A Hierarchical Approximation Algorithm for Large Multichain Product Form Queueing Networks

A Hierarchical Approximation Algorithm for Large Multichain Product Form Queueing Networks
Author: H. R. Bahadori
Publisher:
Total Pages: 51
Release: 1987
Genre:
ISBN:

In recent years we have witnessed an increasing proliferation of local area network-based distributed systems. Very large distributed systems based on wide area networks are already in the design stages in numerous research organizations. In these systems, resources such as processing power, databases, and software are shared among users and jobs at different sites. Modeling and evaluating the performance of such large systems typically require the solution of queueing network models with large numbers of chains (classes), service centers, and populations. These large models preclude any use of exact solution techniques. Therefore, it is important that efficient and cost effective approximate algorithms for the solutions of large multichain queuing networks be devised to aid in the modeling, configuration, planning, performance, evaluation, and design of the systems these models represent. In this paper we propose a hierarchical approximation technique for multiclass separable queuing networks. This technique, which relies on network transformations, provides us with a smooth tradeoff between cost and accuracy. The key elements of the approach entail transforming queuing networks containing multiple infinite servers into ones containing a single infinite server model in the first step. In the next stage at least some of the closed chains are transformed into open chains, resulting in a mixed network; this is done on the basis of the desired error and computational cost. If necessary, a completely open network may be obtained. Furthermore, upper and lower bounds of the performance measures can be computed. These bounds are asymptotically correct. Numerical results are presented which compare this method with those yielding exact values and with other approximate algorithms.

Analysis of Queueing Networks with Blocking

Analysis of Queueing Networks with Blocking
Author: Simonetta Balsamo
Publisher: Springer Science & Business Media
Total Pages: 256
Release: 2013-03-14
Genre: Business & Economics
ISBN: 1475733453

Queueing network models have been widely applied as a powerful tool for modelling, performance evaluation, and prediction of discrete flow systems, such as computer systems, communication networks, production lines, and manufacturing systems. Queueing network models with finite capacity queues and blocking have been introduced and applied as even more realistic models of systems with finite capacity resources and with population constraints. In recent years, research in this field has grown rapidly. Analysis of Queueing Networks with Blocking introduces queueing network models with finite capacity and various types of blocking mechanisms. It gives a comprehensive definition of the analytical model underlying these blocking queueing networks. It surveys exact and approximate analytical solution methods and algorithms and their relevant properties. It also presents various application examples of queueing networks to model computer systems and communication networks. This book is organized in three parts. Part I introduces queueing networks with blocking and various application examples. Part II deals with exact and approximate analysis of queueing networks with blocking and the condition under which the various techniques can be applied. Part III presents a review of various properties of networks with blocking, describing several equivalence properties both between networks with and without blocking and between different blocking types. Approximate solution methods for the buffer allocation problem are presented.

Pamma Noniterative Approximate Solution Method for Closed Multichain Queueing Networks

Pamma Noniterative Approximate Solution Method for Closed Multichain Queueing Networks
Author:
Publisher:
Total Pages: 24
Release: 1987
Genre: Computer science
ISBN:

Approximate MVA algorithms for separable queueing networks are based upon an iterative solution of a set of modified MVA formulas. Although each iteration has a computational time requirement of or less, many iterations are typically needed for convergence to a solution. (M denotes the number of queues and K the number of closed chains or customer classes.) They are suitable for the analysis and design of communication networks which may require tens to hundreds, perhaps thousands, of closed chains to model flow- controlled virtual channels. The basis of our method is the distribution of a chain's population proportional to loads to get initial estimates of mean queue lengths. This is the same basis used in the derivation of proportional upper bounds for single- chain networks; for a multichain network, such a proportional distribution leads to approximations rather than upper bounds of chain throughputs. Nevertheless, these approximate solutions provide chain throughputs, mean end-to-end delays, and server utilizations that are sufficiently accurate for the analysis and design of communication networks and possibly other distributed systems with a large number of customer classes. Three PAM algorithms of increasing accuracy are presented.

Queueing Networks

Queueing Networks
Author: Richard J. Boucherie
Publisher: Springer Science & Business Media
Total Pages: 814
Release: 2010-11-25
Genre: Mathematics
ISBN: 144196472X

This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts: Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow sub networks to be aggregated into single nodes to reduce computational burden. Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the process generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures. Part 3 presents diffusion and fluid results. It specifically looks at the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic. Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks. spanPart 5 enlightens selected applications as spanloss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest. spanThe book shows that spanthe intertwined progress of theory and practicespan will remain to be most intriguing and will continue to be the basis of further developments in queueing networks.