Mookkaiyah Chandran Saravanarajan

In this study, we investigate a single-server retrial queueing system that incorporates balking, immediate feedback, and a Bernoulli working vacation policy. Customers arriving to find the server busy, under repair, or on working vacation may balk; otherwise, they either join the orbit or receive immediate service if the server is available. Upon completion of the service, the customer can request a finite number of immediate feedback services. When the orbit is empty after the completion of a service, the server initiates a working vacation, serving at a reduced rate. If customers are present in the orbit at the end of the vacation, the server resumes normal operation. If the system is empty, the server remains idle or continues the vacation. We analyze the ergodicity conditions to ensure system stability and derive the stationary distribution of the underlying Markov process. Several key performance measures are computed. Furthermore, a comprehensive cost function is developed and optimized using metaheuristic approaches, including particle swarm optimization and the genetic algorithm. The convergence behavior and optimization results are illustrated through graphical analysis, offering insight into improving the efficiency of complex retrial queueing systems.

This paper analyzes the M/G (P1, P2)/1 queue using a single server that provides essential services in both the first phase (FPS) and the second phase (SPS). It was assumed that the server undertakes unreliability due to starting failure (SF) during the beginning of the first phase with probability (α) or service begins by the idle server successfully with probability (1-α) for the arriving or retrial customer. Then immediately took the failed server for repair and launched the customer into orbit. Also, the server operates at varying rates instead of fully ceasing service during its vacation. After returning from vacation, the server resumes normal operations for the customers. It also discussed the system, orbit size, and other significant metrics, utilizing the supplementary variable technique (SVT) and the probability generating function (PGF). Applications for this retrial queueing system incorporating the model and a general decomposition law were discussed. Numerical analysis was established to examine the impact of different factors on the system’s efficiency. MATLAB software was used to establish several impacts of the system’s behavioral measures.

Queueing systems (QS) play a critical role in modeling and optimizing various real-world processes by managing the flow of entities within systems involving queues. To address this, the proposed QS integrates features such as single arrivals, a retrial mechanism, optional re-service, working vacations, and delay repair scenarios. The system’s dynamics are comprehensively analyzed using the supplementary variable technique, which provides deeper insights into its behavior and performance metrics. Furthermore, to enhance operational efficiency, an advanced cost optimization technique is employed to identify the optimal cost structure for the system. This holistic approach not only sheds light on the operational intricacies of the QS but also offers practical strategies for cost reduction and validation of analytical findings, thereby advancing queueing theory and broadening its practical applications across multiple domains.

This research presents a comprehensive analysis of the M/G/1 double retrial queue model with a two-phase optional service and repair, under a working vacation policy. The model addresses scenarios where patients are willing to pay more for enhanced comfort and care. To accommodate this, an optional service phase is introduced, allowing patients to choose between ordinary and premium service levels. The system is further refined by a two-phase service mechanism: in the first phase, patients receive an initial level of service, and depending on their satisfaction or specific needs, they may opt for an enhanced second phase of service. Additionally, the model incorporates feedback and repair processes, reflecting a more realistic representation of queue dynamics. Patients who are dissatisfied with the service or encounter issues can re-enter the system for further attention. The non-Markovian model equations are solved using the probability-generating function approach, which facilitates the analysis of complex queue behaviors and the calculation of key performance indicators, such as expected system length and queue length. The paper includes detailed numerical results with test data to demonstrate the accuracy of the model’s predictions and validate the proposed system design’s effectiveness.

This paper introduces a double-orbit retrial queue model designed to address patient dissatisfaction by taking into account their willingness to pay for enhanced comfort and service. The system incorporates non-Markovian characteristics and employs a probability-generating function approach to solve its equations. Key performance metrics investigated include expected queue length, system length, and the precision of numerical results derived from empirical data. The model’s application is specifically examined within a hospital management system (HMS), underscoring its relevance in healthcare operations. Overall, the paper offers valuable insights into optimizing design strategies for retrial queue systems featuring unreliable servers, with a focus on enhancing patient satisfaction through personalized service offerings.