Inspired by the PageRank and HITS (hubs and authorities) algorithms for Web search, we propose a structural re-ranking approach to ad hoc information retrieval: we reorder the documents in an initially retrieved set by exploiting asymmetric relationships between them. Specifically, we consider generation links, which indicate that the language model induced from one document assigns high probability to the text of another; in doing so, we take care to prevent bias against long documents. We study a number of re-ranking criteria based on measures of centrality in the graphs formed by generation links, and show that integrating centrality into standard language-model-based retrieval is quite effective at improving precision at top ranks.

Abstract. A concept called stochastic complementation is an idea which occurs naturally, although not always explicitly, in the theory and application of finite Markov chains. This paper brings this idea to the forefront with an explicit definition and a development of some of its properties. Applications of stochastic complementation are explored with respect to problems involving uncoupling procedures in the theory of Markov chains. Furthermore, the role of stochastic complementation in the development of the classical Simon–Ando theory of nearly reducible system is presented. Key words. Markov chains, stationary distributions, stochastic matrix, stochastic complementation, nearly reducible systems, Simon–Ando theory

In this paper, we outline a methodology that can be applied to model the behavior of TCP flows. The proposed methodology stems from a Markovian model of a single TCP source, and eventually considers the superposition and interaction of several such sources using standard queueing analysis techniques. Our approach allows the evaluation of such performance indices as throughput, queueing delay and packet loss of TCP flows. The results obtained through our model are validated by means of simulation, under several topology and traffic settings. I. INTRODUCTION According to recent estimates 95% of the traffic carried today over wide-area IP networks uses TCP as transport protocol, which amounts to 80% of the overall end-to-end flow count. These figures alone highlight the key role that TCP plays in delivering a reliable service to the most common network applications such as email programs and Web browsers. During the many years of "honorable" service, TCP has undergone several alteration...

This paper presents a new computational method for steady state analysis of finite QBDprocess with level-dependent transitions. The QBD state space is defined in two-dimension with N phases and K levels. Instead of formulating solutions in matrix-geometric form, the Foldingalgorithm provides a technique for direct computation of ßP = 0, where P is the QBD generator which is an (NK) \Theta (NK) matrix. Taking a finite sequence of fixed-cost binary reduction steps, the K-level matrix P is eventually reduced to a single-level matrix, from which a boundary vector is obtained. Each step halves the matrix size but keeps the QBD form. The solution ß is expressed as a product of the boundary vector and a finite sequence of expansion factors. The time and space complexity for solving ßP = 0 is therefore reduced from O(N 3 K) and O(N 2 K) to O(N 3 log 2 K)andO(N 2 log 2 K), respectively. The Folding-algorithm has a number of highly desirable advantages when it is applied to queueing an...

This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, non-symmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Krylov subspace techniques, single vector power iteration/relaxation procedures and acceleration techniques. We compare the performance of these methods on some realistic problems. Key words: Markov chain models; Homogeneous linear systems; Direct methods; Successive Overrelaxation; Preconditioned power iterations; Arnoldi's method; GMRES. y IRISA, Rennes, France. Research supported by CNRS (87:N 920070). Research Institute for Advanced Computer Science, NASA Ames Research Center. Moffett Field CA 94035. Research supported by Cooperative Agreement NCC 2-387 between the National Aeronautics and S...

By deriving a new set of tight perturbation bounds, it is shown that all stationary probabilities of a finite irreducible Markov chain react essentially in the same way to perturbations in the transition probabilities. In particular, if at least one stationary probability is insensitive in a relative sense, then all stationary probabilities must be insensitive in an absolute sense. New measures of sensitivity are related to more traditional ones, and it is shown that all relevant condition numbers for the Markov chain problem are small multiples of each other. Finally, the implications of these findings to the computation of stationary probabilities by direct methods are discussed, and the results are applied to stability issues in nearly transient chains.

The tutorial introduces structured analysis approaches for continuous time Markov chains (CTMCs) which are a means to extend the size of analyzable state spaces significantly compared with conventional techniques. It is shown how generator matrices of large CTMCs can be represented in a very compact form, how this representation can be exploited in numerical solution techniques and how numerical analysis profits from this exploitation. Additionally, recent results covering implementation issues, tool support, and advanced analysis techniques are surveyed. 1 Introduction Analysis of continuous time Markov chains (CTMCs) is a well established approach to analyze the performance, dependability and performability of computer and communication systems. Systems are modeled using specification techniques like queueing networks (QNs), stochastic Petri nets (SPNs), formal specification techniques to mention only a few. Unfortunately, the size of CTMCs underlying most realistic examples can be ...

. It is well known that if the transition matrix of an irreducible Markov chain of moderate size has a subdominant eigenvalue which is close to 1, then the chain is ill conditioned in the sense that there are stationary probabilities which are sensitive to perturbations in the transition probabilities. However, the converse of this statement has heretofore been unresolved. The purpose of this article is to address this issue by establishing upper and lower bounds on the condition number of the chain such that the bounding terms are functions of the eigenvalues of the transition matrix. Furthermore, it is demonstrated how to obtain estimates for the condition number of an irreducible chain with little or no extra computational e#ort over that required to compute the stationary probabilities by means of an LU or QR factorization. Key words. Markov chains, stationary distribution, stochastic matrix, sensitivity analysis, perturbation theory, character of a Markov chain, condition numbers ...

Introduction In this chapter our attention will be devoted to computational methods for computing stationary distributions of finite irreducible Markov chains. We let q ij denote the rate at which an n-state Markov chain moves from state i to state j. The n \Theta n matrix Q whose off-diagonal elements are q ij and whose i th diagonal element is given by \Gamma P n j=1;j 6=i q ij is called the infinitesimal generator of the Markov chain. It may be shown that the stationary probability vector ß, a row vector whose k-th element denotes the stationary probability of being in state k, can be obtained by solving the homogeneous system of equations ßQ<F34

This note is concerned with the accuracy of the solution of nearly uncoupled Markov chains by a direct method based on the LU decomposition. It is shown that plain Gaussian elimination may fail in the presence of rounding errors. A modification of Gaussian elimination with diagonal pivoting and correction of small pivots is proposed and analyzed. It is shown that the accuracy of the solution is affected by two condition numbers associate with aggregation and the coupling respectively.