Economic and Sensitivity Analyses of Controllable Queues With Customer Feedback and Impatience Using Markovian Modeling

The present investigation proposes a unique strategy for the establishment of a controllable queuing system using Markovian modeling. In comparison to conventional models, this approach combines customer impatience, feedback procedure, and working vacation into the statistical modeling of queues in a novel manner. These aspects contain enormous potential for practical applications but require additional evaluation from an operational or customer service perspective through dynamic investigation. Effective management of customer arrival, as well as departure, can be achieved by the explicit modeling of control strategies rendered feasible by the suggested queuing‐theoretic framework. The study shows how the queue‐size distribution has evolved over time using the Laplace transformation approach. Furthermore, extensive numerical illustrations based on optimal and sensitivity investigations are carried out covering multiple system parameters to confirm the significance of this unique approach. The findings of the study, which are based on stochastic modeling, are shown both tabularly and graphically. Moreover, the research findings obtained through the economic and sensitivity investigations significantly differentiate the aforementioned approach from the current literature by providing enhanced management and applicability to practical queuing circumstances.