Practical Extensions to Cycle Time Approximations for the $G/G/m$-Queue With Applications

Morrison, James R.; Martin, D.P.

doi:10.1109/tase.2007.905975

Cited by 40 publications

(12 citation statements)

References 25 publications

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“…This level of accuracy is higher than the other models in the literature, such as (Morrison and Martin 2007). The complex simulation models that are used in the semiconductor companies can predict the cycle time with at most 90% accuracy.…”

Section: Case With Erlang Distributionmentioning

confidence: 89%

Application of Erlang distribution in cycle time estimation of toolsets with wip-dependent arrival and service in a single product-type single failure-type environment

Akhavan-Tabatabaei¹,

Ucrós²,

Shanthikumar³

2010

Proceedings of the 2010 Winter Simulation Conference

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This paper proposes a methodology based on phase type distributions and a state dependent Markov chain model to estimate the cycle time of workstations (toolsets) in semiconductor manufacturing. Due to implicit operational policies adopted by the line managers the performance of the existing queueing models for toolsets is not satisfactory. On the other hand developing accurate simulation models for toolsets can be very time consuming and hard to maintain. In this paper we propose a Markov chain model with the ability to include implicit operational rules on dispatching and maintenance. We verify the performance of this model via simulation and present the results for a variety of arrival and service distribution shapes.

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Section: Case With Erlang Distributionmentioning

confidence: 89%

Application of Erlang distribution in cycle time estimation of toolsets with wip-dependent arrival and service in a single product-type single failure-type environment

Akhavan-Tabatabaei¹,

Ucrós²,

Shanthikumar³

2010

Proceedings of the 2010 Winter Simulation Conference

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“…Since most of the main container terminals in the world show a M/E k /c queuing system, the above formula is extensively used in their planning process. Another approximate formula (Sakasegawa, 1976;Morrison, 2007), which is applied to the general queue G I /G/c, is defined as…”

Section: Approximate Methodsmentioning

confidence: 99%

Long-term planning of a container terminal under demand uncertainty and economies of scale

et al. 2012

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ABSTRACT. Governments of many developing countries are presently granting concessions to private organizations to operate container terminals. A key element in this process is the technical and economic evaluation of the project. In practice, the demand levels over time are volatile. The first part of the paper deals with a capacity expansion problem with stochastic demand. Next, an optimization model employs a dynamic programming routine to find the best epochs to install new berths. Ship waiting times are computed with queuing models and are introduced into the main model as upper restrictions based on international practice. Finally, a real options analysis is performed with the objective of evaluating the effects of an eventual abandonment of the project at a pre-defined time horizon. The model is then applied to the container terminal of the Port of Rio Grande, Brazil.

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“…This approach should work well when the cost of resources are relatively low and the resource is indeed close to ample. Morrison and Martin (2007) treated a resource contention problem as a special case of the run-based preemptive event. Comparing their approximate model with the simulation results, the errors are reported from 1.4 to 21.3%.…”

Section: Resource Contention In Prior Researchmentioning

confidence: 99%

Classification of queueing models for a workstation with interruptions: a review

2013

International Journal of Production Research

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Queueing theory is commonly used to evaluate the performance of production systems. Due to the complexity of practical production lines, choosing correct queueing models under the existence of interruptions can be intricate, but is critical to the evaluation of system performance. This paper gives a review of research in this area, proposes a systematic way to classify different types of interruptions in manufacturing systems and suggests proper queueing models for each category. The operational definition of service time is given and the decomposition properties for the run-based state-induced and time-based preemptive events are explained. The corresponding G/G/1 approximate models are proposed.

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Practical Extensions to Cycle Time Approximations for the $G/G/m$-Queue With Applications

Cited by 40 publications

References 25 publications

Application of Erlang distribution in cycle time estimation of toolsets with wip-dependent arrival and service in a single product-type single failure-type environment

Application of Erlang distribution in cycle time estimation of toolsets with wip-dependent arrival and service in a single product-type single failure-type environment

Long-term planning of a container terminal under demand uncertainty and economies of scale

Classification of queueing models for a workstation with interruptions: a review

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