A product-form approximation method for general closed queueing networks with several classes of customers

Baynat, Bruno; Dallery, Yves

doi:10.1016/0166-5316(94)00028-x

Cited by 45 publications

(49 citation statements)

References 20 publications

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“…We also employ a class aggregation technique to reduce the complexity of the analysis of a node. However, we use the convolution algorithm to calculate the arrival rate to the aggregate class and not Baynat and Dallery's method [15] since, as we mentioned above, the latter is not scalable.…”

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

“…Second, it requires the computation of the normalization constant in a multi-class queueing network. Baynat and Dallery [15], presented an alternative extension of Marie's method to multi-class queueing networks. Specifically, to avoid the computation of the normalization constant of a multi-class network, they decompose a C-class network into C single-class networks.…”

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

“…They also proposed a class aggregation technique that reduces significantly the complexity of the analysis of a node. However, the arrival rate to the aggregate class is calculated by aggregating the arrival rate to each individual class [15]. This aggregation process takes time that increases exponentially with the number of classes.…”

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

“…This type of multi-class closed non-product-form has been studied in the literature [14], [15], mainly by extending Marie's algorithm [12]. Neuse and Chandy [14] proposed an algorithm called the heuristic aggregation method (HAM) to solve such a queueing network.…”

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

“…We employ the class aggregation technique in Baynat and Dallery's method [15] to obtain the parameters of the service time distribution of the aggregate class at node i. Since the distribution of each class is a two-stage hyper-exponential distribution, the distribution of the aggregate class is also a hyper-exponential distribution, but with more than two stages.…”

Section: ) Class Aggregationmentioning

confidence: 99%

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A queueing network model of an edge optical burst switching node

Perros

Rouskas

IEEE INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37

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Abstract-We consider an edge optical burst switching (OBS) node with or without converters, and with no buffering. The OBS node serves a number of users, each connected to the switch over a fiber link that supports multiple wavelengths. Each wavelength is associated with a 3-state Markovian burst arrival process. The arrival process permits short and long bursts to be modeled. We model the edge OBS node as a closed non-product-form queueing network, with multiple heterogeneous classes, and we develop a suite of approximate decomposition algorithms to analyze it. Our approximate algorithms have a good accuracy, and they provide insight into the effect of various system parameters on the performance of the edge OBS node.

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Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

Section: Analysis Of the Multi-class Queueing Network With Or Wimentioning

confidence: 99%

Section: ) Class Aggregationmentioning

confidence: 99%

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A queueing network model of an edge optical burst switching node

Perros

Rouskas

IEEE INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37

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Analysis of decentralized multi‐product pull systems with lost sales

Gurgur

Altıok

2007

Naval Research Logistics

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Abstract:We study a pull-type, flexible, multi-product, and multi-stage production/inventory system with decentralized two-card kanban control policies. Each stage involves a processor and two buffers with finite target levels. Production stages, arranged in series, can process several product types one at a time. Transportation of semi-finished parts from one stage to another is performed in fixed lot sizes. The exact analysis is mathematically intractable even for smaller systems. We present a robust approximation algorithm to model two-card kanban systems with batch transfers under arbitrary complexity. The algorithm uses phase-type modeling to find effective processing times and busy period analysis to identify delays among product types in resource contention. Our algorithm reduces the effort required for estimating performance measures by a considerable margin and resolves the state-space explosion problem of analytical approaches.Using this analytical tool, we present new findings for a better understanding of some tactical and operational issues. We show that flow of material in small procurement sizes smoothes flow of information within the system, but also necessitates more frequent shipments between stages, raising the risk of late delivery. Balancing the risk of information delays vis-à-vis shipment delays is critical for the success of two-card kanban systems. Although product variety causes time wasted in setup operations, it also facilitates relatively short production cycles enabling processors to switch from one product type to another more rapidly. The latter point is crucial especially in high-demand environments. Increasing production line size prevents quick response to customer demand, but it may improve system performance if the vendor lead-time is long or subject to high variation. Finally, variability in transportation and processing times causes the most damage if it arises at stages closer to the customer.

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