Queueing Systems and the Web

In this chapter, we first discuss some more Markovian queueing systems. The queueing system is a classical application of continuous Markov chains. We then present an important numerical algorithm based on the computation of Markov chains for ranking webpages. This is a modern application of Markov chains though the numerical methods used are classical.

[1]  Wai-Ki Ching Iterative Methods for Queuing and Manufacturing Systems , 2001 .

[2]  Vaidyanathan Ramaswami,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 1999, ASA-SIAM Series on Statistics and Applied Mathematics.

[3]  W. Cheney,et al.  Numerical analysis: mathematics of scientific computing (2nd ed) , 1991 .

[4]  Raymond H. Chan,et al.  Toeplitz-Circulant Preconditioners for Toeplitz Systems and their Applications to Queueing Networks with Batch Arrivals , 1996, SIAM J. Sci. Comput..

[5]  Peter G. Taylor,et al.  Matrix-analytic methods: theory and applications , 2002 .

[6]  Gene H. Golub,et al.  Computing PageRank using Power Extrapolation , 2003 .

[7]  R. Gorenflo,et al.  Multi-index Mittag-Leffler Functions , 2014 .

[8]  O. Axelsson Iterative solution methods , 1995 .

[9]  Marcel F. Neuts,et al.  Algorithmic probability - a collection of problems , 1995, Stochastic modeling series.

[10]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[11]  Wai-Ki Ching,et al.  On Computing Prestige in a Network with Negative Relations , 2005 .

[12]  Peter Buchholz,et al.  Hierarchical Markovian Models: Symmetries and Reduction , 1995, Perform. Evaluation.

[13]  E. Garfield Citation indexes for science. A new dimension in documentation through association of ideas. 1955. , 1955, International journal of epidemiology.

[14]  Sepandar D. Kamvar,et al.  An Analytical Comparison of Approaches to Personalizing PageRank , 2003 .

[15]  Pierre Baldi,et al.  Modeling the Internet and the Web: Probabilistic Method and Algorithms , 2002 .

[16]  Wai-Ki Ching,et al.  Iterative Methods for Queuing Systems with Batch Arrivals and Negative Customers , 2003 .

[17]  W. Ching CIRCULANT PRECONDITIONERS FOR FAILURE PRONE MANUFACTURING SYSTEMS , 1997 .

[18]  Wai-Ki Ching Machine repairing models for production systems , 2001 .

[19]  Erol Gelenbe,et al.  Random Neural Networks with Negative and Positive Signals and Product Form Solution , 1989, Neural Computation.

[20]  Michael K. Ng,et al.  A hybrid algorithm for queueing systems , 2004 .

[21]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[22]  Konstantin Avrachenkov,et al.  Decomposition of the Google Pagerank and Optimal Linking Strategy Decomposition of the Google Pagerank and Optimal Linking Strategy , 2004 .

[23]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[24]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[25]  Sheldon M. Ross Introduction to Probability Models. , 1995 .

[26]  Erol Gelenbe,et al.  Queues with negative arrivals , 1991, Journal of Applied Probability.

[27]  Raymond H. Chan,et al.  Boundary value methods for solving transient solutions of Markovian queueing networks , 2006, Appl. Math. Comput..

[28]  Amy Nicole Langville,et al.  Google's PageRank and beyond - the science of search engine rankings , 2006 .

[29]  P. Buchholz Equivalence Relations for Stochastic Automata Networks , 1995 .

[30]  Michael K. Ng,et al.  Exact algorithms for singular tridiagonal systems with applications to Markov chains , 2004, Appl. Math. Comput..

[31]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[32]  Robert B. Cooper,et al.  Introduction to Queueing Theory , 1973 .

[33]  E. Gelenbe Product-form queueing networks with negative and positive customers , 1991 .

[34]  Taher H. Haveliwala,et al.  The Second Eigenvalue of the Google Matrix , 2003 .

[35]  Madjid Tavana,et al.  Optimal allocation of arrivals to a collection of parallel workstations , 1997 .

[36]  E. Garfield Citation analysis as a tool in journal evaluation. , 1972, Science.

[37]  Qianshun Chang,et al.  Algebraic multigrid method for queueing networks , 1999, Int. J. Comput. Math..

[38]  Xin Yao,et al.  Solving equations by hybrid evolutionary computation techniques , 2000, IEEE Trans. Evol. Comput..

[39]  L. Kaufman Matrix Methods for Queuing Problems , 1983 .

[40]  David C. Bell,et al.  Centrality measures for disease transmission networks , 1999, Soc. Networks.

[41]  R. Quandt The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes , 1958 .

[42]  Peter Buchholz,et al.  A class of hierarchical queueing networks and their analysis , 1994, Queueing Syst. Theory Appl..

[43]  Wai-Ki Ching Iterative methods for manufacturing systems of two stations in tandem , 1998 .

[44]  Phillip Bonacich,et al.  Calculating status with negative relations , 2004, Soc. Networks.

[45]  Raymond H. Chan,et al.  Circulant preconditioners for stochastic automata networks , 2000, Numerische Mathematik.

[46]  Amy Nicole Langville,et al.  A Survey of Eigenvector Methods for Web Information Retrieval , 2005, SIAM Rev..

[47]  Taher H. Haveliwala,et al.  Adaptive methods for the computation of PageRank , 2004 .

[48]  X. Zhou,et al.  Circulant Preconditioners for Markov-Modulated Poisson Processes and Their Applications to Manufacturing Systems , 1997, SIAM J. Matrix Anal. Appl..

[49]  Gene H. Golub,et al.  Matrix computations , 1983 .