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Strong approximations for Markovian service networks
- A. Mandelbaum, W. Massey, M. Reiman
- Mathematics, Computer ScienceQueueing Syst. Theory Appl.
- 14 June 1998
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.
Networks of infinite-server queues with nonstationary Poisson input
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.
Server Staffing to Meet Time-Varying Demand
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.
New stochastic orderings for Markov processes on partially ordered spaces
- W. Massey
- MathematicsThe 23rd IEEE Conference on Decision and Control
- 1 May 1987
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.
Staffing of Time-Varying Queues to Achieve Time-Stable Performance
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).
Strong Approximations for Time-Dependent Queues
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.
The Physics of the Mt/G/∞ Queue
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.
An Analysis of the Modified Offered-Load Approximation for the Nonstationary Erlang Loss Model
M t /G/∞ queues with sinusoidal arrival rates
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…
The Analysis of Queues with Time-Varying Rates for Telecommunication Models
- W. Massey
- BusinessTelecommun. Syst.
- 1 December 2002
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.