Publications with Gagan L. Choudhury

Collaboration with Gagan Choudhury began in 1992 when he spent a year as an intern in the Mathematics of Networks and Systems Department (headed by Debasis Mitra, where I was) in the Mathematical Sciences Research Center at Bell Labs. As a member of the Network Design and Performance Analysis Department (headed by Pat Wirth), Gagan had already established a strong interest in algorithms and performance analysis tools. Thus Gagan was an ideal person to partner with Joe Abate and me in our efforts to develop numerical transform inversion tools.

Gagan is especially attracted to hard problems. Thus he was attracted to the challenging multidimensional numerical transform inversion problems. Indeed, Gagan wrote almost all the multidimensional inversion code. In doing so, Gagan demonstrated extraordinary algorithm and programming skills as well as mastery of the underlying theory. The basic multidimensional numerical transform inversion algorithms are not so difficult (when the dimension is not large), as can be seen from our 1994 Annals of Applied Probability paper. The real difficulty usually lies in developing special methods to treat specific problems. The challenge, and Gagan's great contribution, can be seen by looking at the 1995 J. ACM paper on closed queueing networks, the 1995 ToN paper on stochastic loss networks with state-dependent rates, the 1996 Performance Evaluation paper on polling systems and the 1997 Operations Research paper on the MtGt/1 queue (all appearing below). The algorithms in those papers go well beyond a direct application of the multidimensional inversion algorithm.

In addition to his important direct personal contributions, Gagan also has helped expand the numerical-inversion project by helping to enlist the cooperation of outstanding colleagues from his department such as David Lucantoni and Kin Leung. Gagan also contributed greatly to technology transfer within AT&T by leading the development of the "Q-squared" numerical-inversion-based performance analysis tool in his department.

For an introduction and survey on numerical transform inversion, see An Introduction to Numerical Transform Inversion and its Application to Probability Models, in Computational Probability, W. Grassman (ed.), Kluwer, Boston, 1999, pp. 257-323 (with Joseph Abate). [PostScript] [PDF]

Here are all papers co-authored with Gagan in chronological order:

  1. Calculation of the GI/G/1 steady-State Waiting-Time Distribution and its Cumulants from Pollaczek's Formula. Archiv für Elektronik und Übertragungstechnik, vol. 47, No. 5/6, 1993, pp. 311-321 (with JosephAbate). [published PDF]
  2. Heavy-Traffic Asymptotic Expansions for the Asymptotic Decay Rates in the BMAP/G/1 Queue. Proceedings of the ITC Seminar on Teletraffic Analysis Methods for Current and Future Telecom Networks, Bangalore, India, November 1993, pp. 129-136.
  3. Computing Transient Distributions in General Single-Server Queues. Proceedings of IEEE Globecom 93, No. 29.1, 1993, pp. 1045-1050 (with David M. Lucantoni). [published PDF]
  4. Asymptotics for Steady-State Tail Probabilities in Structured Markov Queueing Models. Stochastic Models, vol. 10, No. 1, 1994, pp. 99-143 (with Joseph Abate). [published PDF]
  5. The Transient BMAP/G/1 Queue. Stochastic Models, vol. 10, No. 1, 1994, pp. 145-182 (with Gagan L. Choudhury and David M. Lucantoni). [published PDF]
  6. Heavy-Traffic Asymptotic Expansions for the Asymptotic Decay Rates in the & BMAP/G/1 Queue. Stochastic Models, vol. 10, No. 2, 1994, pp. 453-498. (with Gagan L. Choudhury) [published PDF]
  7. On the Effectiveness of Effective Bandwidths for Admission Control in ATM Networks. The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks, Proceedings of the 14th International Teletraffic Congress, J. Labetoulle and J. W. Roberts (eds.), Elsevier, Amsterdam, vol. 1a, 1994, pp. 411-420 (with David M. Lucantoni).
  8. Numerical Transform Inversion to Analyze Teletraffic Models. The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks, Proceedings of the 14th International Teletraffic Congress, J. Labetoulle and J. W. Roberts (eds.), Elsevier, Amsterdam, vol. 1b, 1994, 1043-1052 (with David M. Lucantoni). [PostScript] [PDF]
  9. Waiting-Time Tail Probabilities in Queues with Long-Tail Service-Time Distributions. Queueing Systems, vol. 16, 1994, pp. 311-338 (with Joseph Abate and Gagan L. Choudhury). [published PDF]
  10. Multi-Dimensional Transform Inversion with Applications to the Transient M/G/1 Queue. Annals of Applied Probability vol. 4, 1994, pp. 719-740 (with David M. Lucantoni). [published PDF]
  11. An Algorithm for Closed Queueing Networks Based on Numerical Transform Inversion. Proceedings of the 1994 Conference on Information Science and Systems, ed. H. Kobayashi, Department of Electrical Engineering, Princeton University, pp. 7-11 (with Kin K. Leung). [PostScript] [PDF]
  12. An Algorithm for Product-Form Loss Networks Based on Numerical Inversion of Generating Functions. Proceedings IEEE Globecom `94, 1994, pp. 1123-1128 (with Kin K. Leung). [published PDF]
  13. An Algorithm to Compute Blocking Probabilities in Multi-Rate Multi-Class Multi-Resource Loss Models. Computer-Aided Modeling, Analysis and Design of Communication Links and Networks, 1994 (CAMAD '94, 1994, (with Gagan L. Choudhury). [published PDF]
  14. Resource-Sharing Models with State-Dependent Arrivals of Batches. Computations with Markov Chains, W. J. Stewart, ed., Kluwer, Boston, 1995, pp. 255-282 (with Kin K. Leung). [published PDF]
  15. Q2: A New Performance Analysis Tool Exploiting Numerical Transform Inversion. Proceedings of Third International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, (MASCOTS `95), Durham, NC, January 1995, pp. 411-415. [PostScript] [PDF] [published PDF]
  16. An Inversion Algorithm for Loss Networks with State Dependent Rates. Proceedings of IEEE Infocom `95, 1995, pp. 513-521 (with Kin K. Leung). [published PDF]
  17. Computing Transient and Steady-State Distributions in Polling Models by Numerical Transform Inversion. IEEE International Conference on Communications, Seattle, WA, June 1995, pp. 803-809. [PDF file from IEEE] [published PDF]
  18. Calculating Normalization Constants of Closed Queueing Networks by Numerically Inverting Their Generating Functions. Journal of the Association for Computing Machinery, vol. 42, 1995, pp. 935-970 (with Kin K. Leung). [PostScript] [PDF] From ACM Digital Library.
  19. Efficiently Providing Multiple Grades of Service with Protection Against Overloads in Shared Resources. AT&T Technical Journal, vol. 74, No. 4, 1995, pp. 50-63 (with Gagan L. Choudhury and Kin K. Leung). [published PDF]
  20. An Inversion Algorithm to Calculate Blocking Probabilities in Loss Networks with State-Dependent Rates. IEEE/ACM Transactions on Networking, vol. 3, No. 5, 1995, pp. 585-601 (with Gagan L. Choudhury and Kin K. Leung). [ published PDF]
  21. Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times. Operations Research, vol. 43, 1995, pp. 885-901 (with JosephAbate). [published PDF]
  22. An Algorithm to Calculate Blocking Probabilities in Multi-Rate Multi-Class Multi-Resource Loss Models. Advances in Applied Probability, vol. 27, 1995, pp. 1104-1143 (with Kin K. Leung). [published PDF]
  23. Calculating the M/G/1 Busy-Period Density and the LIFO Waiting-Time Distribution by Direct Numerical Transform Inversion. Operations Research Letters, vol. 18, 1995, pp. 113-119 (with Joseph Abate). [published PDF]
  24. Asymptotic Analysis of Tail Probabilities Based on the Computation of Moments. Annals of Applied Probability, vol. 5, 1995, pp. 983-1007 (with Joseph Abate and David M. Lucantoni). [published PDF]
  25. Squeezing the Most Out of ATM. IEEE Transactions on Communications, vol. 44, No. 2, 1996, pp. 203-217 (with David M. Lucantoni). [PostScript] [PDF] [published PDF]
  26. Computing Distributions and Moments in Polling Models by Numerical Transform Inversion. Performance Evaluation, vol. 25, No. 4, 1996, pp. 267-292 (with Gagan L. Choudhury). [published PDF]
  27. Exponential Approximations for Tail Probabilities in Queues, II: Sojourn Time and Workload. Operations Research, vol. 44, 1996, pp. 758-763 (with Joseph Abate). [PostScript] [PDF]
  28. On the Laguerre Method for Numerically Inverting Laplace Transforms. INFORMS Journal on Computing, vol. 8, 1996, pp. 413-427 (with Joseph Abate and Gagan L. Choudhury). [PDF]
  29. Fluid and Diffusion Limits for Queues in Slowly Changing Random Environments. Stochastic Models, vol. 13, No. 1, 1997, pp. 121-146 (with Gagan Choudhury, Avishai Mandelbaum and Martin I. Reiman). [published PDF]
  30. Numerical Solution of Piecewise-Stationary Mt/Gt/1 Queues. Operations Research, vol.~45, No.~3, 1997, pp. 451-463,(with Gagan L. Choudhury and David M. Lucantoni). [published PDF]
  31. Scaling for Numerical Transform Inversion to Analyze Teletraffic Models. Teletraffic Contributions for the Information Age, Proceedings of ITC 15, V. Ramaswami and P. E. Wirth (eds.), Elsevier, Amsterdam, 1997, pp. 933-942.
  32. Probabilistic Scaling for the Numerical Inversion of Non-Probability Transforms. INFORMS Journal on Computing, vol. 9, No. 2, 1997, pp. 175-184. [PDF] [published PDF]
  33. Long-Tail Buffer-Content Distributions in Broadband Networks. Performance Evaluation, Vol. 30, 1997, pp. 177-190. [published PDF]
  34. Numerical Inversion of Multidimensional Laplace Transforms by the Laguerre Method. Performance Evaluation, vol. 31, 1998, pp. 229-243 (with Joseph Abate and Gagan L. Choudhury). [published PDF]
  35. Efficiently Providing Multiple Grades of Service with Protection Against Overloads in Shared Resources, U.S. patent 5,719,854 issued February 17, 1998 (with Kin K. Leung).
  36. An Introduction to Numerical Transform Inversion and its Application to Probability Models, in Computational Probability, W. Grassman (ed.), Kluwer, Boston, 1999, pp. 257-323 (with Joseph Abate). [PostScript] [PDF]