scispace - formally typeset
Journal ArticleDOI

Open and closed models for networks of queues

Ward Whitt
- 01 Nov 1984 - 
- Vol. 63, Iss: 9, pp 1911-1979
TLDR
This paper investigates ways to use open models to approximate closed models with specified expected equilibrium populations, especially effective for approximately solving large closed models, where “large” may mean many nodes or many jobs.
Abstract
This paper investigates the relationship between open and closed models for networks of queues. In open models, jobs enter the network from outside, receive service at one or more service centers, and then depart. In closed models, jobs neither enter nor leave the network; instead, a fixed number of jobs circulate within the network. Open models are analytically more tractable, but closed models often seem more realistic. Hence, this paper investigates ways to use open models to approximate closed models. One approach is to use open models with specified expected equilibrium populations. This fixed-population-mean method is especially effective for approximately solving large closed models, where “large” may mean many nodes or many jobs. The success of these approximations is partly explained by limit theorems: Under appropriate conditions, the fixed-population-mean method is asymptotically correct. In some cases the open-model methods also yield bounds for the performance measures in the closed models.

read more

Citations
More filters
Proceedings ArticleDOI

Large-scale cluster management at Google with Borg

TL;DR: A summary of the Borg system architecture and features, important design decisions, a quantitative analysis of some of its policy decisions, and a qualitative examination of lessons learned from a decade of operational experience with it are presented.
Journal ArticleDOI

CONWIP: a pull alternative to kanban

TL;DR: In this paper, a pull-based production system called CONWIP is described and theoretical arguments in favour of the system are outlined and simulation studies are included to give insight into the system's performance.
Journal ArticleDOI

Scheduling semiconductor wafer fabrication

TL;DR: In this paper, a variety of input control and sequencing rules are evaluated using a simulation model of a representative, but fictitious, semiconductor wafer fabrication, and the simulation results indicate that scheduling has a significant impact on average throughput time, with larger improvements coming from discretionary imput control than from lot sequencing.

Commissioned Paper To Pull or Not to Pull: What Is the Question?

TL;DR: In this article, the authors argue that pull is essentially a mechanism for limiting WIP, and lean is fundamentally about minimizing the cost of buffering variability, and they offer general, but precise definitions of pull and lean.
Journal ArticleDOI

Comparison Methods for Queues and Other Stochastic Models

TL;DR: A new book enPDFd comparison methods for queues and other stochastic models that can be a new way to explore the knowledge and one thing to always remember in every reading time, even step by step is shown.
References
More filters
Journal ArticleDOI

A and V.

Journal ArticleDOI

Open, Closed, and Mixed Networks of Queues with Different Classes of Customers

TL;DR: Many of the network results of Jackson on arrival and service rate dependencies, of Posner and Bernholtz on different classes of customers, and of Chandy on different types of service centers are combined and extended in this paper.
Book

Principles of random walk

Frank Spitzer
TL;DR: In this article, a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space, is studied, and the author considered this high degree of specialization worth while because of the theory of such random walks is far more complete than that of any larger class of Markov chains.
Journal ArticleDOI

Negative Association of Random Variables with Applications

TL;DR: In this article, negative association is defined as the property that a random variable is negatively associated (NA) if for every pair of disjoint subsets $A_1, A_2$ of Ω(1, 2, \cdots, k, k) of a function f(X, i, i = 1, 3, 4, k), f(G, g), g, g, j, j \in A_1), g(G), g), rbrack \leq 0, for all nondecreasing
Journal ArticleDOI

The Queueing Network Analyzer

TL;DR: 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.