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Percy Brill CV

Percy H. Brill, Ph.D.
Professor Emeritus, Management Science
brill@uwindsor.ca

Dr. Percy H. Brill is a Professor Emeritus in the Odette School of Business and Adjunct Professor in the Department of Mathematics and Statistics, University of Windsor

Education 

  • Ph.D.  University of Toronto, Industrial Engineering: Operations Research/Mathematics, 1975.
  • M.A.  Columbia University, New York, USA, Mathematical Statistics.
  • B.Sc. Bachelor of Science, Carleton University, Ottawa, Canada, Mathematics / Physics.

Books 

  • Brill, P. (2023).  Introduction to Stochastic Level Crossing Techniques.  Taylor & Francis Group (Boca Raton, London, New York).  255 pages, 9 chapters, 59 figures and 82 exercises. ISBN: 9780367277352
  • Brill, P. (2017).  Level Crossing Methods in Stochastic Models (2nd Ed. ed.) Springer.  559 pages, 124 illustrations, 27 illustrations in colour.  ISBN: 978-3-319-50332 Springer International Series in Operations Research & Management Science.
  • Brill, P. (2008).  Level Crossing Methods in Stochastic Models Springer Science+Business Media.   Description: Part of Springer 'Series in Operations Research & Management Science', Frederick S. Hiller [Ed.]  ISBN: 978-0-387-09421-2

Chapters 

  • Brill, P. H. (1996). Level Crossing Methods. Encyclopedia of Operations Research and Management Science. Kluwer Academic Publications.  Description: ISBN: 978-1-4419-1154-4

Articles – Peer-Reviewed

  • Brill, P., & Huang, M. L. (2022).  On approximation of the analytic fixed finite time large t probability distributions in an extreme renewal process with no-mean inter-renewals.   Probability in the Engineering and Informational Sciences.  [May]
  • Brill, P. H., Huang, M. L., & Hlynka, M. (2020).  On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers.   European Journal of Operational Research, 283 (1), 235-243.  [May]
  • Zhang, Y., Hlynka, M., & Brill, P. H. (2019).  First passage and collective marks.   International Journal of Statistics and Probability, 8 (6), 47-50.  [November]. Published by the Canadian Centre of Science and Education.
  • Brill, P. H., Cheung, C. H., Hlynka, M., & Jiang, Q. (2018).  Reversibility checking for Markov chains.   Communications on Stochastic Analysis, 12 (2), 129-135.
  • Brill, P. H. (2015).  Note on the service time in M/G/1 queues with bounded workload.   Statistics & Probability Letters, 96 (2015), 162-169.  [January]
  • Brill, P. H. (2014).  Alternative analysis of finite-time probability distributions of renewal theory.   Probability in the Engineering and Informational Sciences, 28 (2), 183-201.  [April]
  • Huang, M. L., Coia, V., & Brill, P. H. (2013).  A cluster truncated pareto distribution and its applications.   ISRN Probability and Statistics (Ceased in 2014), 2013.
  • Brill, P. H., & Hlynka, M. (2012).  Server workload in an M/M/1 queue with bulk arrivals and special delays.   Applied Mathematics, 3 (12), 2174-2177.  [December]
  • Yu, K., Huang, M. L., & Brill, P. H. (2012).  An algorithm for fitting heavy-tailed distributions via generalized hyper-exponentials.   INFORMS Journal on Computing, 24 (1), 42-52.
  • Brill, P. H., & Yu, K. (2011).  Analysis of risk models using a level crossing technique.   Insurance: Mathematics and Economics, 49 (3), 298-309.  [November]
  • Hlynka, M., Brill, P. H., & Horn, W. (2010).  A method for obtaining Laplace transforms of order statistics of Erlang random variables.   Statistics & Probability Letters, 80, 9-18.  [January]
  • Brill, P. H. (2009).  Note on a series for M/G/1 queues.   International Journal of Operational Research, 5 (3), 363-373.  [May]
  • Brill, P. H. (2009).  Compound cycle of a renewal process and applications.   INFOR: information systems and operational research, 47 (4), 273-281.  [January]
  • Brill, P. H., Huang, M. L., & Hlynka, M. (2009).  Note on an (s, S) inventory system with decay.   IAENG International Journal of Applied Mathematics, 39 (3), 171-174.
  • Shortle, J. F., Fischer, M. J., & Brill, P. H. (2007).  Waiting-time distribution of M/Dn/1 queues through numerical Laplace inversion.   INFORMS Journal on Computing, 19 (1), 112-120.  [February]
  • Mandelbaum, M., Hlynka, M., & Brill, P. H. (2007).  Nonhomogeneous geometric distribution with relations to birth and death processes.   TOP: An official journal of the Spanish Society of Statistics and Operations Research, 15 (2), 281-296.  [July]
  • Shortle, J. F., & Brill, P. H. (2005).  Analytical distribution of waiting time in the M/{iD}/1 queue.   Queueing Systems, 50 (2-3), 185-197.  [July]
  • Wu, X., Brill, P. H., Hlynka, M., & Wang, J. (2005).  An M/G/1 retrial queue with balking and retrials during service.   International Journal of Operational Research, 1 (1-2), 30-51.  [July]
  • Shortle, J. F., Brill, P. H., Fischer, M. J., Gross, D., & Masi, D. M. (2004).  An algorithm to compute the distribution of the waiting time in the M/G/1 queue.   INFORMS Journal on Computing, 16 (2), 152-161.  [May]
  • Huang, M. L., & Brill, P. H. (2004).  A distribution estimation method based on level crossings.   Journal of Statistical Planning and Inference, 124 (1), 45-62.  [August]
  • Brill, P. H., & Hlynka, M. (2002).  A geometric interpretation of 2 x 2 markov transition matricies.   Missouri Journal of Mathematical Sciences, 14 (3), 159-174.
  • Huang, M. L., & Brill, P. H. (2001).  On estimation in M/G/c/c queues.   International Transactions in Operational Research, 8 (6), 647-657.  [December]
  • Huang, M. L., & Brill, P. H. (2001).  A nonparametric regression method.   Nonlinear Analysis: Theory, Methods & Applications, 47 (3), 1467-1475.  [August]
  • Brill, P. H., & Hlynka, M. (2000).  An exponential queue with competition for service.   European Journal of Operational Research, 126 (3), 587-602.  [November]
  • Harris, C. M., Brill, P. H., & Fischer, M. J. (2000).  Internet-type queues with power-tailed interarrival times and computational methods for their analysis.   INFORMS Journal on Computing, 12 (4), 448-458.  [November]
  • Huang, M. L., & Brill, P. H. (1999).  A level crossing quantile estimation method.   Statistics & Probability Letters, 45 (2), 111-119.  [November]
  • Brill, P. H., & Hlynka, M. (1998).  A single server n-line queue in which a customer may receive special treatment.   Communications in Statistics. Stochastic Models, 14 (4), 905-931.  [May]
  • Huang, M. L., & Brill, P. H. (1997).  A level crossing density estimation method.   Nonlinear Analysis: Theory, Methods & Applications, 30 (7), 4403-4414.  [December]
  • Brill, P., & Harris, C. M. (1997).  M/G/1 queues with markov-generated server vacations.   Communications in Statistics. Stochastic Models, 13 (3), 491-521.  [January]
  • Brill, P. H., & Chaouch, A. B. (1995).  An EOQ model with random variations in demand.   Management Science, 41 (5), 927-936.
  • Azoury, K. S., & Brill, P. H. (1992).  Analysis of net inventory in continuous review models with random lead time.   European Journal of Operational Research, 59 (3), 383-392.  [June]
  • Brill, P. H., & Harris, C. M. (1992).  Waiting times for M/G/1 queues with service-time or delay-dependent server vacations.   Naval Research Logistics, 39 (6), 775-787.  [October]
  • Huang, M. L., & Brill, P. H. (1991).  Recurrence relations for the minimum variance unbiased estimator of the probability function of the R distribution.   Communications in Statistics - Theory and Methods, 20 (12), 4005-4019.  [September]
  • Brill, P. H., & Mandelbaum, M. (1990).  Measurement of adaptivity and flexibility in production systems.   European Journal of Operational Research, 49 (3), 325-332.  [December]
  • Mandelbaum, M., & Brill, P. H. (1989).  Examples of measurement of flexibility and adaptivity in manufacturing systems.   Journal of the Operational Research Society, 40 (6), 603-609.
  • Brill, P. H. (1988).  Single server queues with delay-dependent arrival streams.   Probability in the Engineering and Informational Sciences, 2 (2), 231-247.  [April]
  • Brill, P. H., & Mandelbaum, M. (1987).  On measures of flexibility in manufacturing systems.   International Journal of Production Research, 27 (5), 747-756.  [November]
  • Azoury, K., & Brill, P. H. (1986).  An application of the system-point method to inventory models under continuous review.   Journal of Applied Probability, 23 (3), 778-789.
  • Brill, P., & Hornik, J. (1984).  A system point approach to nonuniform advertising insertions.   Operations Research, 32 (1), 7-22.  [February]
  • Brill, P. H., & Green, L. (1984).  Queues in which customers receive simultaneous service from a random number of servers: A system point approach.   Management Science, 30 (1), 51-68.  [January]
  • Brill, P. H., & Posner, M. (1981).  The system point method in exponential queues: A level crossing approach.   Mathematics of Operations Research, 6 (1), 31-49.  [February]
  • Brill, P. H., & Posner, M. (1981).  A two-server queue with non-waiting customers receiving specialized service.   Management Science, 27 (8), 914-925.  [August]
  • Brill, P. H., & Moon, R. F. (1980).  An application of queuing theory to pharmacokinetics.   Journal of Pharmaceutical Sciences, 69, 558-560.
  • Brill, P. H. (1979).  An embedded level crossing technique for dams and queues.   Journal of Applied Probability, 16 (1), 174-186.
  • Brill, P. H., & Posner, M. (1977).  Level crossings in point processes applied to queues: Single server case.   Operations Research, 25 (4), 662-673.
  • Brill, P. (1976).  The system point process in queueing.   Advances in Applied Probability, 9 (2), 216.  [June]
  • Brill, P. (1975).  A new methodology for modelling a broad class of exponential queues.   Advances in Applied Probability, 8 (2), 242.  [June] [Invited by J. Keilson & R. Syski)

Articles – Other

  • Fischer, M. J., Masi, D. M., Brill, P. H., Gross, D., & Shortle, J. F. (2002).  Structural properties of the transform approximation method and recursion method.   Telecommunications Review, 13, 121-128.
  • Brill, P. (2000).  A Brief Outline of the Level Crossing Method in Stochastic Models.   CORS Bulletin (Canadian Operational Research Society), 34 (4), 9-21.  [November].  Synopsis of a keynote presentation presented by Dr. Brill at CanQueue 2000, London, ON, on September 15, 2000.

 Conference Proceedings 

  • Brill, P. & Huang, M.L. (August 2023). Stochastic level-crossing estimation of stationary probability distributions in stochastic models.  2023 JSM Proceedings, Statistical Computing Section, Monte Carlo and Simulations, Alexandria, VA: American Statistical Association, pp. 1-8.  https://doi.org/10.5281/zenodo.8349713.
  • Huang, M. L., Kenig, A., & Brill, P. H. (2020).  A nonparametric extreme quantile regression.   Joint Statistical Meetings (JSM), American Statistical Association, Seattle.
  • Brill, P. H., & Huang, M. L. (2018).  The posterior service time in an M/G/1 queue with a workload barrier and extreme prior service times.   Joint Statistical Meetings (JSM), American Statistical Association, Vancouver, 1051-1056.
  • Brill, P., & Huang, M. L. (2017).  Approximating probability distributions in an extreme renewal process.   Joint Statistical Meetings (JSM), American Statistical Association, Baltimore, 1395-1401.
  • Brill, P., & Huang, M. L. (2017).  Approximating Probability Distributions in an Extreme Renewal Process.   Joint Statistical Meetings (JSM) 2017, Baltimore, MD.
  • Huang, M. L., Mottola, J., & Brill, P. H. (2015).  On a mixture pareto distribution.   Joint Statistical Meetings (JSM), American Statistical Association, Seattle, 1416-1427.
  • Brill, P., & Huang, M. L. (2014).  Example of a renewal process with no-mean interarrival times.   Joint Statistical Meetings (JSM), American Statistical Association, Boston, 633-642.
  • Huang, M. L., Thorpe, L., & Brill, P. H. (2013).  A nonparametric method for extreme values.   Joint Statistical Meetings (JSM), American Statistical Association, Montreal, 2905-2914.
  • Huang, M. L., Coia, V., & Brill, P. H. (2012).  A mixture truncated pareto distribution.   Joint Statistical Meetings (JSM), American Statistical Association, San Diego, 2488-2498.
  • Huang, M. L., Brill, P. H., & Gross, D. (2005).  A weighted estimation method for the pareto variance.   Joint Statistical Meetings (JSM), American Statistical Association, Minneapolis, 1649-1654.
  • Fischer, M. J., Masi, D. M., Gross, D., Shortle, J. F., & Brill, P. H. (2005).  Development of procedures to analyze queueing models with heavy-tailed interarrival and service times.   NSF Design, Service, and Manufacturing Grantees and Research Conference, Scottsdale.
  • Fischer, M. J., Masi, D. M., Brill, P. H., Gross, D., & Shortle, J. (2004).  Development of procedures to analyze queueing models with heavy-tailed interarrival and service times.  In R. Kovacevic (Ed.)   NSF Design, Service, and Manufacturing Grantees and Research Conference, Dallas.
  • Fischer, M. J., Masi, D. M., Brill, P. H., Gross, D., & Shortle, J. (2003).  Development of procedures to analyze queueing models with heavy-tailed interarrival and service times - a status report.  In R.G. Reddy (Ed.)   NSF Design, Service, and Manufacturing Grantees and Research Conference, Birmingham, AL.
  • Fischer, M. J., Masi, D. M., Gross, D., Shortle, J., & Brill, P. H. (2003).  Applying the TAM recursion method (TRM) to analyze an internet type congestion problem.   Applied Telecommunications Symposium, Orlando.
  • Huang, M. L., & Brill, P. H. (2002).  On rank tests for experimental designs.   American Statistical Association (Statistical Computing Section) Proceedings, New York, 1502-1506.
  • Fischer, M. J., Masi, D. M., Gross, D., Shortle, J., & Brill, P. H. (2001).  Using quantile estimates in simulation internet queues with pareto service times.  In B.A. Peters; J.S. Smith, D.J. Medeiros & M.W. Rohrer (Eds.)   Proceedings of the 2001 Winter Simulation Conference (IEEE), Arlington, VA, IEEE, 477-485.
  • Brill, P., & Mandelbaum, M. (1999).  Queueing flexibility in production systems.  In M.T. Hillery & H.J. Lewis (University of Limerick) (Eds.)   Conference on Production Research, 15th International Conference, Limerick, Ireland, 465-467.
  • Huang, M. L., & Brill, P. H. (1999).  A weighted regression method.   American Statistical Association (Statistical Computing Section) conference, Baltimore, 143-156.
  • Huang, M. L., & Brill, P. H. (1996).  A nonparametric quantrile estimation method.   American Statistical Association (Statistical Computing Section) conference, 206-211.
  • Brill, P., & Huang, M. L. (1995).  A new weighted estimation method.   International Statistical Institute 50th Session, Beijing, 120-121.
  • Huang, M. L., & Brill, P. H. (1995).  A new weighted density estimation method.   American Statistical Association (Statistical Computing Section) conference, 125-130.
  • Brill, P., & Mandelbaum, M. (1995).  Measures of flexibility in queueing systems.   13th Conference on Production Research, Jerusalem, 518-520.
  • Huang, M. L., & Brill, P. H. (1994).  Some estimation problems in systems of M/G/c/c queues.   American Statistical Association (Science and Engineering Section) Proceedings, 149-154.
  • Brill, P. H., & Huang, M. L. (1993).  System point estimation of the probability distribution of the waiting time in variants of the M/Ga,b/1 queues.   American Statistical Association (Statistical Computing Section) conference, 236-241.
  • Huang, M. L., & Brill, P. H. (1992).  On estimation of the R distribution.   American Statistical Association (Statistical Computing Section) conference, 140-145.
  • Brill, P. H. (1991).  Estimation of stationary distributions in storage processes using level crossing theory.   American Statistical Association (Statistical Computing Section) conference, 172-177.
  • Huang, M. L., & Brill, P. H. (1991).  Recurrence relations forthe minimum variance unbiased estimator of the probability function of the more generalized stirling function of the second kind.   American Statistical Association (Statistical Computing Section) conference, 89-94.
  • Brill, P. H. (1990).  Examples of level crossing estimation in M/G/1 queues.   American Statistical Association (Statistical Computing Section) conference, 151-154.
  • Brill, P., & Mandelbaum, M. (1987).  Measures of flexibility in production systems.   International Conference on Production Research, 9th, 2474-2481.

Presentations 

  • Huang, M. L., Kenig, A., & Brill, P. H. (2020, August). A nonparametric extreme quantile regression.  JSM 2020 (virtual), Philadelphia.
  • Nantais, J., Hlynka, M., & Brill, P. H. (2020, August). Completing a task with interruptions.  CanQueue 2020 - Canadian Queueing Theorists and Practitioners Conference (online), Banff.
  • Brill, P. H. (2019, November). Relating the workload-barrier M/D/1 queue to a renewal process and an (s, S) inventory. Invited presentation at AMS 2019-American Mathematics Society - Special conference in honour of M.M. Rao.
  • Brill, P. H., Huang, M. L., & Hlynka, M. (2019, August). A workload barrier M/G/1 queue with accepted and blocked customers.  CanQueue 2019, Rotman School of Business, Toronto.
  • Brill, P. & Huang, M. L. (2018, August). The posterior service time in an M/G/1 queue with a workload barrier and extreme prior service times.  JSM 2018, Vancouver, Canada.
  • Brill, P. & Huang, M. L. (2018, June). An M/G/1 queue with a workload barrier and extreme service times.  CORS 2018 (Canadian Operational Research Society), Halifax.
  • Brill, P. & Huang, M. L. (2016, October). A Renewal Process for Extremes.  International Conference on Statistical Distributions and Applications (ICOSDA) conference, Niagara Falls, Canada.
  • Brill, P. (2015, June). On the service time in an M/G/1 queue with bounded workload.  CORS/INFORMS 2015, Montreal.
  • Brill, P. (2014). Example of a renewal process with no-mean interval-arrival times.  Joint Statistical Meetings (JSM) 2014, Boston.
  • Brill, P. (2013). On a renewal process with no-means inter-arrival times. Invited presentation at CanQueue 2013, University of Waterloo, Waterloo, Canada.
  • Brill, P. (2013, August). Level crossing method in stochastic models.  Workshop, Brock University, St. Catherines, Canada.
  • Brill, P. (2013, August). Level crossing method in stochastic models.  Workshops, University of Waterloo and University of Windsor, Waterloo, Canada.
  • Huang, M. L., Coia, V., & Brill, P. H. (2012). A mixture truncated Pareto distribution.  Joint Statistical Meetings (JSM) 2012, San Diego, California.
  • Brill, P. (2012, June). On M/G/1 queues with reneging.  CORS 2012, Niagara Falls, Canada-Ontario.
  • Brill, P. (1976, June). The system point process in queueing.  6th Conference on Stochastic Models and their Applications, Tel Aviv, Israel.
  • Brill, P. (1975, June). A new methodology for modelling a broad class of exponential queues.  5th Conference on Stochastic Models and their Applications.

Research Reports 

  • 2008: Hlynka, M., & Brill, P.H., A result for a counter problem., submitted to University of Windsor Mathematics and Statistics Report, WMSR-08-01
  • 2007: Hlynka, M., & Brill, P.H., Stability in M/M/1 queues with reneging., submitted to University of Windsor Mathematics and Statistics Report, WMSR-07-09
  • 2006: Mandelbaum, M., Hlynka, M., & Brill, P.H., Nonhomogeneous geometric distribution representation and queuing., submitted to University of Windsor Mathematics and Statistics Report, WMSR-06-03
  • 2005: Wu, X., Brill, P.H., & Hlynka, M., An M/DN/1 retrial queue, submitted to University of Windsor Mathematics and Statistics Report, WMSR-02-05
  • 2004: Wu, X., Brill, P.H., & Wang, J., An M/G/1 retrial queue with retrials of the customer and balking, submitted to University of Windsor Mathematics and Statistics Report, WMSR-04-03
  • 2002: Brill, P. H., Properties of the waiting time in M/DN/1 queues, submitted to University of Windsor Mathematics and Statistics Report, WMSR-02-01
  • 1999: Huang, M. L., & Brill, P.H., A level crossing method, submitted to University of Windsor Mathematics and Statistics Report, WMSR-99-01, pp. 1-28
  • 1999: Huang, M. L., & Brill, P.H., A level crossing method, submitted to University of Windsor Mathematics and Statistics Report, WMSR-99-01
  • 1998: Brill, P. H., & Hlynka, M., Companion results to L = xW, submitted to University of Windsor Mathematics and Statistics Report, WMSR-98-01
  • 1997: Chen, P., & Brill, P.H., Sieve of Eratosthenes and Bose's packing problem, submitted to Colorado State University Department of Statistics, Technical Report #97-12
  • 1997: Brill, P. H., & Hlynka, M., A geometric interpretation of markov transition matrices, submitted to University of Windsor Mathematics and Statistics Report, WMSR-97-01
  • 1997: Brill, P. H., & Hlynka, M., A multiple servers who's next queue, submitted to University of Windsor Mathematics and Statistics Report, WMSR-97-03
  • 1996: Huang, M. L., & Brill, P.H., Empirical distribution based on level crossings, submitted to University of Windsor School of Business.  Working Paper #W96-01, ISSN: 1714-6191 (19 pp)
  • 1996: Huang, M. L., & Brill, P.H., A density estimator based on level crossings, submitted to University of Windsor School of Business, Working Paper # W96-02, ISSN: 1714-6191 (35 pp)
  • 1995: Brill, P. H., & Harris, C.M., Queues with markov-connected server vacations: Theory and computations, submitted to George Mason University Department of Operations Research and Engineering, Fairfax, Virginia.  Technical Report TR # 089501, 2 (23 pp)
  • 1994: Chaouch, A., & Brill, P.H., Stationary properties of an inventory system with irregular shipment pattern, submitted to University of Windsor School of Business, Working Paper # 94-13, ISSN: 1714-6191 (21 pp)
  • 1993: Brill, P. H., & Hlynka, M., The who's next queue with two lines, submitted to University of Windsor School of Business, Working Paper # 98-08 ISSN: 1714-6191 (20 pp)
  • 1993: Brill, P. H., & Chaouch, A., An EOQ model with random variations in demand, submitted to University of Windsor School of Business, ISSN: 1714-6191 (30 pp)
  • 1989: Brill, P. H., & Harris, C.M., Waiting times for M/G/1 queues with service-time-dependent server vacations, submitted to George Mason University Department of Operations Research and Engineering, Fairfax, Virginia.  Technical Report # GMU/22474/110 (18 pp) Accession # ADA209597
  • 1988: Brill, P. H., Waiting times in queues with state dependent bulk service, submitted to University of Windsor School of Business, Working Paper # 88-02 (23 pp)
  • 1988: Brill, P. H., A technique for transient distributions in stochastic models, submitted to University of Windsor School of Business, Working Paper # 88-13 (20 pp)
  • 1988: Brill, P. H., The time-dependent system point method in queues, dams and inventories, submitted to University of Windsor School of Business, Working Paper # 88-16 (25 pp)
  • 1988: Mandelbaum, M., & Brill, P.H., Motivational examples for flexibility and adaptivity in production systems, submitted to University of Windsor School of Business, Working Paper # 88-01 (29 pp)
  • 1988: Brill, P. H., The time dependent system point level crossing method for exponential queues., submitted to University of Windsor School of Business.  WP #88-18 (33 pp)
  • 1987: Brill, P. H., & Mandelbaum, M., Measures of flexibility in production systems, submitted to University of Windsor School of Business. WP # 87-01 (8 pp)
  • 1987: Brill, P., & Mandelbaum, M., Adaptivity and flexibility in production systems, submitted to University of Windsor School of Business. WP # 87-17 (18 pp)
  • 1987: Brill, P. H., Single server queues with delap dependent arrival streams, submitted to University of Windsor School of Business. WP # 87-16 (36 pp)
  • 1987: Brill, P. H., System-point computation of virtual waiting time distributions in multiple server queues, submitted to University of Windsor School of Business. WP # 87-15 (32 pp)
  • 1987: Brill, P. H., Bounds for distributions of waiting times in priority queues, submitted to University of Windsor School of Business. WP # 87-11 (31 pp)
  • 1987: Brill, P. H., Bounds for distributions of waiting times in priority queues, submitted to University of Windsor School of Business. WP # 87-11 (31 pp)
  • 1987: Brill, P. H., System-point computation of distributions in queues, dams and inventories, submitted to University of Windsor School of Business. WP # 87-12 (32 pp)
  • 1987: Brill, P. H., & Covert, D., A level crossing modelling technique for waiting time in two class M/G/1 priority queues, submitted to University of Windsor School of Business. WP # 87-10 (28 pp)
  • 1987: Brill, P. H., & Mandelbaum, M., On measures of flexibility in manufacturing systems, submitted to University of Windsor School of Business. WP # 87-08 (18 pp)
  • 1983: Brill, P. H., Queues with reneging depending on required wait, submitted to University of Waterloo Department of Statistics and Actuarial Science. Technical Report # 83-06 (72 pp)
  • 1983: Brill, P. H., System-point Monte Carlo simulation of stationary distributions of waiting times in single server queues, submitted to University of Waterloo Department of Statistics and Actuarial Science. Technical Report # 83-10 (30 pp)
  • 1983: Azoury, K., & Brill, P.H., A system-point approach to inventory models, submitted to University of Waterloo Department of Statistics and Actuarial Science. Technical Report # 83-07 (47 pp)
  • 1982: Green, L., & Brill, P.H., Queues in which customers receive simultaneous service from a random number of servers - A system point approach, submitted to Columbia University, Graduate School of Business. Research Working Paper # 466A (25 pp)
  • 1976: Brill, P. H., Embedded level crossing processes in dams and queues, submitted to University of Toronto Department of Industrial Engineering. WP # 76-022 (24 pp)
  • 1976: Brill, P. H., & Posner, M.J., A characterization of exponential queues with hereogeneous servers, submitted to University of Toronto Department of Industrial Engineering. WP # 76-021 (24 pp)
  • 1975: Brill, P., & Posner, M.J., Level crossing in point process applied to queues: Single server case, submitted to University of Toronto Department of Industrial Engineering. WP # 75-009 (25 pp)
  • 1974: Brill, P. H., & Posner, M.J., Two server queues with service time depending on waiting time, submitted to University of Toronto Department of Industrial Engineering. WP # 74-005 (61 pp)
  • 1974: Brill, P. H., & Posner, M.J., On the equilibrium waiting time distribution for a class of exponential queues, submitted to University of Toronto Department of Industrial Engineering. WP # 74-012 (34 pp)
  • 1974: Brill, P. H., & Posner, M.J., Applications of a conjecture on the waiting time probability density function for queues in equilibrium, submitted to University of Toronto Department of Industrial Engineering. WP 74-011 (29 pp)
  • 1974: Brill, P. H., & Posner, M.J., A multiple server queue with service time depending on waiting time, submitted to University of Toronto Department of Industrial Engineering. WP # 74-008 (30 pp)

Grants 

  • 2004-2008: Brill, P.H. (Principal Investigator), Stochastic Models and Methods in Operations Research, Applied Probability, and Related Areas.  SSHRC.  Total amount: $107,580.