[Applies continued fractions to compute the values of Laplace transforms for the purpose of performing numerical transform inversion. This technique is applied to calculate the distributions of first passage times in general birth-and-death processes. This technique is also used to calculate Laplace transforms of Pareto distributions, which are now often used as service-time distributions in queueing models. Also see: other papers co-authored with Joseph Abate and other papers on numerical transform inversion.]
[Uniform acceleration expansions are derived for general finite-state continuous-time Markov chains with time-varying transition rates. These justify and provide refinements of the pointwise-stationary approximation for queues with time-varying arrival rates, as treated directly in The Pointwise Stationary Approximation for M_{t}/M_{t}/s Queues is Asymptotically Correct as the Rates Increase. Management Science, vol. 37, No. 3, 1991, pp. 307-314. [published PDF]. The results are illustrated by a numerical example for the Erlang loss model with time-varying arrival rate. Also see: other papers co-authored with Bill Massey and other papers on the non-stationary behavior of queueing models.]
[Shows how numerical transform inversion can be used to calculate time-dependent performance measures for the Erlang loss model as a function of the initial state. Shows how scaling can be used to calculate performance measures for large systems from calculations for much smaller systems. Also see: other papers co-authored with Joseph Abate, other papers on numerical transform inversion and other papers on the non-stationary behavior of queueing models.]
[In communication networks, it is common to require very small cell (or packet) loss due to buffer overflow. Although losses are measured, it is difficult to interpret the measurements to determine if the requirements are being met. Methods for doing so are introduced here. A key idea is to focus on clusters of losses. Batch Poisson processes and reflected Brownian motion are used. Also see other papers co-authored with Kerry Fendick.]
[Contributes to the literature on multi-processor load balancing. We consider schemes in which the rebalancing is done periodically, every T time units. We thus only need state information at those periodic times. In fact, the procedure may be effective even if the state information is somewhat stale. We consider fluid and diffusion approximations obtained by considering a large number of queues and a heavy load. These approximations yield relatively simple descriptions of performance, which help determine how to set the value of T. Also see other papers on heavy-traffic limits and diffusion approximations for queues.]
[Deterministic fluid approximations are developed to show how large multi-server systems (modelled as infinite-server queues) recover from rare congestion events. Large deviation results are established. Focuses on the impact of the service-time distribution, considering the possibility that it may have a heavy tail. Also see: other papers co-authored with Nick Duffield and other papers on the non-stationary behavior of queueing models.]
[Heavy-traffic limits are established for queues that operate in a slowly-changing random environment, with the queue being unstable in some environment states. Appropriate scaling leads to insightful limits. Numerical transform inversion is exploited to show that the approximations are remarkably accurate. Also see: other papers co-authored with Gagan Choudhury, other papers co-authored with Avishai Mandelbaum. and other papers on heavy-traffic limits and diffusion approximations for queues.]
[In order to reduce aliasing and roundoff errors in numerical transform inversion, a new scaling technique is introduced in which a non-probability function is transformed into a probability density function (pdf) and the point of inversion t is transformed into the mean of that pdf. This new scaling technique is even useful for probability functions, because it helps compute very small values at large time arguments with small relative error. Also see: other papers co-authored with Gagan Choudhury and other papers calculating performance measures by numerical transform inversion.]
[It is shown that numerical transform inversion can be applied to calculate both transient and steady-state performance measures for a large class of polling models. Also see: other papers co-authored with Gagan Choudhury and other papers calculating performance measures by numerical transform inversion.]
[Heavy-traffic stochastic-process limits are established to develop formulas approximating the asymptotic variance of four different estimators of the steady-state blocking probability in a multiserver loss system. In addition to producing estimates of the required simulation run length, the analysis shows that the estimators perform very differently in different regions. This is a sequel to Planning Queueing Simulations. Management Science, vol. 35, No. 11, 1989, pp. 1341-1366. [published PDF]. Also see: the sequel, Variance Reduction in Simulations of Loss Models. Operations Research, vol. 47, No. 4, July-August 1999, pp. 509-523 (again with Rayadurgam Srikant), related papers on simulation methodology, related papers on simulation of queueing models and other papers co-authored with Rayadurgam Srikant.]
[Motivated by telecommunications applications, investigates ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval. Ordinary least squares, iterated least squares and maximum likelihood methods are considered. Also see: other papers co-authored with Bill Massey and other papers on the non-stationary behavior of queueing models.]
[Investigates operators mapping one probability distribution on the positive half line into another via their Laplace transforms. The goal is to assist stochastic modelling in conjunction with numerical transform inversion software. Infinitely divisible distributions and Levy processes play a prominent role. Also see other papers co-authored with Joseph Abate.]
[New version of the Laguerre or Weeks method to numerically invert Laplace transforms. Wynn's epsilon algorithm is used to accelerate convergence of the Laguerre series. Also see the sequel, 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], other papers numerical transform inversion, other papers co-authored with Joseph Abate and other papers co-authored with Gagan Choudhury.]
[Optimal gambling and investment strategies - to maximize logarithmic utility - are derived for a simple random walk in a random environment, i.e., where the model parameters are random variables. The optimal control is a generalization of the celebrated Kelly criterion. Convergence to the Kiefer process is proved. Also see other papers co-authored with Sid Browne and other papers on economics, games and optimization.]
[An effective new "industrial-strength" technique - based on numerical transform inversion - for calculating the normalization constant of a closed Markovian queueing network. Large examples are considered. Also see: other papers co-authored with Gagan Choudhury, other papers co-authored with Kin Leung, other papers on calculating performance measures by numerical transform inversion and other papers on stochastic networks.]
[Develops ways to provide multiple grades of service and protection against overloads in multi-class systems. Introduces performance targets under the condition that other classes are in overload. In order to keep the product-form structure, upper-limit and guaranteed-minimum bounds are proposed as controls. Numerical transform inversion is exploited to evaluate performance with these relatively complex controls. A key point is that performance can be effectively computed. Also see: other papers co-authored with Gagan Choudhury, other papers co-authored with Kin Leung and other papers on communication networks.]
[Develops a general stochastic model for wireless systems based on Poisson random measures - the Poisson-Arrival-Location Model (PALM) - that allows for dependence on both time and space. Provides a theoretical foundation for Traffic Models for Wireless Communication Networks, IEEE Journal on Selected Areas in Communication, vol. 12, No. 8, 1994, pp. 1353-1364 (with Kin K. Leung and William A. Massey) [published PDF]. Also see: other papers co-authored with Bill Massey, other papers on the non-stationary behavior of queueing models and other papers on communication networks.]
[This paper provides a rigorous mathematical basis for the modified-offered-load (MOL) approximation for multi-server loss models with time-varying arrival rate. The MOL approximation uses the steady-state distribution of the stationary model with a time-dependent offered load obtained from the associated infinite-server model with time-varying arrival rate. Also see: the recent review paper, Coping with Time-Varying Demand when Setting Staffing Requirements for a Service System., Production and Operations Management (POMS), forthcoming (with Linda V. Green and Peter J. Kolesar) [PDF], other papers co-authored with Bill Massey and other papers on the non-stationary behavior of queueing models.]
[Necessary and sufficient conditions are established for cumulative processes (associated with regenerative processes) to obey several classical limit theorems, such as central limit theorems, laws of large numbers, laws of the iterated logarithm, and their functional versions. Also see the sequel, Necessary Conditions in Limit Theorems for Cumulative Processes. Stochastic Processes and Their Applications, vol. 98, 2002, pp. 199-209 (also with Peter W. Glynn). [published PDF] and other papers co-authored with Peter W. Glynn.]
[Applies numerical transform inversion with formulas derived by Pollaczek to calculate the distribution of the steady-state GI/GI/1 waiting time in essentially full generality. Also see: other papers co-authored with Joseph Abate, other papers co-authored with Gagan Choudhury and other papers calculating performance measures by numerical transform inversion.]
[Provides a theoretical framework for studying sequential stopping rules for stochastic simulations. General conditions are established for a sequential stopping rule to be asymptotically valid as the prescribed volume of the confidence set converges to zero. Also see: other papers co-authored with Peter Glynn and other papers on simulation methodology.]
[As indicated by the title, a review of the fundamental conservation law, L = W, which has received additional attention since Little (1961), including central-limit-theorem versions applied in paper 24. Also see: other papers on fundamental principles in queueing.]
[Methods are proposed, including the index of dispersion for work (IDW), to approximately characterize input (arrival process together with service requirements) to a queueing system, and the congestion it will produce. This paper extends the more frequently cited Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE Journal on Selected Areas in Communications, vol. SAC-4, No. 6, September 1986, pp. 833-846 (with K. Sriram) [published PDF]. Also see: other papers on approximating point processes and characterizing traffic other papers on communication networks and other papers co-authored with Kerry Fendick.]
[Shows how central-limit-theorem versions of L = W can be applied to improve simulation efficiency. Provides additional insight into control-variate estimators. Shows that nonlinear controls are asymptotically equivalent to linear controls. Also see: other papers co-authored with Peter Glynn, other papers on simulation methodology and other papers on fundamental principles of queueing theory.]
[Establishes a central-limit-theorem version of the fundamental conservation law L = . Shows how to further exploit the fundamental relation between cumulative processes which is the basis for the well-known relation between limiting averages. Implications for estimation are discussed in the "Indirect Estimation" paper above.]
[A technique is developed to compare a non-Markov process to a Markov process. It is applied to help establish a bound on blocking probabilities in stochastic loss networks in the more frequently referenced Blocking When Service is Required from Several Facilities Simultaneously. AT&T Technical Journal, vol. 64, No. 8, October 1985, pp. 1807-1856. [published PDF]. Indeed, this paper is mystery reference [31] there (uncited by Bell Labs policy). Also see: other papers on stochastic comparisons for queueing models, other papers on stochastic orderings and other papers on stochastic networks.]
[Investigates the relation between open and closed queueing network models. Proposes approximating the more difficult closed queueing network by an associated open queueing network with the same mean population(s): the so-called fixed-population-mean method for closed models. Also see: other papers on stochastic networks.]
[What service-time distribution minimizes expected delays in a GI/G/1 queue with given interarrival-time distribution? It is natural to conjecture that the minimum always is achieved with the deterministic service-time distribution, but we show that is false. In fact, for hyperexponential interarrival-time distributions, the deterministic service-time distribution yields the maximum. Also see other papers on stochastic comparisons.]
[Investigates the range of possible values for the mean steady-state queue length in the GI/M/1 queue, given the first two moments of the interarrival-time distribution and the mean of the exponential service time. The first paper exploits the Lapalce transform stochastic ordering to get the full range of possible values, identifying the upper and lower bounds. With the aid of mathematical programming, the second paper shows that the range of possible values can be reduced substantially - to within limits acceptable for practical approximations - if realistic shape constraints are imposed. There third paper supports the second, theoretically, by establishing ordering within mixtures of exponential distributions. Also see other papers on stochastic comparisons for queues and other papers on approximations for queues.]
[Establishes economies of scale in the Erlang loss and delay models (when the service-time distribution is the same for all customers) via several different stochastic comparisons. Also see: other papers on stochastic comparisons for queueing models and papers on call centers.]
[Establishes relations between stochastic-process limits for undiscounted processes and stochastic process limits for associated discounted stochastic processes by exploiting continuous mapping theorems on the functions space D. Also see related papers on stochastic-process limits.]