Four Canadian Contributions to Stochastic Modeling

Abstract We outline the history, significance, and impact of four important contributions by Canadian researchers to stochastic modeling for operational research: the use of the uniformization method to compute transient probabilities for Markov chains, pioneered by Winfried K. Grassmann, contributions to Markov decision processes by Martin L. Puterman, contributions to the development of random number generators by Pierre L'Ecuyer, and contributions to queueing theory software by Armann Ingolfsson.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[2]  A. Jensen,et al.  Markoff chains as an aid in the study of Markoff processes , 1953 .

[3]  R. Kalaba.  ON NONLINEAR DIFFERENTIAL EQUATIONS, THE MAXIMUM OPERATION, AND MONOTONE CONVERGENCE, , 1959 .

[4]  Ronald A. Howard,et al.  Dynamic Programming and Markov Processes , 1960 .

[5]  Rutherford Aris,et al.  Discrete Dynamic Programming , 1965, The Mathematical Gazette.

[6]  E. Denardo.  CONTRACTION MAPPINGS IN THE THEORY UNDERLYING DYNAMIC PROGRAMMING , 1967 .

[7]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[8]  P. Mandl.  Analytical treatment of one-dimensional Markov processes , 1968 .

[9]  Donald Ervin Knuth,et al.  The Art of Computer Programming, Volume II: Seminumerical Algorithms , 1970 .

[10]  M. Puterman.  Sensitive Discount Optimality in Controlled One-Dimensional Diffusions , 1974 .

[11]  W. Grassmann.  Transient solutions in Markovian queues : An algorithm for finding them and determining their waiting-time distributions , 1977 .

[12]  M. Puterman.  Optimal control of diffusion processes with reflection , 1977 .

[13]  Charles Ernest Love.  Purchase/replacement rules for decaying service facilities , 1977, Comput. Oper. Res..

[14]  Winfried K. Grassmann.  Transient solutions in markovian queueing systems , 1977, Comput. Oper. Res..

[15]  Ward Whitt,et al.  Heavy-Traffic Limits for Queues with Many Exponential Servers , 1981, Oper. Res..

[16]  W. Grassmann.  The GI/PH/1 Queue: a Method to Find The Transition Matrix , 1982 .

[17]  D. R. Miller.  Reliability calculation using randomization for Markovian fault-tolerant computing systems , 1982 .

[18]  Micha Yadin,et al.  Numerical Computation of Sojourn-Time Distributions in Queuing Networks , 1984, JACM.

[19]  Micha Yadin,et al.  Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes , 1984, Oper. Res..

[20]  Donald Gross,et al.  The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes , 1984, Oper. Res..

[21]  Winfried K. Grassmann,et al.  Regenerative Analysis and Steady State Distributions for Markov Chains , 1985, Oper. Res..

[22]  Edmundo de Souza e Silva,et al.  Calculating Cumulative Operational Time Distributions of Repairable Computer Systems , 1986, IEEE Transactions on Computers.

[23]  Pierre L'Ecuyer.  Efficient and portable 32-bit random variate generators , 1986, WSC '86.

[24]  Winfried K. Grassmann,et al.  Means and variances of time averages in Markovian environments , 1987 .

[25]  Pierre L'Ecuyer,et al.  Efficient and portable combined random number generators , 1988, CACM.

[26]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[27]  Edmundo de Souza e Silva,et al.  Calculating availability and performability measures of repairable computer systems using randomization , 1989, JACM.

[28]  P. L’Ecuyer,et al.  Structural properties for two classes of combined random number generators , 1990 .

[29]  Liliane Pintelon,et al.  Handbooks in operations research and management science volume 2: Stochastic models , 1991 .

[30]  Pierre L'Ecuyer,et al.  Implementing a random number package with splitting facilities , 1991, TOMS.

[31]  Winfried K. Grassmann,et al.  Rounding errors in certain algorithms involving Markov chains , 1993, TOMS.

[32]  P. L’Ecuyer,et al.  On the lattice structure of certain linear congruential sequences related to AWC/SWB generators , 1994 .

[33]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[34]  Pierre L'Ecuyer,et al.  Uniform random number generation , 1994, Ann. Oper. Res..

[35]  Juan A. Carrasco,et al.  Regenerative randomization: theory and application examples , 1995, SIGMETRICS '95/PERFORMANCE '95.

[36]  Shu Tezuka,et al.  Uniform Random Numbers , 1995 .

[37]  Pierre L'Ecuyer,et al.  Orbits and lattices for linear random number generators with composite moduli , 1996, Math. Comput..

[38]  Pierre L'Ecuyer,et al.  Maximally equidistributed combined Tausworthe generators , 1996, Math. Comput..

[39]  Pierre L'Ecuyer,et al.  Combined Multiple Recursive Random Number Generators , 1995, Oper. Res..

[40]  Pierre L'Ecuyer,et al.  Distribution properties of multiply-with-c arry random number generators , 1997, Math. Comput..

[41]  Pierre L'Ecuyer,et al.  Bad Lattice Structures for Vectors of Nonsuccessive Values Produced by Some Linear Recurrences , 1997, INFORMS J. Comput..

[42]  R. Syski,et al.  Fundamentals of Queueing Theory , 1999, Technometrics.

[43]  Pierre L'Ecuyer,et al.  Tables of maximally equidistributed combined LFSR generators , 1999, Math. Comput..

[44]  Pierre L'Ecuyer,et al.  Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators , 1999, Oper. Res..

[45]  E. D. S. E. Silva,et al.  Transient Solutions for Markov Chains , 2000 .

[46]  Yong Wu.  A Survey and Experimental Comparison of Service Level Approximation Methods For Non-Stationary M/M/s Queueing Systems , 2002 .

[47]  Avishai Mandelbaum,et al.  Designing a Call Center with Impatient Customers , 2002, Manuf. Serv. Oper. Manag..

[48]  Gianfranco Ciardo,et al.  SMART: stochastic model-checking analyzer for reliability and timing , 2002, Proceedings International Conference on Dependable Systems and Networks.

[49]  Pierre L'Ecuyer,et al.  An Object-Oriented Random-Number Package with Many Long Streams and Substreams , 2002, Oper. Res..

[50]  M. Puterman,et al.  Learning and pricing in an internet environment with binomial demands , 2005 .

[51]  Winfried K. Grassmann,et al.  Simulating markov-reward processes with rare events , 2005, TOMC.

[52]  Jing-Sheng Song,et al.  On "The Censored Newsvendor and the Optimal Acquisition of Information" , 2005, Oper. Res..

[53]  Fátima Ferreira,et al.  Analysis of GI/M/s/c queues using uniformisation , 2006, Comput. Math. Appl..

[54]  Pierre L'Ecuyer,et al.  Improved long-period generators based on linear recurrences modulo 2 , 2004, TOMS.

[55]  Joti Jain,et al.  A Course on Queueing Models , 2006 .

[56]  Xudong Wu,et al.  A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline , 2007, INFORMS J. Comput..

[57]  Anna Gavling,et al.  The ART at , 2008 .

[58]  Maurice Queyranne,et al.  Dynamic Multipriority Patient Scheduling for a Diagnostic Resource , 2008, Oper. Res..

[59]  Pierre L'Ecuyer,et al.  Efficient Jump Ahead for 2-Linear Random Number Generators , 2006, INFORMS J. Comput..

[60]  Pierre L'Ecuyer,et al.  F2-Linear Random Number Generators , 2009 .

[61]  U. Rieder,et al.  Markov Decision Processes , 2010 .

[62]  Dimitri P. Bertsekas,et al.  Approximate Dynamic Programming , 2017, Encyclopedia of Machine Learning and Data Mining.

[63]  L. Breuer.  Introduction to Stochastic Processes , 2022, Statistical Methods for Climate Scientists.