Simple relationships among moments of queue lengths in product form queueing networks (original) (raw)

1988, IEEE Transactions on Computers

... a2G(N)/(aOkJ)&amp;#x27; can also be obtained by Corollary I: taking the derivative of (2.3) with respect to OkJ. V~J(Z) = [ 1 + L~J(E-&amp;amp;) - Lkj(*)]Lkj(z) f Xk(E)akj VkJ(E-e&amp;#x27;,)+ CVklJ(i%e&amp;quot;,) ;#IS (2.9a) t#k 1 aZc(E) (aekJ Substituting for aG(E)/aOkJ from (2.3), we obtain ...

On the Cycle Time Distribution in a Two-Stage Cyclic Network with Blocking

IEEE Transactions on Software Engineering, 2000

... blocking mechanisms in congested networks," in <i>Flow Control of Congested Networks </i>, Nato ASI Series, Comput. Syst. Sci., vol. 38, AR Odoni, L. Bianco, and G. Szegö, Eds. New York: Springer-Verlag, 1987, pp. 243-254. 3. ...

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A convolution algorithm for product-form queueing networks with blocking

Annals of Operations Research, 1998

Queueing network models with finite capacity and blocking can be used to represent various systems with finite resources, including communication and computer systems, as well as production and manufacturing systems, to evaluate their performance. Various blocking types have been defined to represent various system behaviors. Queueing networks with blocking show a product-form solution under special constraints. We present a convolution

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Queueing Networks

2007

The purpose of this tutorial is to survey queueing networks, a class of stochastic models extensively applied to represent and analyze resource sharing systems such as communication and computer systems. Queueing networks (QNs) have been proved to be a powerful and versatile tool for system performance evaluation and prediction. First we briefly survey QNs that consist of a single service center, i.e., the basic queueing systems defined under various hypotheses, and we discuss their analysis to evaluate a set of performance indices, such as resource utilization and throughput and customer response time. Their solution is based on the introduction of an underlying stochastic Markov process. Then, we introduce QNs that consist of a set of service centers representing the system resources that provide service to a collection of customers that represent the users. Various types of customers define the customers classes in the network that are gathered in chains. We consider various analytical methods to analyze QNs with single-class and multiple-class. We mostly focus on product-form QNs that have a simple closed form expression of the stationary state distribution that allows to define efficient algorithms to evaluate average performance measures. We review the basic results, stating from the BCMP theorem that defines a large class of product-form QNs, and we present the main solution algorithms for single-class e multiple-class QNs. We discuss some interesting properties of QNs including the arrival theorem, exact aggregation and insensitivity. Finally, we discuss some particular models of product-form QNs that allow to represent special system features such as state-dependent routing, negative customers, customers batch arrivals and departures and finite capacity queues. The class of QN models is illustrated through some application examples of to analyze computer and communication systems.

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An Algorithm For Closed Queueing Networks Based On Numerical Transform Inversion

We propose a new algorithm for closed queueing networks and related product-form models based on numerical inversion of the generating function of the normalization constant (or partition function). It is known that the generating function of the normalization constant often has a remarkably simple form, but numerical inversion evidently has not been considered before. We also show that moments of steady-state distributions can be calculated directly by only performing two inversions. For closed queueing networks with p closed chains, the generating function is p dimensional. For these generating functions, the algorithm recursively performs p one-dimensional inversions. The required computation grows exponentially in the dimension, but we show that the dimension can often be reduced dramatically by exploiting special structure. Other key ingredients in the algorithm are scaling and the computation of large sums efficiently by Euler summation. Numerical examples indicate that this n...

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Performance of Client/Server Systems

2000

Client/server (C/S) systems are composed of client processes that submit requests to one or more server processes. Servers passively await for client requests and may enlist other servers in order to reply to a request originating from a client. These processes, clients and servers, are usually organized in a multi-tiered software architecture. Usually, clients and servers execute on different machines connected by networks.

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The tree MVA algorithm

Performance Evaluation, 1985

ABSTRACT A new algorithm to solve product form queueing networks, especially those with large numbers of centers and chains, is presented. This algorithm is a Tree version of Mean Value Analysis (MVA). Tree MVA is analogous to the Tree version of Convolution developed by Lam and Lien. Like Tree Convolution, Tree MVA allows exact solution of large networks which are intractable with previous sequential algorithms. As with the sequential versions of Convolution and MVA, Tree MVA has better numerical properties than Tree Convolution. Further, Tree MVA avoids the computational complexity of sequential MVA in networks with several queue dependent centers. Thus, we consider Tree MVA to be the best algorithm for general product form networks.

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