A note on many-server queueing systems with ordered entry, with an application to conveyor theory

Nawijn, W.M.

doi:10.2307/3213728

Cited by 18 publications

(3 citation statements)

References 3 publications

(4 reference statements)

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“…With a focus on heterogeneous systems with retrial, surveys by Muth and White (1979) [24] and Nazzal and El-Nashar (2007) [25] are noted for simulation works. Nawijn (1983Nawijn ( , 1984 [26,27] studied the analytical model of two heterogeneous servers with recirculation, while Pourbabai (1987) [28] studied the asymptotic performances of random access and an ordered entry G/M/K/O with approximate expressions. Recently, Boysen et al (2019) [29] presented a revision focused on the operation and not on modeling.…”

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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“…With the focus on heterogeneous systems with retrial, it can be remarked the surveys by Muth and White (1979) [24], and Nazzal and El-Nashar (2007) [25] for simulation works. Nawijn (1983Nawijn ( , 1984 [26,27] studied the analytical model of two heterogeneous servers with recirculation, Pourbabai (1987) [28], the asymptotic performances of random access, and an ordered entry G/M/K/O with approximate expressions. Recently, Boysen et al (2019) [29] have presented a revision focused on the operation and not on modeling.…”

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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“…For a review of the literature on closed-loop conveyor systems, see Sonderman (1982). For a review of the related queueing systems literature, see Nawijn (1983b ).…”

Section: Introductionmentioning

confidence: 99%

Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers

Pourbabai¹,

Sonderman²

1986

Journal of Applied Probability

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Approximation expressions for the server utilization factor of each server in a heterogeneous-server G/G/n queueing loss system with ordered entry are derived. The system is assumed to face a stationary counting process. Service times are generally distributed with possibly different service rates. The numerical results from this approximation method are then compared with those from a simulation study.

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A note on many-server queueing systems with ordered entry, with an application to conveyor theory

Cited by 18 publications

References 3 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

Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers

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