Publications 1977 and later

For Books: See Books
  1. W. Grassmann and J. Tavakoli, 2019. The Distribution of the Line Length in a Discrete Time GI/G/1 Queue. Performance Evaluation 131, pp. 43-53
  2. W. Grassmann and J. Tavakoli. A Numerical Method to Determine the Waiting Time and the Idle Time Distributions of a GI/G/1 Queue when Inter-arrival Times and/or Service Times have Geometric Tails. INFOR 57(2), pp. 286-295.
  3. W. Grassmann. 2016. Solutions of Equations Reducible to the Form z^n(1-z)^m. Alabama Journal of Mathematics 40, pp. 1-6.
  4. W. Grassmann and J. Tavakoli, 2014. Efficient Methods to find the Equilbrium Distribution of the Number of Customers in GI/M/c Queues. INFOR 52(4), pp. 197-205.
  5. W. K. Grassmann, Factors Affecting Warm-up Periods in Discrete Event Simulation. Simulation vol. 90.1, pp. 11-23.
  6. W. K. Grassmann, A Computer Built with Relays and a Mechanical Memory, and ALGOL The Computer Journal 2012, vol 55(11), 1309-1316.
  7. W. K. Grassmann. Rethinking the Initialization Bias Problem in Steady-State Discrete Event Systems Proceeding of the 2011 Winter Simulation Conference, 2011, 593-599.
  8. W. K. Grassmann, A New Method for Finding the Characteristic Roots of the En/Em/1 Queue, Methodol Comput Appl Probab 2011, vol 13, 873-886
  9. W. K. Grassmann, J. Tavakoli, Comparing Some Algorithms for Solving QBD Processes Exhibiting Special Structures INFOR 2010, vol 48, 133-141.
  10. W. K. Grassmann, J. Tavakoli. Transient Solutions for Multi-server Queues with Finite Buffers. Queueing Systems 2009, vol 62, 35-49.
  11. W. K. Grassmann, J. Tavakoli. Spectrum of Certain Tridiagonal Matrixes when Their Dimension Goes to Infinity. Linear Algebra and Its Applications 2009, vol 431, 1208-1217.
  12. W. K. Grassmann, When, and when not to Use Warm-up Periods in Discrete Event Simulation. SimuTools 2009, Rome 2009.
  13. W. K. Grassmann. Stochastic and Substochastic Solutions for Infinite-State Markov Chains with Applications to Matrix-Analytic Methods. Adv. Appl. Prob. 2008, vol 40, 1157-1173.
  14. W. K. Grassmann, M. L. Puterman, P. L'Ecuyer, A. Ingolfsson. Three Canadian Contributions to Stochastic Modeling. INFOR, 2008. vol 46(1), 3-14.
  15. W. K. Grassmann. Warm-Up Periods in Simulation can be Detrimental, Probability in the Engineering and Informational Sciences,, 2008, vol 22, 415-429.
  16. W. K. Grassmann, S. Drekic. Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes Methodology and Computing in Applied Probability. , 2008, vol. 10, 73-83.
  17. W. K. Grassmann and J. Tavakoli. The Continuous Spectrum for the M/M/1 Queue. Linear and Multilinear Algebra, vol 56(3), 2008, 319-331.
  18. W. K. Grassmann and J. Tavakoli, A Baysian Approach to Find Random-Time Probabilities from Embedded Markov Chain Probabilities. Probability in the Engineering and Informational Sciences. vol. 21, 2007, 551-556.
  19. W. K. Grassmann, J. Tavakoli. Two-station Queueing Networks with Moving Servers, Blocking, and Customer Loss Electronic Journal of Linear Algebra, vol. 13, 2005.
  20. W. K. Grassmann, J. Luo. Simulating Markov-Reward Processes with Rare Events, ACM Transactions on Modeling and Computer Simulation. vol, 15(2), April 2005, pp. 138-154,
  21. J. Luo and W. K. Grassmann, 2004. Rate Tilting for Fast Simulation of Level/Phase Processes, Linear Algebra and its Applications 386, 261-284.
  22. W. K. Grassmann, 2004. Finding Equilibrium Probabilities of QBD Processes by Spectral Methods when Eigenvalues Vanish, Linear Algebra and its Applications 386, 207-223.
  23. W. K. Grassmann, 2003. The Use of Eigenvalues for Finding Equilibrium Probabilities of Certain Markovian Two-dimensional Queueing Problems. INFORMS Journal on Computing, vol. 15(4), 412-421.
  24. S. Drekic and W. K. Grassmann. 2002. An Eigenvalue Approach to Analyzing a Finite Source Queueing Model. Annals of Operations Research 112, 139-152.
  25. W. K. Grassmann. 2002. Real Eigenvalues of Certain Tridiagonal Matrix Polynomials, with Queueing Applications. Linear Algebra and its Applications, vol. 342, 93-106.
  26. W. K. Grassmann and J. Tavakoli. 2002. A Tandem Queue with a Movable Server: An Eigenvalue Approach. SIAM Journal on Matrix Analysis and Applications, vol. 24(2), 465-474.
  27. S. Drekic and W. K. Grassmann. 2002. An Eigenvalue Approach to Analysing a Finite Source Priority Queueing Model. Annals of Operations Research, vol. 112, 139-152.
  28. W. K. Grassmann, X. Chen, B. R. K. Kashyap. 2001. Optimal Service Rates for the State-dependent M/G/1 Queue in Steady State. Operations Research Letters, vol. 29, 57-63.
  29. D. A. Stanford and W. K. Grassmann. 2000. Bilingual Server Call Centres. in: Analysis of Communication Networks: Call Centres, Traffic and Performance, D. R. McDonald and S. R. E. Turner, editors. Fields Institute Communications, 31-47.
  30. W. K. Grassmann and S. Drekic. 2000. An Analytical Solution for a Tandem Queue with Blocking. Queueing Systems, vol. 36, 221-235.
  31. W. K. Grassmann. 1998. Finding Test Data for Markov Chains with Repeating Columns, in: Advances in Matrix-Analytic Methods for Stochastic Systems, A.S. Alfa, S. R. Chakravarthy, editors, Notable Publications, Inc., New Jersey, pp 261-278.
  32. W. K. Grassmann, Y. Zhao. 1996. Heterogeneous Multiserver Queues with General Input. INFOR 35, 208-224.
  33. W. K. Grassmann. 1996. Optimizing Steady State Markov Chains by State Reduction, European Journal of Operational Research 89 (1996), 277-284
  34. W. K. Grassmann, X. Chen. 1995. The Use of Derivatives for Optimizing Steady State Queues. Journal of the Operational Research Society 46, 104-115.
  35. W. K. Grassmann, Y. Wang. 1995. Immediate Events in Markov Chains. In: W. J. Stewart, Computations with Markov Chains, Kluwer Academic Publishers, 163-176.
  36. Yiqiang Zhao, Winfried K. Grassmann. 1995. Queueing Analysis of a Jockeying Model. Operations Research 43, 520-529.
  37. Winfried Grassmann. 1993. Rounding Errors in Certain Algorithms Involving Markov Chains, ACM Transaction on Mathematical Software, 496-508.
  38. D. A. Stanford, W. K. Grassmann. 1993. The Bilingual Server System: a Queueing Model Featuring Fully and Partially Qualified Servers. INFOR 31, 261-277.
  39. Winfried Grassmann, Daniel Heyman, 1993. Computation of Steady-State Probabilities for Infinite-State Markov Chains with Repeating Rows. ORSA Journal on Computing, 282-303.
  40. W. K. Grassmann, 1993, Means and Variances of Markov Reward Systems. Linear Algebra, Markov Chains, and Queueing Models, Book edited by C. D. Meyer and R. J. Plemmons, 193-204.
  41. Y. Zhao and W. k. Grassmann. 1991. A Numerical Stable Algorithm for Two Server Queue Models. Queueing Systems 8, pp. 59-80.
  42. W. K. Grassmann. 1991. Finding Transient Solutions in Markovian Event Systems Through Randomization. Numerical Solution of Markov Chains, W.J. Stewart, editor. pp.357-371.
  43. M. I. Taksar. 1991. Probabilistic Approach to Computational Algorithms for Finding Stationary Distributions of Markov Chains. Journal of Computational and Applied Mathematics 36, pp. 131-136.
  44. Y. Zhao and W. K. Grassmann. 1990. The Shortest Queue Model with Jockeying.. Naval Research Logistics 37, pp. 773-787.
  45. W. K. Grassmann and D. P. Heyman. 1990. Equilibrium Distribution of Block-structured Markov Chains with Repeating Rows. Journal of Applied Probability 27, pp. 557-576.
  46. W. K. Grassmann and J. Jain. 1989. Numerical Solutions of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI/G/1 Queue. Operations Research 37(1), pp. 141-150.
  47. W. K. Grassmann. 1989. A Probabilistic Analysis of Rounding Errors of Floating Point Numbers. Congressus Numeratium 68, pp. 171-182.
  48. W. K. Grassmann. 1988. Finding the Right Number of Servers in Real-World Queueing Systems. Interfaces 18(2), pp. 94-104.
  49. J. L. Jain and W. K. Grassmann. 1988. Numerical Soluton for the Departure Process from the GI/G/1 Queue. Computers and Operations Research 15(3), pp.293-296.
  50. W. K. Grassmann. 1987. Means and Variances of Time Averages in Markovian Environments. European Journal of Operational Research 31, 132-139.
  51. S. Kumar and W. Grassmann and R. Billinton. 1987. A Stable Algorithm to Calculate Steady-State Probability and Frequency of a Markov System. IEEE Transaction on Reliability R-36(1), pp. 58-62.
  52. W. K. Grassmann. 1987. The Asymptotic Variance of a Time Average in a Birth-Death Process. Annals of Operations Research 8, pp. 165--174.
  53. W.K. Grassmann. 1986. Is the Fact that the Emperor Wears No Clothes a Subject Worthy of Publication. Interfaces 16(2), pp. 43-51.
  54. W. K. Grassmann, M. I. Taksar and D. P. Heyman. 1985. Regenerative Analysis and Steady State Distributions for Markov Chains. Operations Research 33(5), pp. 1107-1116.
  55. W. K. Grassmann. 1985. The Factorization of Queueing Equations and Their Interpretation. Journal of the Operational Research Society 36(11), pp. 1041-1050.
  56. W. Grassmann. 1983. The Convexity of the Mean Queue Size of the M/M/1 Queue with Respect to the Traffic Intensity. Jouranl of Applied Probability 20, pp. 916-919.
  57. W. K. Grassmann. 1982. Initial Bias and Estimation Error in discrete Event Simulation. Proceedings of the 1982 Simulation conference, pp. 377-384.
  58. W. K. Grassmann. 1982. The GI/PH/1 Queue: A Method to Find the Transition Matrix. INFOR 20(2), pp. 144-156.
  59. W. K. Grassmann and M. L. Chaudhry. 1982. A New Method to Solve Steady State Queueing Equations. Naval Research Logistic Quarterly 29(3), pp. 461-473.
  60. W. K. Grassmann. 1981. The Optimal Estimation of the Expected Number in a M/D/infty Queueing System. Operations Research 29(6) pp. 1208-1211.
  61. W. K. Grassmann. 1980. Transient and Steady State Results for Two Parallel Queues. OMEGA 8(1), pp. 105-112.
  62. M. V. Cromie, M. L. Chaudhry and W. K. Grassmann. Further Results for the Queueing System M^X/M/c. Journal of the Operational Research Society 30(8), pp. 755-763.
  63. D. F. Holman, W. K. Grassmann and M. L. Chaudhry. 1980. Some Results for the Queueing System E_k^X/M/c. Naval Research Logistics Quarterly 27(2), pp. 217-222.
  64. W. K. Grassmann. 1979. The Economic Service Rate. Journal of the Operational Research Society 30(2), pp. 19-155. < li> W. K. Grassmann. 1977. Transient Solutions in Markovian Queueing Systems. Computers and Operations Research 4, pp. 47-53.
  65. W. K. Grassmann. 1977. Transient Solutions in Markovian Queues. European Journal of Operational Research 1, pp. 396-402.

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