Speaker
Description
communication networks, computer systems, and service industries. Traditional models often assume complete vacations, but more realistic scenarios include working vacations, where the server operates at a reduced service rate. At the same time, modern applications must also account for impatient customer behaviors such as balking and reneging, as well as feedback mechanisms where unsatisfied customers may rejoin the system.
In this paper, we investigate an $M/M/1/K$ queueing system with hybrid vacations (a combination of working and complete vacations), Bernoulli feedback, balking, reneging, and retention. Recursive techniques are employed to compute the steady-state probabilities, which are then used to derive a variety of performance measures, including average queue length, waiting times, balking and reneging rates, and system utilization.
Furthermore, recognizing the importance of cost-efficiency, we formulate a cost optimization problem that balances service quality and operational expense. To solve this optimization task, we apply the Grey Wolf Optimizer (GWO), a powerful swarm intelligence algorithm.
Additionally, we implement a Multilayer Perceptron (MLP) model trained on analytical data generated from the system. The MLP is used to approximate performance metrics such as the average queue length, offering a machine-learning-based alternative to exact analytical computation. Numerical experiments demonstrate that the MLP achieves high accuracy with low error rates, closely matching theoretical results.
Our contributions include:
A comprehensive analytical framework integrating multiple realistic features (hybrid vacations, feedback, and impatience).
The development of optimization strategies using GWO.
Validation of analytical results with a data-driven MLP model.
This study provides both theoretical and practical insights into the design and management of modern queueing systems, ensuring a balance between efficiency and service quality.
