Mathematical modeling of Multi-Server Queueing Model for vacations and impatient customer

Abstract

This study proposes a new Multi-Server Queueing Model that has been developed to represent the dynamic nature of server trips and restless customers in service-intensive organisations. The act of conjoining the elements of different servers, holidays, and client patience combines an entire system that surpasses standard queueing theory as the precision of the model was corroborated through broad recreations, close congruity with the classical M/M/c/K queueing incident can be hinted from the M/Gamma/c/NII model. The sensitivity analyses revealed the model’s responsiveness to fluctuating anxiety thresholds and server travel routes, highlighting the model’s adaptability in reflecting complexities in the flow of the control graph. Yesterday to the working environment of a call center, proved the implementation by the approved demonstration, predicted the significant repeating chances with accuracy. Comparisons with existing literature underscored the interesting commitments of the coordinates shown in giving an all-encompassing understanding of modern benefit frameworks. The proposed model's viability in optimizing asset utilization and making strides in client fulfillment positions it as an important instrument for decision-makers in service-oriented industries. The coordinates demonstrate illustrated exact forecasts in comparison to the M/M/c/K demonstrate, with blocking probabilities closely coordinating in different scenarios. Sensitivity investigation uncovered diminishing blocking probabilities with expanding restlessness edges.