Analysis Of Queueing Networks Research Articles

The generalized expansion method for open finite queueing networks

Blocking makes the exact analytical analysis of open queueing networks with finite capacities intractable except for very small networks, therefore, approximation approaches are needed to analyze these types of networks. For exponential open finite queueing networks, some methods have been proposed but little has been done so far on nonexponential open finite queueing networks. This paper introduces a new approximation technique for the analysis of general open finite queueing networks. Extensive numerical examples are performed for different network topologies and the results are compared with simulation.

An application of interactive analysis and computer graphics in stochastic modeling

This paper will describe the application of an interactive queueing network analyzer and an interactive graphics system to the analysis of a multiple processor computer system. The application of these tools greatly increased the productivity of the modelers and resulted in insights which would have otherwise been difficult, if not impossible, to obtain. With this experience as background, we discuss how the increasing availability of computing resources, especially high resolution interactive computer graphics and sophisticated modeling packages, is likely to have a profound influence on the applied stochastic modeler.

First-order perturbation analysis of a simple multi-class finite source queue

Perturbation analysis is an efficient method to compute parameter sensitivities for discrete event systems. This paper considers a simple multi-class finite source queue which models a computer system with multi-type programs. It is shown that first-order analysis is needed. Detailed discussions on the example system reveal the main features of multi-class queueing networks. An algorithm based on first-order analysis is proposed. This algorithm yields an asymptotically unbiased estimate of the sensitivity for the example system based on only one sample path of the system. The accuracy of first-order perturbation analysis for general queueing networks is also discussed.

Convergent Iterations for Computing Stationary Distributions of Markov Chains

Classical iterative schemes such as the Gauss–Seidel method and its variations constitute powerful tools for computing stationary distribution vectors for large-scale Markov process, such as those arising in queueing network analysis. The coefficient matrix A in these processes in a Q-matrix, i.e., a singular irreducible M-matrix with zero column sums and, unlike the nonsingular case, the classical iterations for A do not always converge. The purpose of this paper is to survey the recent literature and to analyze the behavior of these methods completely in terms of the graph structure of A. The results given here hold under somewhat weaker assumptions on A.

A decomposition approach for the stationary analysis of fault tolerant queueing systems

The increasing interest in the combined evaluation of performance and reliability of fault-tolerant computing systems requires new approaches in modelling and analysis. Based on decomposition principles allowing for the separate analysis of a system's performance and availability behavior, an algorithm for the stationary analysis of fault-tolerant queueing networks has been developed. The sample system under study is a fault-tolerant multiprocessor capable of operating on different levels of degradation. N tasks are cycling between the multiprocessor and its environment. The algorithm developed is well suited for exploring vast parameter spaces in the early design phases of degradable systems.

Modeling FMS by Closed Queuing Network Analysis Methods

The problem of scheduling concurrent lots of different components on a flexible manufacturing system (FMS) structured with a closed transportation network is approached. The production model and hence the decision/control process is seen here decomposed in two hierarchical levels. 1) At the lowest (microscopic) level, with a heuristic closed queuing network analysis, the average throughputs of the different lots contemporaneously present in the system are estimated. Routing of parts has the objective of balancing machine utilization. 2) At the highest (macroscopic) level, given the throughput estimates, lots are scheduled in order to optimize a production performance index and to satisfy release and due date constraints. Time-phased orders formaterials and decisions for sequencing lots on the FMS are generated.

A new 'building block' for performance evaluation of queueing networks with finite buffers

We propose a new 'building block', for analyzing queueing networks. This is a model of a server with a variable buffer-size. Such a model enables efficient analysis of certain queueing networks with blocking due to limited buffer spaces, since it uses only product-form submodels. The technique is extensively tested, and found to be reasonably accurate over a wide range of parameters. Several examples are given, illustrating practical situations for which our model would prove to be a useful performance analysis tool, specially since it is simple to understand, and easy to implement using standard software for closed queueing networks.

Equivalent Queueing Networks and Their Use in Approximate Equilibrium Analysis

Most Markovian queueing networks that arise as models of stochastic congestion systems (e.g., communication networks and multiprogrammed computer systems) do not have a product form in their stationary probability distributions, and hence are not amenable to the simplicity of product-form analysis. In this paper we suggest an approach for systematically examining the validity of a class of approximation schemes that is based on the idea of equivalent networks and is used for the approximate equilibrium analysis of nonproduct-form networks. We study equivalent networks, and prove a generalization of the so-called “Norton's” Theorem for closed product-form networks in order to study and generalize the equivalent flow method for the approximate analysis of nonproduct-form queueing networks. We then present the results of a study of the approximation scheme as applied to a type of network model (called a central-server model) that arises frequently in modeling multiprogrammed computer systems. In this model the central server uses a priority discipline, so the resulting network is nonproduct form. This study demonstrates the situations under which the approximation can be expected to do well or poorly and the kinds of errors it introduces.

Performance of the Queueing Network Analyzer

This paper describes the performance of the Queueing Network Analyzer (QNA), a software package developed at Bell Laboratories to calculate approximate congestion measures for networks of queues. QNA is compared with simulations and other approximations of several open networks of single-server queues. This paper illustrates how to apply QNA and indicates the quality that can be expected from the approximations. The examples here demonstrate the importance of the variability parameters used in QNA to describe non-Poisson arrival processes and nonexponential service-time distributions. For these examples, QNA performs much better than the standard Markovian algorithm, which does not use variability parameters. The accuracy of the QNA results (e.g., the expected delays) in these examples is satisfactory for engineering purposes.

The Queueing Network Analyzer

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. The first version of QNA analyzes open networks of multiserver nodes with the first-come, first-served discipline and no capacity constraints. An important feature is that the external arrival processes need not be Poisson and the service-time distributions need not be exponential. Treating other kinds of variability is important. For example, with packet-switched communication networks we need to describe the congestion resulting from bursty traffic and the nearly constant service times of packets. The general approach in QNA is to approximately characterize the arrival processes by two or three parameters and then analyze the individual nodes separately. The first version of QNA uses two parameters to characterize the arrival processes and service times, one to describe the rate and the other to describe the variability. The nodes are then analyzed as standard GI/G/m queues partially characterized by the first two moments of the interarrival-time and service-time distributions. Congestion measures for the network as a whole are obtained by assuming as an approximation that the nodes are stochastically independent given the approximate flow parameters.

The use of decomposition techniques for the analysis of open restricted queuing networks

A number of approximation methods for the analysis of restricted queuing networks that have been presented in the literature are applied to three simple networks. The techniques are shown to be quite fragile in that under reasonable and very general conditions they compute throughout rates which exceed theoretically derived upper bounds.

Queuing network analysis for a mixed voice and data communication network with end‐to‐end window flow control policy

Abstract A Mixed Voice and Data Communication Network (MVDNET) with end‐to‐end (ETE) window flow control policy is modeled by a closed multichain queuing network. Using an approximate solution of the Mean Value Analysis (MVA) algorithm, the computational complexity of analysing a large‐scale MVDNET and various commodities is dramatically reduced by several orders of magnitude over that required by traditional product‐form solution. We consider the problems concerned with the choice of window size, the effect of voice interruption, the number of voice‐grade (VG) channels per internode link and the selection of appropriate packet length. It is shown that the analytic results are very close to the simulation ones using GPSS language, and that the extensive MVA algorithm is a practical and valuable tool for solving the MVDNET analytical model with ETE window flow control policy.

Transient behaviour of queueing networks

In most contemporary queueing network analysis, the assumption is made that a network is in a state of equilibrium. That is, the network's state space probabilities are assumed to be time independent. It is therefore important to be able to quantify precisely when this assumption is valid. Furthermore there are also situations in which it is desirable to model the transient behaviour of networks which occur in practice, such as computer and communication systems. For example, the immediate effects of component failure or instantaneous alteration of system status may be predicted.In this paper an iterative solution is derived to the time-dependent Kolmogorov equations of queueing networks, and is shown to be convergent. From the solution, modelling of transient situations becomes possible and the time periods during which the equilibrium assumption can and should not be made may be identified; for example in terms of a time constant which is easily computed to a first-order approximation.

Transient behaviour of queueing networks

In most contemporary queueing network analysis, the assumption is made that a network is in a state of equilibrium. That is, the network's state space probabilities are assumed to be time independent. It is therefore important to be able to quantify precisely when this assumption is valid. Furthermore there are also situations in which it is desirable to model the transient behaviour of networks which occur in practice, such as computer and communication systems. For example, the immediate effects of component failure or instantaneous alteration of system status may be predicted. In this paper an iterative solution is derived to the time-dependent Kolmogorov equations of queueing networks, and is shown to be convergent. From the solution, modelling of transient situations becomes possible and the time periods during which the equilibrium assumption can and should not be made may be identified; for example in terms of a time constant which is easily computed to a first-order approximation.

A Queueing Network Analysis of Computer Communication Networks with Window Flow Control

A computer communication network with window flow control is modeled by a closed multichain queueing network. The severe computational limitation of previous solution algorithms is overcome with a heuristic derived from the recently found mean value analysis. A large numerical example is given.

Approximate Analysis of General Queuing Networks by Decomposition

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.

Medical Facilities Planning Using General Queueing Network Analysis

Medical Facilities Planning Using General Queueing Network Analysis

A generating function approach to queueing network analysis of multiprogrammed computers

A generating function approach to queueing network analysis of multiprogrammed computers