QROOT is a root-finding software package developed by M.L. Chaudhry, Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada, K7K 5L0. The package finds real or complex roots of characteristic equations which may be of polynomial (with or without complex coefficients) or transcendental type. Although the user-friendly QROOT package was originally designed to find roots of equations that occur in queueing theory, it is capable of finding roots of equations that may occur in several other areas such as mathematics, engineering, and econometrics. In fact, it has been tested on several examples in non-queueing fields. QROOT finds roots inside and outside a circle of a given radius, even when there is a large number of them. Roots that are outside may be brought inside the unit circle using a suitable transformation. The details on how the package works, worked-out examples, as well as a set of problems are available in the user’s manual. The main part of the manual explains with examples how to use the user-friendly package and what the error messages mean. QROOT is a very robust, fast and accurate method of finding roots. Since it bypasses both deflation and suppression, it works where all existing methods fail. It has been used to find roots even up to 5000. For some interesting examples, see the attached pages. Also, the attached examples show how it compares with MAPLE and MATHEMETICA.

References in zbMATH (referenced in 16 articles )

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  1. Banik, A. D.; Chaudhry, M. L.; Wittevrongel, Sabine; Bruneel, Herwig: A simple and efficient computing procedure of the stationary system-length distributions for (G I^X / D / c) and (B M a P / D / c) queues (2022)
  2. Goswami, Veena; Chaudhry, M. L.: The queue (Geo^X/G/1/N+1) revisited (2022)
  3. Chaudhry, M. L.; Goswami, Veena: The queue (\mathrmGeo/\mathrmG/1/N + 1) revisited (2019)
  4. Chaudhry, Mohan L.; Kim, James J.; Banik, Abhijit D.: Analytically simple and computationally efficient results for the (GI^X/ Geo /c) queues (2019)
  5. Chaudhry, Mohan L.; Kim, James J.: Analytically elegant and computationally efficient results in terms of roots for the (\mathrmGI^X/\mathrmM/c) queueing system (2016)
  6. Winands, E. M. M.; Adan, I. J. B. F.; Van Houtum, G. J.; Down, D. G.: A state-dependent polling model with (k)-limited service (2009)
  7. Kim, Nam K.; Chaudhry, Mohan L.: Equivalences of batch-service queues and multi-server queues and their complete simple solutions in terms of roots (2006)
  8. Chaudhry, Mohan L.; Kim, Nam K.: A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times. (2003)
  9. Chaudhry, Mohan L.: On numerical computations of some discrete-time queues (2000)
  10. Chaudhry, M. L.; Gupta, U. C.: Queue-length and waiting-time distributions of discrete-time (\textGI^X/\textGeom/1) queueing systems with early and late arrivals (1997)
  11. Iravani, S. M. R.; Posner, M. J. M.: An (M/G/1) queue with cyclic service times (1996)
  12. Wang, P. Patrick: Markovian queueing models with periodic-review (1996)
  13. Chaudhry, M. L.: On computations of the mean and variance of the number of renewals: A unified approach (1995)
  14. Chaudhry, Mohan L.; Zhao, Yiqiang Q.: First-passage-time and busy-period distributions of discrete-time Markovian queues: (\textGeom(n)/\textGeom(n)/1/N) (1994)
  15. Zhao, Yiqiang: Analysis of the (GI^ X/M/c) model (1994)
  16. Chaudhry, M. L.: Alternative numerical solutions of stationary queueing-time distributions in discrete-time queues: (GI/G/1) (1993)