Journal of Quality Engineering and Management

Improving the Quality of M/M/m/K Queueing Systems Using System Cost Function Optimization

Document Type : Original Article

Authors

Iman Makhdoom 1
Shahram Yaghoobzadeh Shahrastani 2

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

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

https://doi.org/10.48313/jqem.2023.208474
Abstract
In this article, a queuing system with finite capacity, referred to as M/M/m/K, is analyzed for m ≥ 2, where K represents the system's capacity and m indicates the number of servers. Initially, a function known as the system cost function is introduced. This function is based on the number of customers present in the queue and the number of servers available. The main objective is to identify the optimal number of servers, termed mOpt, that minimizes the system cost function. This optimal configuration, denoted as M/M/mOpt/K, is termed the optimal system. To illustrate the concept, a numerical example is provided, showcasing various values of K to determine the optimal systems. The analysis covers key performance metrics such as the average number of customers in the queue and the entire system, the average waiting time of the customers both in the queue and the system, and a metric referred to as the average degree of customer satisfaction within these queuing systems. Through this comprehensive approach, the study aims to provide valuable insights into optimizing queuing systems for better efficiency and customer satisfaction.

Keywords

The M/M/m/K queuing system
Optimal system
Cost function
Optimal number of servers
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Journal of Quality Engineering and Management
Volume 13, Issue 3
Autumn 2023
Pages 267-280

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