Publications with Joseph Abate

Collaboration with Joe Abate began in the mid 80's while we both were at Bell Labs. Joe had earned a Ph.D. in theoretical physics from Courant Institute (New York University) in 1967, after which he did engineering and performance analysis. Joe was at AT&T Bell Laboratories from 1971 to 1990. When we met, Joe was at the Whippany facility, leading a group in the development of capacity models and performance analysis tools for the Loop Maintenance Operations Support (LMOS) system - a large on-line computer system which supports loop repair operations for telephone companies (i.e., handling "611" calls). Joe subsequently led a group at Whippany developing an experimental signal processing system, concerned with processing active sonar signals to support long-range surveillance, to meet "the silent threat". That experience (vicarious for me) enhanced my reading of The Hunt for the Red October.

In addition to having a strong practical engineering focus, Joe has a passion for serious research and scholarship. Joe is interested in the "grundlagen", wanting to understand what is fundamental and wanting to put important ideas in proper historical perspective. Thus, throughout his career, Joe has pursued research interests in his spare time (when he is not cooking or gardening), focusing on Laplace transforms, numerical transform inversion, classical applied mathematics (especially asymptotics associated with Laplace transforms) and queueing models.

So, back in the 80's I was fortunate to have a phone call from Joe. I had done a few papers focusing on ways to obtain simple approximations to describe queueing performance, and Joe wanted to discuss some of his ideas. That initial interaction led to an active research collaboration. The two main topics of our joint research became: (1) exact and approximate methods to describe the transient behavior of queues and (2) numerical transform inversion.

Laplace transforms and numerical transform inversion are used throughout our work, from the very beginning. When we started, I knew little (was totally ignorant) about these interesting and useful tools (and much of classical applied mathematics, more generally). I have been fortunate to have Joe as a teacher, helping me to remedy this deficiency. Because of Joe, numerical transform inversion and its application to analyze the performance of complex systems has become one of my main research interests. When we met, Joe had already been using numerical transform inversion for 20 years. Our numerical transform inversion work builds on Joe's long experience, as can be seen from his seminal paper, H. Dubner and J. Abate, "Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform." J. ACM, vol. 15, 1968, pp. 115-123.

For a quick introduction to basic algorithms for numerically inverting Laplace transforms, see:

Numerical Inversion of Laplace Transforms of Probability Distributions. ORSA Journal on Computing, vol. 7, 1995, pp. 36-43. [published PDF]

For a recent introduction and survey of our work 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 Gagan L. Choudhury). [PostScript] [PDF] (Books have been started.)

For papers that capture some of Joe's interesting perspective, see:

An Operational Calculus for Probability Distributions Via Laplace Transforms. Advances in Applied Probability, vol. 28, 1996, pp. 75-113. [published PDF]

Computing Laplace Transforms for Numerical Inversion Via Continued Fractions. INFORMS Journal on Computing, vol. 11, No. 4, Fall 1999, pp. 394-405. [published PDF]

Address:  Joseph Abate, 900 Hammond Road, Ridgewood, NJ 07450-2908, Fax: 201-447-0477

Here are our joint papers in chronological order:

  1. Transient Behavior of the M/M/1 Queue: Starting at the Origin. Queueing Systems: Theory and Applications, vol. 2, No. 1, 1987, pp. 41-65. [published PDF]
  2. Transient Behavior of Regulated Brownian Motion I: Starting at the Origin. Advances in Applied Probability, vol. 19, No. 3, September 1987, pp. 560-598. [published PDF]
  3. Transient Behavior of Regulated Brownian Motion, II: Non-Zero Initial Conditions. Advances in Applied Probability, vol. 19, No. 3, September 1987, pp. 599-631. [published PDF]
  4. Transient Behavior of the M/M/1 Queue Via Laplace Transforms. Advances in Applied Probability, vol. 20, No. 1, March 1988, pp. 145-178. [published PDF]
  5. The Correlation Functions of RBM and M/M/1. Stochastic Models, vol. 4, No. 2, 1988, pp. 315-359. [published PDF]
  6. Approximations for the M/M/1 Busy Period. Queueing Theory and its Applications, Liber Amicorum for Professor J. W. Cohen North-Holland, Amsterdam, 1988, pp. 149--191 [published PDF]
  7. Simple Spectral Representations for the M/M/1 Queue. Queueing Systems, vol. 3, No. 4, 1988, pp. 321-346. [published PDF]
  8. Spectral Theory for Skip-Free Markov Chains. Probability in the Engineering and Information Sciences, vol. 3, No. 1, 1989, pp. 77-88. [published PDF]
  9. Calculating Time-Dependent Performance Measures for the M/M/1 Queue. IEEE Transactions on Communications, vol. 37, No. 10, 1989, pp. 1102-1104. [published PDF]
  10. Decompositions of the M/M/1 Transition Function. Queueing Systems, vol. 9, No. 3, 1991, & pp. 323-336. [published PDF]
  11. The Fourier-Series Method for Inverting Transforms of Probability Distributions. Queueing Systems, vol. 10, No. 1, 1992, pp. 5-88. [published PDF]
  12. Numerical Inversion of Probability Generating Functions. Operations Research Letters, vol. 12, No. 4, 1992, pp. 245-251. [published PDF]
  13. Solving Probability Transform Functional Equations for Numerical Inversion. Operations Research Letters, vol. 12, 1992, pp. 275-281. [published PDF]
  14. 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 Gagan L. Choudhury). [published PDF]
  15. Asymptotics for Steady-State Tail Probabilities in Structured Markov Queueing Models. Stochastic Models, vol. 10, No. 1, 1994, pp. 99-143 (with Joseph Abate and Gagan L. Choudhury). [published PDF]
  16. 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]
  17. Transient Behavior of the M/G/1 Workload Process. Operations Research, vol. 42, No. 4, 1994, pp. 750-764. [published PDF]
  18. A Heavy-Traffic Expansion for the Asymptotic Decay Rates of Tail Probabilities in Multi-Channel Queues. Operations Research Letters, vol. 15, 1994, pp. 223-230. [PostScript] [PDF]
  19. Numerical Inversion of Laplace Transforms of Probability Distributions. ORSA Journal on Computing, vol. 7, 1995, pp. 36-43. [published PDF]
  20. Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times. Operations Research, vol. 43, 1995, pp. 885-901 (with Joseph Abate and Gagan L. Choudhury). [published PDF]
  21. Limits and Approximations for the Busy-Period Distribution in Single-Server Queues. Probability in the Engineering and Informational Sciences, vol. 9, 1995, pp. 581-602. (with Joseph Abate) [published PDF]
  22. 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 and Gagan L. Choudhury). [published PDF]
  23. Asymptotic Analysis of Tail Probabilities Based on the Computation of Moments. Annals of Applied Probability, vol. 5, 1995, pp. 983-1007 (with Joseph Abate, Gagan L. Choudhury and David M. Lucantoni). [published PDF]
  24. An Operational Calculus for Probability Distributions Via Laplace Transforms. Advances in Applied Probability, vol. 28, 1996, pp. 75-113. [published PDF]
  25. Exponential Approximations for Tail Probabilities in Queues, II: Sojourn Time and Workload. Operations Research, vol. 44, 1996, pp. 758-763 (with Gagan L. Choudhury). [published PDF]
  26. 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). [published PDF]
  27. Asymptotics for M/G/1 Low-Priority Waiting-Time Tail Probabilities. Proceedings of 34th Allerton Conference on Communication, Control and Computing, S. P. Meyn and W. K. Jenkins (eds.) 1996, pp. 923-931.
  28. Asymptotics for M/G/1 Low-Priority Waiting-Time Tail Probabilities. Queueing Systems, vol. 25, 1997, pp. 173-223. [published PDF]
  29. Limits and Approximations for the M/G/1 LIFO Waiting-Time Distribution. Operations Research Letters, vol. 20, 1997, pp. 199-206. [published PDF]
  30. Numerical Inversion of Multidimensional Laplace Transforms by the Laguerre Method. Performance Evaluation, vol. 31, 1998, pp. 229-243 (with Gagan L. Choudhury). [published PDF]
  31. Calculating Transient Characteristics of the Erlang Loss Model by Numerical Transform Inversion. Stochastic Models, vol. 14, No. 3, 1998, pp. 663-680. (with Joseph Abate) [PDF] [published PDF]
  32. Modeling Service-Time Distributions with Non-Exponential Tails: Beta Mixtures of Exponentials. Stochastic Models, vol. 15, No. 3, 1999, pp. 517-546. (with Joseph Abate) [PDF] [published PDF]
  33. Explicit M/G/1 Waiting-Time Distributions for a Class of Long-Tail Service-Time Distributions. Operations Research Letters, vol. 25, No. 1, August 1999, pp. 25-31. [published PDF]
  34. 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 Gagan L. Choudhury). [PostScript] [PDF]
  35. Infinite-Series Representations of Laplace Transforms of Probability Density Functions for Numerical Inversion. Journal of Operations Research Society of Japan, vol. 42, No. 3, September 1999, pp. 268-285. [published PDF]
  36. Computing Laplace Transforms for Numerical Inversion Via Continued Fractions. INFORMS Journal on Computing, vol. 11, No. 4, Fall 1999, pp. 394-405. [published PDF]
  37. A Unified Framework for Numerically Inverting Laplace Transforms.. INFORMS Journal on Computing, vol. 18, No. 4, 2006, pp. 408-421. [PDF]
  38. Integer Sequences from Queueing Theory. Journal of Integer Sequences, vol. 13, 2010, article 10.5.5. [PDF]
  39. Brownian Motion and the Generalized Catalan Numbers.. Journal of Integer Sequences, under review. [PDF]