<p>This paper presents a comprehensive analytical study of a multi-server queueing-inventory system that incorporates the novel concepts of synergistic servers and encouraged customer arrivals. The system comprises two distinct groups of servers: a traditional set catering to regular customers, and a synergistic set where pairs of servers collaborate to serve premium customers requesting expedited service. Customer arrivals follow an encouraged arrival pattern, influenced by past promotional activities and discounts. A quasi-birth-death process is developed to model the system mathematically, and the steady-state joint probability vector is obtained using matrix-analytic methods. Extensive numerical investigations are conducted to evaluate the system’s performance, with a focus on total cost, waiting times, and resource utilisation. The impact of parameters on the expected total cost has been studied, and a comparison with the synergistic server model and the traditional server model is carried out. Additionally, a parametric sensitivity analysis is performed to examine the effect of system parameters on the average number of occupied busy servers. The results demonstrate the significant advantages of server synergy in enhancing system throughput, reducing customer waiting times, and optimising resource allocation.</p>