Formulation and Performance Assessment for Multiple Server Queueing Models

Queueing theory has grown in prominence as it provides the numerical foundation for decision-making assessment. Queueing models with multiple servers provide extensive decision-making data, which is critical for evaluating a server's performance. The purpose of this study is to formulate multiple server queueing models and provides a performance assessment to evaluate the appropriate models. A three-phased structured approach has been used to model and analyze performance for multiple server queueing models. The "Multiple Server Finite Queue Length Infinite Queue Population Model" is most desirable for a customer who has to wait for less time (approximately 43.14%) in the system as well as in the queue (approximately 62.16%) and reduces the system length by approximately 47.02% and the queue length by approximately 64.76%. However, the "Multiple Server Infinite Queue Length Infinite Queue Population Model" is preferable from a managerial perspective, as the "Multiple Server Finite Queue Length Infinite Queue Population Model" has fewer customers in the system, indicating a loss from a managerial standpoint. When the arrival rate of customers, service rate, and the number of servers are increased, length of the system and queue remain nearly constant, whereas the waiting time in the system nearly doubles for both queueing models. The paper develops a performance evaluation of the “Multiple Server Infinite Queue Length Infinite Queue Population Model” and “Multiple Server Finite Queue Length Infinite Queue Population Model”, which are capable of adapting to an unpredictable decision in any service system. Furthermore, this study provides decision-makers with a perspective-based evaluation of the mentioned servers, with a focus on a manager and a customer.