Analysis of a Multi-server Queueing System with Balking, Reneging and Encouraged Arrivals Embedded in Dynamic Inputting Probability

Abstract

This paper develops a state-dependent queueing model incorporating balking, reneging, and motivating service mechanisms, with a novel integration of encouraged arrivals embedded within the dynamic inputting probability. Unlike traditional models that assume monotonic arrival behaviour, the proposed framework introduces a non-monotonic inputting function to capture both attraction and discouragement effects based on system congestion. The model is formulated as a birth–death process, and steady-state probabilities are derived. Key performance measures, including expected system size, queue length, and waiting times, are obtained. Numerical analysis and statistical validation using regression techniques demonstrate that the proposed model provides a significantly improved fit to real-world data compared to classical models. The results highlight the importance of incorporating encouragement effects to accurately represent modern service systems influenced by customer perception and incentives.