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.
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.
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.
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 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.
This paper facilitates applications of the continuous mapping theorem by determining when several important functions and sequences of functions preserve convergence.
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.
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 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.