A survey of bottleneck analysis in closed networks of queues

Schweitzer, Paul J.; Serazzi, Giuseppe; Broglia, Marco

doi:10.1007/bfb0013865

Cited by 34 publications

(39 citation statements)

References 9 publications

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“…This result, proven recently in [40] and [3] under different perspectives, is known to have relationships with the proportionally-fair allocation achieved in communication networks with congestion control, and, to the best of our knowledge, it has not been applied to revenue maximization in the sense of (6). By investigating the KKT conditions of the resulting formulation, it is possible to establish a connection between this asymptotic formulation and the most common formulation of the revenue maximization problem based on the BardSchweitzer approximate MVA algorithm [33], which probably is the approximation for closed models that is most popular among practitioners [29].…”

Section: Revenue Maximization In Heavy-trafficmentioning

confidence: 99%

“…Recall that, for a closed multiclass queueing network, the BardSchweitzer approximation is a non-linear system of equations used to approximate performance indexes in constant time with respect to the total customer population [33]. One can readily reformulate (6) in such a way to use the Bard-Schweitzer approximation for the computation of the performance indexes.…”

Section: Connection To Bard-schweitzer Formulationmentioning

confidence: 99%

“…• bs: the heavy-traffic formulation in Theorem 2 with (18b) replaced by the Bard-Schweitzer's fixed-point equation [33]:…”

Section: Solution Techniquesmentioning

confidence: 99%

“…We here instead focus on closed systems, where a fixed population of customers cyclically issues requests to the servers; in these models, the problem becomes even more difficult because, besides remaining non-convex, a single evaluation of the objective function is often much more expensive [17,24,38]. This holds because non-iterative expressions for the stationary performance indexes are lacking for multiclass closed models, thus most formulations require to use gradient-hill methods in combination with some model evaluation technique [10,17,24], e.g., approximate mean-value analysis (MVA) [15,33,43]. These formulations are popular in applications [5,16,31,39] but, as we show in the paper, they often fail to converge to a local optimum at the short timescales of minutes at which online capacity management systems operate today.…”

Section: Introductionmentioning

confidence: 99%

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Heavy-traffic revenue maximization in parallel multiclass queues

Anselmi

Casale

2013

Performance Evaluation

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Motivated by revenue maximization in server farms with admission control, we investigate optimal scheduling in parallel processor-sharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describe a heavy-traffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case with M queues and R classes, we prove that our heuristic is (1 + 1 M −1 )-competitive in heavy-traffic. Experimental results indicate that the proposed heuristic is remarkably accurate, despite its negligible computational costs, both in random instances and using service rates of a web application measured on multiple cloud deployments. 1

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Section: Revenue Maximization In Heavy-trafficmentioning

confidence: 99%

Section: Connection To Bard-schweitzer Formulationmentioning

confidence: 99%

“…• bs: the heavy-traffic formulation in Theorem 2 with (18b) replaced by the Bard-Schweitzer's fixed-point equation [33]:…”

Section: Solution Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Heavy-traffic revenue maximization in parallel multiclass queues

Anselmi

Casale

2013

Performance Evaluation

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“…For larger networks, approximations based on the MVA have been proposed in the literature. qnetworks provides the Bard and Schweitzer approximation [18,14] …”

Section: Queueing Networkmentioning

confidence: 99%

The qnetworks Toolbox: A Software Package for Queueing Networks Analysis

Marzolla

2010

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. Queueing Networks (QNs) are a useful performance modelling notation. They can be used to describe many kinds of systems, and efficient solution techniques have been developed for some classes of QN models. Despite the fact that QNs have been extensively studied, very few software packages for QN analysis are available today. In this paper we describe the qnetworks toolbox, a free software package for QN analysis for GNU Octave. qnetworks provides implementations of solution algorithms for single station queueing systems as well as for product and some non product form QN models. Exact, approximate and bound analysis can be performed. Additional utility functions and algorithms for Markov Chains analysis are also included. The qnetworks package is available as free and open source software, allowing users to study, modify and extend the code. This makes qnetworks a viable teaching tool.

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An analytical method for the performance evaluation of echelon kanban control systems

Koukoumialos

Liberopoulos

2006

Stochastic Modeling of Manufacturing Systems

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We develop a general purpose analytical approximation method for the performance evaluation of a multi-stage, serial, echelon kanban control system. The basic principle of the method is to decompose the original system into a set of nested subsystems, each subsystem being associated with a particular echelon of stages. Each subsystem is analyzed in isolation using a product-form approximation technique. An iterative procedure is used to determine the unknown parameters of each subsystem. Numerical results show that the method is fairly accurate. IntroductionIn this paper, we develop an analytical approximation method for the performance evaluation of an echelon kanban control system, used for the coordination of production in a multi-stage, serial, production/inventory system. We then test the behavior of this method on several numerical examples. The term "echelon kanban" was introduced in [19]. The basic principle of the operation of the echelon kanban control system is very simple: When a part leaves the last stage of the system to satisfy a customer demand, a new part is demanded and authorized to be released into each stage. It is worth noting that the echelon kanban control system is equivalent to the integral control system described in [8]. The echelon kanban control system differs from the conventional kanban control system, which is also referred to as installation kanban control system or policy in [19], in that in the conventional kanban control system, a new part is demanded and authorized to be released into a stage when a part leaves this particular stage and not when a part leaves the last stage, as is the case with the echelon kanban control system. This implies that in the conventional kanban control system, the placement of a demand and an authorization for the production of a new part into a stage

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A survey of bottleneck analysis in closed networks of queues

Cited by 34 publications

References 9 publications

Heavy-traffic revenue maximization in parallel multiclass queues

Heavy-traffic revenue maximization in parallel multiclass queues

The qnetworks Toolbox: A Software Package for Queueing Networks Analysis

An analytical method for the performance evaluation of echelon kanban control systems

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