• Publications
  • Influence
Heavy-Traffic Limits for Queues with Many Exponential Servers
TLDR
Two different kinds of heavy-traffic limit theorems have been proved for s -server queues and the resulting approximation is better than the earlier ones for many-server systems operating at typically encountered loads.
An Introduction to Stochastic-Process Limits and their Application to Queues
  • W. Whitt
  • Computer Science, Mathematics
  • 2002
TLDR
This paper discusses statistical regularity in applications, the Framework for Stochastic-Process Limits, and heavy-Traffic Limits for Fluid Queues.
The Queueing Network Analyzer
  • W. Whitt
  • Computer Science
    The Bell System Technical Journal
  • 1 November 1983
TLDR
This paper describes the Queueing Network Analyzer (QNA), a software package developed at Bell Laboratories to calculate approximate congestion measures for a network of queues and uses two parameters to characterize the arrival processes and service times.
Numerical Inversion of Laplace Transforms of Probability Distributions
  • J. Abate, W. Whitt
  • Mathematics, Computer Science
    INFORMS J. Comput.
  • 1 February 1995
TLDR
A simple algorithm for numerically inverting Laplace transforms is presented, designed especially for probability cumulative distribution functions, but it applies to other functions as well.
The Fourier-series method for inverting transforms of probability distributions
  • J. Abate, W. Whitt
  • Mathematics, Computer Science
    Queueing Syst. Theory Appl.
  • 3 January 1992
TLDR
This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions and describes two methods for inverting Laplace transform based on the Post-Widder inversion formula.
Comparison methods for queues and other stochastic models
TLDR
Comparison properties of random variables and stochastic processes are given and are illustrated by application to various queueing models and questions in experimental design, renewal and reliability theory, PERT networks and branching processes.
Some Useful Functions for Functional Limit Theorems
  • W. Whitt
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1 February 1980
TLDR
This paper facilitates applications of the continuous mapping theorem by determining when several important functions and sequences of functions preserve convergence.
Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data
TLDR
This paper analyzes a model of a multiplexer for packetized voice and data using the index of dispersion for intervals (IDI), which describes the cumulative covariance among successive interarrival times.
Fitting mixtures of exponentials to long-tail distributions to analyze network performance models
TLDR
This work develops an algorithm for approximating a long-tail distribution by a finite mixture of exponentials, where an exponential component is fit in the largest remaining time scale and then the fitted exponential components are subtracted from the distribution.
APPROXIMATIONS FOR THE GI/G/m QUEUE
TLDR
Approximations for a basic queueing model, which has m identical servers in parallel, unlimited waiting room, and the first-come first-served queue discipline, are developed and evaluated and are useful supplements to algorithms for computing the exact values that have been developed in recent years.
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