Journal ArticleDOI
Approximate Analysis of General Queuing Networks by Decomposition
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An approximate method for the analysis of general queuing networks is proposed, based on the method of decomposition where the total network is broken up into subsystems; e.g., queuing stations of the type GI/G/1 or subnets.Abstract:
In this paper an approximate method for the analysis of general queuing networks is proposed. The queuing network is of the open network type, having N single server queuing stations with arbitrary interconnections. Customers may enter the network at any queuing station. The interarrival times of the exogenous arrival processes and the service times at the queuing stations are generally distributed. The analysis is based on the method of decomposition where the total network is broken up into subsystems; e.g., queuing stations of the type GI/G/1 or subnets. The subsystems are analyzed individually by assuming renewal arrival and departure processes. All related processes are considered with respect to their first two moments only. An analysis procedure is reported which reduces the total problem to a number of elementary operations which can be performed efficiently with the aid of a computer. Numerical results are reported together with simulation results to demonstrate the accuracy of the new method. The paper concludes with a short discussion of possible extensions of the method.read more
Citations
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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.
Journal ArticleDOI
Strategic analysis of integrated production-distributed systems: models and methods
Morris A. Cohen,Hau L. Lee +1 more
TL;DR: This paper presents a comprehensive model framework for linking decisions and performance throughout the material-production-distribution supply chain to support analysis of alternative manufacturing material/service strategies.
Journal ArticleDOI
Approximating a Point Process by a Renewal Process, I: Two Basic Methods
TL;DR: The purpose here is to provide a better understanding of these procedures and a general framework for making new approximations, in particular, the two basic procedures can be used as building blocks to construct refined composite procedures.
Journal ArticleDOI
Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines
H.T. Papadopoulos,Cathal Heavey +1 more
TL;DR: A bibliography of material concerned with modeling of production and transfer lines using queueing networks, which denotes production lines as flow lines with asynchronous part transfer, while transfer lines have synchronous part transfer.
Journal ArticleDOI
Performance of the Queueing Network Analyzer
TL;DR: The examples here demonstrate the importance of the variability parameters used in QNA to describe non-Poisson arrival processes and nonexponential service-time distributions and show that QNA performs much better than the standard Markovian algorithm, which does not use variability parameters.
References
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Book
The theory of stochastic processes
David Cox,Hilton D. Miller +1 more
TL;DR: This book should be of interest to undergraduate and postgraduate students of probability theory.
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.
Journal ArticleDOI
Networks of Waiting Lines
TL;DR: What is perhaps the simplest theoretical question related to this class of problems, and derives expressions for certain steady-state parameters for discrete, statistically varying flows through complex networks.
Journal ArticleDOI
The Output of a Queuing System
TL;DR: For a queuing system with Poisson input, a single waiting line without defections and identically distributed independent negative exponential service times, the equilibrium distribution of the number of service completions in an arbitrary time interval is shown to be the same as the input distribution, for any number of servers as discussed by the authors.