An extension to Norton's equivalent

Hsiao, M.-T.T.; Lazar, Aurel A.

doi:10.1007/bf01225328

Cited by 16 publications

(10 citation statements)

References 8 publications

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“…The aggregation technique was introduced by Chandy, Herzog, and Woo (1975) to study the performance of BCMP queueing networks (Baskett et al 1975). The technique has been extended for more general multiclass queueing networks by Kritzinger, Van Wyk, and Krzesinski (1982), Walrand (1983), Hsiao and Lazar (1989), and Boucherie and van Dĳk (1993). Based on Norton's theorem, the idea of the aggregation technique is to decompose the queueing network into subnetworks and to replace each subnetwork with a flow equivalent single server with load-dependent service rates.…”

Section: Aggregation Techniquementioning

confidence: 99%

Conveyor Merges in Zone Picking Systems: A Tractable and Accurate Approximate Model

Gaast

Koster

Adan

2018

Transportation Science

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Sequential zone picking systems are popular conveyor-based picker-to-parts order picking systems that divide the order picking area in work zones. When designing a zone picking system, it is important to know whether the throughput capability of the system can meet customer demand. However, the performance and maximum throughput capability of a zone picking system is largely determined by congestion and blocking that occur at the various conveyor merges in the system. In this paper we develop an analytical model to study the impact of conveyor merges in sequential zone picking systems. Because of finite buffers, blocking, recirculation, and merging, the resulting queueing model does not have a product-form stationary queue-length distribution which makes exact analysis practically infeasible. Therefore, we develop an approximate solution by using an aggregation technique and matrix-geometric methods to study the throughput capability of the system. The model is suitable to support rapid design of complex zone picking systems, in terms of number and length of zones, input and output buffer capacities, and storage allocation of products to zones to meet prespecified performance targets. Comparison of the approximation results to simulation show that for a wide range of parameters the mean relative error in the system throughput is typically less than 5%. The model accurately predicts the loss in throughput due to congestion and blocking at the merges, and can be used to allocate input and output buffer spaces to maximize the throughput capability of the system.

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Section: Aggregation Techniquementioning

confidence: 99%

Conveyor Merges in Zone Picking Systems: A Tractable and Accurate Approximate Model

Gaast

Koster

Adan

2018

Transportation Science

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“…Two streams of literature developed in parallel: results based on partial balance (e.g. [25][26][27][28][29]) and results based on quasi-reversibility (e.g. [30][31][32][33]).…”

Section: Decompositionmentioning

confidence: 99%

A - and -invariant characterization of product form and decomposition in stochastic Petri nets

Kortbeek¹,

Boucherie²

2012

Performance Evaluation

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“…As noted by Hsiao and Lazar [9], the first-order equivalence yields a simplified proof of Norton's theorem (see also Walrand [39]).…”

Section: First-order Equivalencementioning

confidence: 99%

Event and time averages: a review

Brémaud

Kannurpatti

Mazumdar

1992

Advances in Applied Probability

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This article reviews results related to event and time averages (EATA) for point process models, including PASTA, ASTA and ANTIPASTA under general hypotheses. In particular, the results for the stationary case relating the Palm and martingale approach are reviewed. The non-stationary case is discussed in the martingale framework where minimal conditions for ASTA generalizing earlier work are presented in a unified framework for the discrete- and continuous-time cases. In addition, necessary and sufficient conditions for ASTA to hold in the stationary case are discussed in the case even when stochastic intensities may not exist and a short proof of the ANTIPASTA results known to date are given.

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An extension to Norton's equivalent

Cited by 16 publications

References 8 publications

Conveyor Merges in Zone Picking Systems: A Tractable and Accurate Approximate Model

Conveyor Merges in Zone Picking Systems: A Tractable and Accurate Approximate Model

A - and -invariant characterization of product form and decomposition in stochastic Petri nets

Event and time averages: a review

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