Analysis of GI / M / n / n queueing system with ordered entry and no waiting line

Isguder, H. Okan; Uzunoglu-Kocer, Umay

doi:10.1016/j.apm.2013.07.029

Cited by 14 publications

(4 citation statements)

References 32 publications

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“…Further extensions in parallel heterogeneous system studies can be found in Boxma et al (1994) [17], who gave a comprehensive view of solution methods for the epoch. Isguder and Uzunoglu (2014) [18] dealt with the semi-Markov process of GI/M/n/0 and loss quantification; more recently, Melikov et al (2020) [19] presented an exact formulation but with an approximate resolution for ordered entry. Specifically, for systems using the ordered entry process, one can also refer to the work of Cooper (1976) [20], who concluded the need for a multi-dimensional birth-and-death process to represent the system.…”

Section: Introductionmentioning

confidence: 99%

Production Systems with Parallel Heterogeneous Servers of Limited Capacity: Accurate Modeling and Performance Analysis

Calvo,

Arteaga

2024

Applied Sciences

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Heterogeneous systems of limited capacity have general applications in manufacturing, but also in logistic or service systems due to the differences in server or workstation performance or work assignment; this is in close relationship with system flexibility, where saturation and blocking are ordinary situations of systems with high demand and limited capacity, and thus, accurate loss quantification is essential for performance evaluation. Multi-class systems of limited capacity have been studied much less than parallel homogeneous systems (Erlang models). In this context, accurate models for parallel heterogeneous ordered-entry systems were developed: without any prior queue, i.e., M/Mi/c/c, and with a k-capacity queue, i.e., M/Mi/c/c + k. These new matrix models gave an exact state formulation, and their accuracy was verified using discrete event simulation and comparison with literature results. Also, the effect of the queue capacity was studied in relationship to the pattern of service rates. Next, the heterogeneous recirculating system model was also developed with good approximation results. Finally, the proposed models were applied to evaluate systems with non-exponential service times using a new hybrid methodology by combining the Markovian model and the Monte Carlo method (MCM) for normal or lognormal service times, which also yielded useful good approximations to the simulated system.

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Section: Introductionmentioning

confidence: 99%

Production Systems with Parallel Heterogeneous Servers of Limited Capacity: Accurate Modeling and Performance Analysis

Calvo,

Arteaga

2024

Applied Sciences

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“…Further extensions in parallel heterogeneous system studies can be found in Boxma et al (1994) [17], who gave a comprehensive view of solution methods at the epoch. Isguder and Uzunoglu (2014) [18] dealt with the semi-Markov process of GI/M/n/0 and loss quantification; and more recently Melikov et al (2020) [19] with an exact formulation, but approximate resolution for ordered entry. Specifically, systems under the ordered entry discipline can also be referred to the work of Cooper (1976) [20] that concludes the need for a multi-dimensional birth-and-death process to represent the system.…”

Section: Introductionmentioning

confidence: 99%

Production systems with parallel heterogeneous servers of limited capacity: accurate modeling and performance analysis

Calvo,

Arteaga

2023

Preprint

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Heterogeneous systems of limited capacity have general applications in manufacturing, but also for logistic or service systems, due to the differences in server or workstation performance or work assignment, in close relationship with system flexibility, where saturation and blocking are ordinary situations of systems with high demand and limited capacity, so accurate loss quantification is essential for performance evaluation. Multi-class systems of limited capacity have been studied much less than parallel homogeneous systems (Erlang models). In this context, accurate models for parallel heterogeneous ordered-entry systems are developed: without any prior queue, M/Mi/c/c, and with a k capacity queue M/Mi/c/c+k. These new matrix models give an exact state formulation, and their accuracy is verified through discrete event simulation and comparison with literature results. Also, the effect of queue capacity is studied in relationship with the pattern of service rates. Next, the heterogeneous recirculating system model is also developed with good approximation results. Finally, the proposed models are applied to evaluate systems with non-exponential service times, through a new hybrid methodology by combining the Markovian model and the Monte Carlo Method (MCM) for normal or lognormal service times that also yield useful good approximations to the simulated system.

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“…In [1], devoted to the study of QHS models, a Markovian infinite-queue system is studied, in which one of the free servers is assigned to service jobs of equal probability (this scheme is called randomized access). An analysis of the available literature has shown that the vast majority of studies investigate QHS models, which adopt randomized access schemes [1][2][3] and ordered access schemes [4][5][6][7][8]. An overview of these studies can be found in [9,10].…”

Section: Introductionmentioning

confidence: 99%

On the problem of the switching of the fast server

Bayramov¹,

Mehbaliyeva²

2022

Informatics and Control Problems

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A Markovian model of a system with two heterogeneous servers is investigated, in which the slow server is always on, and the fast server can turn on when the job queue length reaches a certain value. Models with unlimited and limited size of the buffer of waiting jobs are considered. A numerical method for calculating the probability distribution of states and characteristics of the systems under study is developed. The results of numerical experiments are given.

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Analysis of GI / M / n / n queueing system with ordered entry and no waiting line

Cited by 14 publications

References 32 publications

Production Systems with Parallel Heterogeneous Servers of Limited Capacity: Accurate Modeling and Performance Analysis

Production Systems with Parallel Heterogeneous Servers of Limited Capacity: Accurate Modeling and Performance Analysis

Production systems with parallel heterogeneous servers of limited capacity: accurate modeling and performance analysis

On the problem of the switching of the fast server

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