Optimal Cost Analysis for Discrete-Time Recurrent Queue with Bernoulli Feedback and Emergency Vacation

Abstract

This paper evaluates the efficacy of a discrete-time GeoX/G/1 recurrent model with Bernoulli feedback and two independent types of vacations, one of them is a non-exhaustive vacation which is needed urgently whilst performing named as emergency vacation and the other is a compulsory (usual) vacation. In the selected framework, we acquire generating functions for distinct server states. Continuing, using the generating function methodology, we accomplish a steady-state analysis. We have also retrieved a wide variety of different performance indices such as long run probabilities while the server is available for service, on occupied state, on ordinary vacation and on compulsory vacation. These derived measures are then envisioned and validated with the assistance of tables and graphs. Further, this study is expedited to induce the best (optimal) cost for the system using different methodologies such as direct search, particle swarm optimization (PSO), artificial bee colony (ABC), Cuckoo search (CS), and genetic algorithm (GA) and we also studied the convergence of these optimization techniques through figures. In addition to this, we have used an adaptive neuro-fuzzy interface system soft computing technology to compare the analytical results with that of neuro-fuzzy results.