Journal of Quality Engineering and Management

Optimization for enhancing the quality of the queueing model family {M/Er/1,r∈N} based on the cost function, probability of system stationary, and customer satisfaction under a finite time horizon

Document Type : Original Article

Authors

Shahram Yaghoobzadeh Shahrastani
Amrollah Jafari
Iman Makhdoom

Department of Statistics, Payame Noor University, Tehran, Iran.

https://doi.org/10.48313/jqem.2025.537574.1567
Abstract
Purpose: This study aims to determine the optimal model within the family of queueing models, where interarrival times follow an exponential distribution and service times follow an Erlang distribution, under a finite stopping time TTT. The significance of this research lies in its application to optimizing the performance of service systems using queueing theory.
Methodology: To select the optimal model, a cost function and a performance metric, namely the average customer satisfaction level, are first defined. Subsequently, a new index, named ORS, is introduced based on the cost function, average customer satisfaction, and the system's stability probability. The optimal model is identified as the one with the highest ORS value. Numerical analysis is employed to demonstrate the procedure for determining the optimal model.
Findings: The numerical results indicate that the ORS index is an effective criterion for evaluating and comparing different queueing models, enabling optimal model selection by incorporating multiple performance aspects.
Originality/Value: The main contribution of this research is the introduction of the ORS index as a novel and comprehensive measure for optimal model selection in queueing systems. This approach can enhance service system design and improve customer satisfaction levels in practical applications.

Keywords

Erlang distribution
Cost function
Average degeree of customer satisfaction
Family of modela {M/Er/1
r&‌‌‌‌isin
N}
Stationary probability
Subjects
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Journal of Quality Engineering and Management
Volume 15, Issue 3
Autumn 2025
Pages 271-280

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