Statistical Analysis Of Multi-Phase Single Server And Multi-Phase Multi Server: Comparison Study

Abstract

Queues, or waiting lines, are ubiquitous in various facets of daily life. The study of queuing models proves invaluable for optimizing the operation of systems where waiting times for customers are a critical consideration. This research paper delves into the comparative analysis of two prominent queuing models—multi-phase single-server and multi-phase multi-server—aiming to establish the superiority of the latter in terms of operational efficiency and customer satisfaction. The investigation begins by acknowledging the omnipresence of queues and their impact on service-oriented environments. Recognizing the significance of minimizing customer waiting times, the research focuses on queuing models as effective tools for system optimization. The primary objective is to validate the assertion that the multi-phase multi-server queuing model outperforms its single-server counterpart in delivering enhanced service quality. Through rigorous statistical analysis, the research examines key performance metrics, including throughput, response time, and resource utilization, to provide a comprehensive understanding of the operational dynamics of both queuing models. By comparing the outcomes under varying workloads and conditions, the study aims to delineate the strengths and weaknesses inherent in each system architecture. Also this paper aims to construct  code of the Chi-Square Test using MATLAB Software. The findings of this research contribute valuable insights to decision-makers across diverse industries, offering guidance on optimal queuing system design. The multi-phase multi-server queuing model's superiority is substantiated by empirical evidence, paving the way for informed decision-making in sectors ranging from telecommunications and manufacturing to service-oriented industries. Furthermore, the research explores the implications of adopting the multi-phase multi-server approach, emphasizing its potential to address challenges related to scalability and resource allocation. As queues continue to play a pivotal role in shaping customer experiences, this study endeavors to offer practical recommendations for enhancing operational efficiency and customer satisfaction through the implementation of advanced queuing models.