Mathematical modelling of Multi-Server Queueing Model for Vacations and Impatient Customers

Abstract

This research presents a novel Multi-Server Queueing Model planned to recreate benefit frameworks considering both server excursions and customer impatience, tending to a basic hole in existing writing. The demonstration is approved through an arrangement of tests investigating the effect of varying arrival rates, benefit rates, server vacation frequencies, and restlessness limits on framework execution. Results illustrate that compared to conventional models, joining server excursions leads to an increment in normal holding-up time and a diminishment in server utilization. Also, considering customer impatience altogether raises the customer deserting rate. The tests emphasize the model's capacity to reflect the nuanced flow of real-world benefit scenarios, uncovering trade-offs between framework productivity and client fulfilment. This research contributes a comprehensive system for understanding and optimizing service-oriented businesses, progressing past the customary queueing hypothesis.