neural and queueing networks

We survey results concerning a new stochastic network we have developed [1–7], which was initially motivated by neural network modelling [1], or — as we called it — by queueing networks with positive and negative customers [2, 3]. Indeed, it is well known that signals in neural networks are formed by impulses or action potentials, traveling much like customers in a queueing network. We call this model a G-network because it serves as a unifying basis for diverse areas of stochastic modelling in queueing networks, computer networks, computer system performance and neural networks. In its simplest version, negative and positive signals or customers circulate among a finite set of units, modelling inhibitory and excitatory signals of a neural network, or negative and positive customers of a queueing network. Signals can arrive either from other units or from the outside world. Positive signals are accumulated at the input of each unit, and constitute its signal potential. The state of each unit or neuron is its signal potential (which is equivalent to the queue length), while the network state is the vector of signal potentials at each neuron. If its potential is positive, a unit or neuron fires, and sends out signals to the other neurons or to the outside world. As it does so, its signal potential is depleted. In the Markovian case, this model has product form, i.e. the steady-state probability distribution of its potential vector is the product of the marginal probabilities of the potential at each neuron. The signal flow equations of the network, which describe the rate at which positive or negative signals arrive to each neuron, are non-linear. We discuss the relationship between this model and the usual connectionist (formal) model of neural networks, and present applications to combinatorial optimization and to image texture processing. Extensions of the model to the case of multiple signal classes, and to networks with triggered customer motion are presented. We also examine the general stability conditions which guarantee that the network has a well-defined steady-state behaviour.     

Weak Nonlinearity in a Model Which Arises from the Helmert Transformation

Nowadays, the algorithm most frequently used for determination of the estimators of parameters which define a transformation between two coordinate systems (in this case the Helmert transformation) is derived under one unreal assumption of errorless measurement in the first system. As it is practically impossible to ensure errorless measurements, we can hardly believe that the results of this algorithm are optimal.In 1998, Kubáek and Kubáková proposed an algorithm which takes errors in both systems into consideration. It seems to be closer to reality and at least in this sense better. However, a partial disadvantage of this algorithm is the necessity of linearization of the model which describes the problem of the given transformation. The defence of this simplification especially with respect to the bias of linear functions of the final estimators, or better to say the specification of conditions under which such a modification is statistically insignificant is the aim of this paper.     

Occupation time large deviations of the voter model

This paper is a sequel to [5] and [6]. We continue our study of occupation time large deviation probabilities for some simple infinite particle systems by analysing the so-called voter model _t (see e.g., [11] or [8]). In keeping with our previous results, we show that the large deviations are classical in high dimensions (d5 for _t) but fat in low dimensions (d4). Interaction distinguishes the voter model from the independent particle systems of [5] and [6], and consequently exact computations no longer seem feasible. Instead, we derive upper and lower bounds which capture the asymptotic decay rate of the large deviation tails.Dedicated to Frank Spitzer on his 60th birthdayPartially supported by the National Science Foundation under Grant DMS-831080Partially supported by the National Science Foundation under Grant DMS-841317Partially supported by the National Science Foundation under Grant DMS-830549     

A new class of cutting planes for the symmetric travelling salesman problem

A comprehensive class of cutting planes for the symmetric travelling salesman problem (TSP) is proposed which contains the known comb inequalities, the path inequalities and the 3-star constraints as special cases. Its relation to the clique tree inequalities is discussed. The cutting planes are shown to be valid for a relaxed version of the TSP, the travelling salesman problem on a road network, and—under certain conditions—to define facets of the polyhedron associated with this problem.