This work develops limit theorems for a large class of stochastic service network models where parameters like arrival and service rates, routing topologies for the network, and the number of servers at a given node are all functions of time as well as the current state of the system.Expand

A more general Poisson-arrival-location model (PALM) is introduced in which arrivals move independently through a general state space according to a location stochastic process after arrivingaccording to a nonhomogeneous Poisson process.Expand

An approximate procedure based on a time-dependent normal distribution, where the mean and variance are determined by infinite-server approximations is developed, which is effective by making comparisons with the exact numerical solution of the Markovian M t /M/s t model.Expand

A unified theory of stochastic ordering for Markov processes on partially ordered state spaces is developed and found to be quite useful when analyzing multi-dimensional Stochastic models such as queueing networks.Expand

This paper develops methods to determine appropriate staffing levels in call centers and other many-server queueing systems with time-varying arrival rates with flexible simulation-based iterative-staffing algorithm (ISA) for the Mt/G/st + G model---with nonhomogeneous Poisson arrival process (the Mt) and customer abandonment (the + G).Expand

This work derives period-dependent, pathwise asymptotic expansions for its queue length, within the framework of strong approximations, supported by a functional strong law of large numbers and diffusion approximation, and a functional central limit theorem.Expand

It is significant that the well known insensitivity property of the stationary M/G/∞ model does not hold for the nonstationary Mt/G/, and the time-dependent mean function m depends on the service-time distribution beyond its mean.Expand

In this paper we describe the mean number of busy servers as a function of time in an Mt/G/∞ queue having a nonhomogeneous Poisson arrival process with a sinusoidal arrival rate function. For an… Expand

Canonical queueing models with time-varying rates are given and the necessary mathematical tools are developed to analyze them and the use of these models through various communication applications is illustrated.Expand