Heavy-Traffic Limits for Queues with Many Exponential Servers
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
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 ScienceBell Labs technical journal
- 1 November 1983
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
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
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
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
- MathematicsMathematics of Operations Research
- 1 February 1980
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
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
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.
A Unified Framework for Numerically Inverting Laplace Transforms
A framework for constructing algorithms to invert Laplace transforms numerically and it is shown that it can be advantageous to use different one-dimensional algorithms in the inner and outer loops.