The papers are classified by topic and co-author at the end.
1-10
[Algorithm to calculate approximate performance measures for a non-Markovian network of queues, subsequently applied to communication networks, computer systems and manufacturing facilities. First version of the QNA software package, exploiting the parametric-decomposition method. A focal point for research on approximations of performance measures in complex queueing systems, such as in papers 2, 15, 19, 21, 27 and 35 here. Also see: recent Variability Functions for Parametric-Decomposition Approximations of Queueing Networks. Management Science, vol. 41, No. 10, 1995, pp. 1704-1715. [PDF], related papers on approximations for queueing models and related papers on queueing network approximations.]
[Performance analysis methods for communication networks, specifically packet multiplexers for voice and data. Introduces indices of dispersion to approximately characterize the dependence structure in complex superposition arrival processes to queues. Builds on papers 1 and 15, extended further in paper 21 and in Measurements and Approximations to Describe the Offered Traffic and Predict the Average Workload in a Single-Server Queue. Proceedings of the IEEE, vol. 77, No. 1, 1989, pp. 171-194, (with Kerry W. Fendick) [published PDF]. Also see: related papers on communication networks related papers on approximating stochastic point processes (arrival processes to queues) and other papers co-authored with Kotikalapudi Sriram.]
[Initiates expanded use of numerical transform inversion in applied probability, proposes specific methods and provides a broad survey. Precursor to papers 6, 8, 20, 36, 37, 41, 43, 45, 47 and 50 below. Extended to multidimensional inversion in paper 36 below. Also see: the review book chapter, 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 and Gagan L. Choudhury). [PDF], related papers on numerical transform inversion and other papers co-authored with Joe Abate.
[Establishes large-deviation results for general single-server queues (without specific Markovian or independence structure), thus providing a theoretical basis for the concept of effective bandwidths in communication networks, such as in papers 7 and 42 below. Also see: related papers on large deviations and tail probability asymptotics and other papers co-authored with Peter Glynn.]
[An algorithm to approximate a heavy-tail (or long-tail) probability distribution by a mixture of exponentials, which can be convenient to carry out further analysis. Shows that such an approximation can effectively capture the essential character of the heavy-tailed distribution. Also see: related papers on performance impact of heavy-tailed distributions, as in references 10, 20, 31 and 43 below.]
(Anja Feldmann was a colleague at AT&T Labs. She is now on the faculty of the Computer Science Department at the Technical University of Munich.)
[Exposes the limitations of approximations based on effective bandwidths stemming from large deviations, as in papers 4 and 7 here, in the presence of many sources (without directly doing many-source asymptotics), by making comparisons with exact performance measures calculated by numerical transform inversion. Presents effective alternative approximations. An earlier conference version is paper 45 below. Also see: related papers on effective bandwidths, large deviations and tail probability asymptotics, including papers 4, 7, 25, 27, 38, 42 and 45 here, other papers co-authored with Gagan Choudhury and other papers co-authored with David Lucantoni.]
(David Lucantoni was also a colleague at Bell Labs. He is currently running his own consulting business.)
[Derives large deviation results and effective-bandwidth approximations for general queueing systems with multiple sources, without explicit Markov assumptions. Shows applied relevance of paper 4. For a more informal paper emphasizing applied relevance, as well as extension to priorities, see paper 42. Also see: related papers on effective bandwidths, large deviations and tail probability asymptotics, as in papers 4, 6, 25, 27, 38, 42 and 45 here.]
[Short version of part of paper 3 above, quickly specifying an effective algorithm for numerically inverting Laplace transforms: "Euler" (Fourier-series method). See paper 47 below for the short generating function version. Extended to higher dimensions in paper 36. Also see: related papers on numerical transform inversion and other papers co-authored with Joe Abate.]
[Pair of papers establishing heavy-traffic stochastic-process limits for multi-channel queues and networks of such queues, exploiting weak convergence in the function space D, as discussed in the book appearing next. Also see: early paper 48 below, related papers on heavy-traffic limits and diffusion approximations for queues and other papers co-authored with Donald L. Iglehart.]
Also see: Internet Supplement to the Book.
[Provides an introduction to (i) stochastic-process limits, in which a sequence of stochastic processes converges to another stochastic process, and (ii) heavy-traffic stochastic-process limits for queues, as used in the two 1970 papers above. However, there is a substantial amount of new material: Motivated by the complex traffic found in the Internet, the book focuses on alternative scaling associated with heavy-tailed probability distributions and long-range dependence. In addition to limit processes related to Brownian motion, the book discusses nonstandard limit processes related to stable Levy motion and fractional Brownian motion. From a technical point of view, an interesting feature is the focus on stochastic-process limits, in which the limit process has jumps (discontinuous sample paths) unmatched by the converging processes; e.g., the converging processes might have continuous sample paths. More common is for the converging processes to have jumps that are asymptotically negligible, as in scaled queue-length processes, and yet the accumulation of many small jumps in the converging processes produces jumps in the limit process. That phenomenon requires a nonstandard topology on the function space D; in particular, the Skorohod M1 topology is used.
The book may be regarded as an updated view of papers 9, 14 and 48 here, touching on related issues such as in papers 11, 13, 20, 21 and 40. Also see related papers on heavy-traffic limits and diffusion approximations for queues, related papers on performance impact of heavy-tailed distributions and related papers on probability theory.
11-20
[Establishes a new heavy-traffic limiting regime for many-server queues, now often called the Quality-and-Efficiency-Driven (QED) heavy-traffic regime, in which the number of servers is allowed to increase together with the arrival rate, while the service-time distribution is held fixed, so that the probability of delay approaches a non-degenerate limit. The applied relevance is discussed in paper 35 below. The results are also applied in paper 19 below. Extensions appear in Heavy-Traffic Limits for the G/H2*/n/m Queue. Mathematics of Operations Research, vol. 30, No. 1, February 2005, pp. 1-27, [published PDF], and A Diffusion Approximation for the G/GI/n/m Queue. Operations Research, vol. 52, No. 6, November-December 2004, pp. 922-941. [publishedPDF]. An error is corrected there. Also see: related papers on heavy-traffic limits and diffusion approximations for queues related papers on customer contact centers and other papers co-authored with Shlomo Halfin.]
(Shlomo Halfin was a colleague at Bell Labs. He retired from Bellcore. He is currently an active member of the Chatham, New Jersey, Emergency Squad).
[Establishes supporting theory for the Erlang fixed-point approximation for stochastic loss networks, including a limit as the network grows and a stochastic comparison. Also see: related papers on stochastic networks and related papers on limits for stochastic networks as the network grows.
[Shows how heavy-traffic limits for queues can be used to help determine the required simulation run length to achieve desired statistical precision in a queueing simulation and, thus, can help plan simulation experiments for queueing systems. Also see: related papers on simulation methodology and related papers on simulation of queueing models.
[Establishes the continuity of several useful functions on the function space D arising in heavy-traffic limits for queues and related stochastic models, as discussed in the book, Stochastic-Process Limits, published by Springer in 2002. Also see related papers on heavy-traffic limits and diffusion approximations for queues.]
[Framework for creating two-parameter approximations for arrival processes to queues in support of approximations for queueing networks, as contained in the first two papers above. The two methods are the asymptotic method and the stationary-interval method. Also see: related papers on queueing network approximations and related papers on approximating arrival processes to queues.
[Develops a stochastic model for wireless systems, exploiting Poisson random measures, that allows for dependence on both time and space. Builds on previous paper A Stochastic Model to Capture Space and Time Dynamics in Wireless Communication Systems, Probability in the Engineering and Informational Sciences, vol. 8, 1994, pp. 541-569. (with William A. Massey) [PDF]. Also see: other papers co-authored with Bill Massey, other papers co-authored with Kin K. Leung and related papers on communication networks.]
[Proposes an algorithm, based on offered-load analysis (an infinite-server approximation, see paper 46 below) to staff a many-server queue with a time-varying arrival rate to meet specified performance targets. Also see: other papers co-authored with Bill Massey, other papers co-authored with Avishai Mandelbaum, other papers on offered-load approximations, other papers queues with time-dependent arrival rates and new papers on the same topic.]
[Presents counterexamples showing that it is not optimal to join the shortest queue for all service-time distributions. Proof exploits light-traffic asymptotic expansion. Also see: other papers on economics, games and stochastic optimization.]
[Develops approximations for a large class of performance measures for the general multi-server queueing model. Improves upon approximations in paper 1 above. Also see: papers 27 and 35 below, the more recent A Diffusion Approximation for the G/GI/n/m Queue. Operations Research, vol. 52, No. 6, November-December 2004, pp. 922-941. [publishedPDF] and other papers on approximations for steady-state distribution of a queue.]
[Studies asymptotic behavior of waiting-time tail probabilities in the GI/G/1 queue when the service-time distribution has a heavy tail. Introduces the Pareto-mixture-of-exponential (PME) family of heavy-tailed distributions, having convenient explicit Laplace transforms and moments. Establishes asymptotic behavior and evaluates performance by using numerical transform inversion to calculate the exact values. Exposes the limitations of asymptotics in the heavy-tailed setting. Also see: papers 31 and 43, related papers on performance impact of heavy-tailed distributions, other papers co-authored with Joe Abate and other papers co-authored with Gagan Choudhury.]
21-30
[Exposes the dependence in packet traffic in a communication network with multiple sources and different packet sizes, shows how to characterize it and how to analyze congestion experienced by this traffic, continuing work in paper 2 above. Also see: Measurements and Approximations to Describe the Offered Traffic and Predict the Average Workload in a Single-Server Queue. Proceedings of the IEEE, vol. 77, No. 1, 1989, pp. 171-194, (with Kerry W. Fendick). (Reprinted in Stochastic Analysis of Computer and Communication Systems (ed. H. Takagi), North-Holland, Amsterdam, 1990, pp. 3-56.) Also see: [published PDF], related papers on heavy-traffic limits and diffusion approximations for queues, other papers on approximating arrival processes to queues other papers on communication networks other papers co-authored with Kerry Fendick and other papers co-authored with Vikram Saksena.]
[Presents a framework for characterizing the efficiency of simulation estimators, going beyond the variance to include the computational effort. Presents theory supporting a principle stated by Hammersely and Handscomb (1964). Also see: related papers on simulation methodology and other papers co-authored with Peter Glynn.]
[Discusses ways to characterize the possible dependence between two real-valued random variables with known distributions. Motivated by desire to study the antithetic-variate simulation variance-reduction technique. Also see other papers on simulation methodology and other papers on stochastic ordering.]
[Establishes results for networks of infinite-server queues with nonhomogeneous Poisson arrival processes, extending the single-queue results in paper 46. Also see: other papers on offered-load approximations, other papers queues with time-dependent arrival rates and other papers co-authored with Bill Massey.]
[Develops a framework for effective bandwidths, based on large deviations, for multiple classes with different priorities. See paper 42 for a more informal treatment, emphasizing applied relevance. Relates to papers 4, 6 and 7 above. Also see: related papers on effective bandwidths, large deviations and tail probability asymptotics and other papers co-authored with Arthur Berger.]
[Motivated by queues with service interruptions, establishes tractable results for a storage model with a two-state random environment, with the content increasing in one environment state and decreasing in the other. Also see other papers co-authored with Offer Kella.]
[Develops approximations for the waiting-time distribution in general single-server and multi-server queues based on tail-probability asymptotics. Gives an alternative approach to the methods in paper 19 above. Also see other papers co-authored with Joseph Abate, other papers co-authored with Gagan Choudhury and related papers on large deviations and tail probability asymptotics.]
[An investigation of advanced reservation in communication networks. Develops and evaluates a method for sharing bandwidth among customers who make advanced reservations with other customers that make immediate requests. Also see the sequel Resource Sharing for Book-Ahead and Instantaneous-Request Calls Using a CLT Approximation. Telecommunication Systems, vol. 16, March-April 2001, pp. 233-253 (with Riyadurgam Srikant). [PDF], related papers on communication networks, other papers co-authored with Rayadurgam Srikant and other papers co-authored with Albert Greenberg.]
[Establishes hydrodynamic limits for the departure process from n single-server queues as n goes to infinity. Uses strong approximations and the subadditive ergodic theorem. Also see other papers co-authored with Peter Glynn.]
[Establishes model continuity for the GSMP stochastic process and its steady-state distribution. These general stochastic models can serve as representations of discrete-event simulations. Also see other papers on simulation methodology and other papers on limits for queueing models.]
31-40
[Provides general conditions under which the steady-state buffer content distribution will have a heavy tail, indicating that large buffers will be required in broadband communication networks. A lower bound is established for the buffer-content tail probability in an infinite-capacity stochastic fluid model with a general stationary environment process. Also see: paper 20, related papers on performance impact of heavy-tailed distributions, and other papers co-authored with Gagan Choudhury.]
[Establishes a general framework for approximating dynamic programs with the discounted present-value criterion by smaller dynamic programs. A way to address the notorious curse of dimensionality. Also see: other papers on economics, games and optimization.]
[Simulation experiments supporting the algorithm to approximate the performance of queueing networks in paper 1 above. Also see: related papers on approximations for queueing models and related papers on queueing network approximations.]
[The general theory of stochastic integration is applied to identify a useful martingale associated with storage models having Levy process input. Can be applied to derive steady-state distributions, generalizing the Pollaczek-Khintchine transform. Also see other papers co-authored with Offer Kella.]
[Exposes the applied significance of the many-server heavy-traffic limit established in paper 11 above. Presents useful practical approximations for many-server queues. Also see: related papers on heavy-traffic limits and diffusion approximations for queues and related papers on customer contact centers.]
[Develops multi-dimensional generalizations of the Fourier-series method for inverting Laplace transforms and generating functions, as in papers 3, 8 and 47, and applies them to compute transient performance measures for the M/G/1 queue. Also see: related papers on numerical transform inversion, related papers on the transient behavior of queueing models, other papers co-authored with Gagan Choudhury and other papers co-authored with David Lucantoni.]
[An algorithm to analyze complex product-form Markovian loss networks, based on numerically inverting the generating functions of the normalization constant (partition function). Also see: paper 50 below, related papers on stochastic networks, related papers on numerical transform inversion, other papers co-authored with Gagan Choudhury and other papers co-authored with Kin Leung.]
[Tauberian theorems are applied with known transforms to establish tail-probability asymptotics for the steady-state distributions of general BMAP/G/1 and MAP/MSP/1 queues. Also see: papers 27 and 43, related papers on large deviations and tail probability asymptotics, other papers co-authored with Joseph Abate and other papers co-authored with Gagan Choudhury.]
[Early use of sample-path and failure-rate stochastic orderings to show that congestion increases when arrivals come more quickly or service takes longer. Also see: other papers on stochastic comparisons for queueing models.]
[Establishes relatively simple descriptions of the moments of one-dimensional RBM as a function of time. With initial condition 0, the moments can be regarded as cumulative distribution functions (cdf's) after normalization by the steady-state limits, which have nice structure. Also see related papers on the transient behavior of queueing models and other papers co-authored with Joseph Abate.]
41-50
[Derives the two-dimensional transform of the transient workload and queue-length distributions in this general queueing model with batch-Markovian arrival process and general service-time distribution. An algorithm is developed - based on two-dimensional numerical transform inversion - for calculating transient performance measures. Extends algorithms developed for steady-state distributions and applied in the more frequently cited Squeezing the Most Out of ATM. IEEE Transactions on Communications, vol. 44, No. 2, 1996, pp. 203-217 (with Gagan L. Choudhury and David M. Lucantoni) [published PDF]. Also see: other papers co-authored with Gagan Choudhury, other papers co-authored with David Lucantoni and other papers on the non-stationary behavior of queueing models.]
[From an engineering perspective, shows how the effective-bandwidth concept can be extended to multiple priority classes. Relates to papers 4, 6, 7 and 25 above. Also see related papers on large deviations and tail probability asymptotics and other papers co-authored with Arthur Berger.]
[It is shown that the steady-state low-priority waiting time can be represented as a geometric random sum, just like the M/G/1 FIFO waiting time. Asymptotic behavior of tail probabilities is derived. The M/G/1 busy period plays a prominent role. Non-exponential tail asymptotics is emphasized. Also see: other papers co-authored with Joseph Abate, other papers on the performance impact of heavy-tailed distributions and other papers calculating performance measures by numerical transform inversion.]
[This paper investigates the impact upon performance in a service system, such as a call center, of giving customers state information. Multi-server queueing models with and without delay announcements are compared. Also see: other papers on call centers and other papers on multi-server queues.]
[Conference version of paper 6 above. Exposes the limitations of approximations based on effective bandwidths stemming from large deviations, as in papers 4 and 7 here, in the presence of many sources (without directly doing many-source asymptotics), by making comparisons with exact performance measures calculated by using numerical transform inversion. Presents effective alternative approximations. Also see: related papers on effective bandwidths, large deviations and tail probability asymptotics, including papers 4, 7,25, 27 and 38 here, other papers co-authored with Gagan Choudhury and other papers co-authored with David Lucantoni.]
[Initiates sustained research th Bill Massey on the performance of many-server queues with time-varying arrival rates. In this first paper, attention is focused on exploiting previously established performance descriptions for the infinite-server queue with nonhomogeneous Poisson arrival process in order to better understand the performance. This analysis is applied for the practical problem of server staffing in the more frequently cited Server Staffing to Meet Time-Varying Demand, Management Science, vol. 42, No. 10, 1996, pp. 1383-1394 (with Otis B. Jennings, Avishai Mandelbaum and William A. Massey) [published PDF]. Also see: other papers co-authored with Bill Massey and other papers on the non-stationary behavior of queueing models.]
[Short version of part of paper 3 above, quickly specifying an effective algorithm for numerically inverting generating transforms, using the Fourier-series method. Also see: related papers on numerical transform inversion and other papers co-authored with Joe Abate.]
[Of historical interest, because it establishes heavy-traffic stochastic-process limits for a multi-class queue using the framework of weak convergence on the function space D. Exhibits the phenomenon of state-space collapse. This paper complements the more frequently cited Multiple Channel Queues in Heavy Traffic II: Sequences, Networks, and Batches, Advances in Applied Probability, vol. 2, No. 2, Autumn 1970, pp. 355-369 (with Donald L. Iglehart) [published PDF]. For a recent account, see Stochastic-Process Limits, a book published by Springer in 2002 (602 pages), and related papers on heavy-traffic limits and diffusion approximations for queues.]
[Necessary and sufficient conditions for arrivals to see time averages (ASTA) are determined, extending PASTA. This is one of several key papers at this time establishing a firm foundation for the fundamental principles of queueing theory. Also see: other papers on fundamental principles in queueing and other papers co-authored with Ben Melamed.]
[Extends paper 37 above by applying numerical transform inversion to calculate steady-state blocking probabilities in product-form loss networks based on numerically inverting the generating function of the normalization constant (partition function). The extension allows general state-dependent arrival rates and service rates, which make it possible to treat more general models. As before, non-complete-sharing policies are considered involving upper-limit and guaranteed-minimum bounds. Also see: related papers on stochastic networks, related papers on numerical transform inversion, other papers co-authored with Gagan Choudhury and other papers co-authored with Kin Leung.]
Principal Topics of the 50 papers above:
Co-Authors - in order of appearance above: