Metaheuristics and strategic behavior of markovian retrial queue under breakdown, vacation and bernoulli feedback

This research article addresses the performance analysis of Markovian retrial queueing system with two types of customers, unreliable server, and Bernoulli feedback. Both regular customers (RC) and prime customers (PC) may either join, or balk from the system based on the trade-off between service profit and delay cost. When the system is busy, the regular customers have to choose whether to join a retrial orbit and make re-attempts or leave the system. Furthermore, due to congestion among regular customers, the server may discontinue the service during breakdown. Due to the unavailability of the service process, customers may experience dissatisfaction. Therefore, our objective is to introduce a Bernoulli feedback service process to enhance service quality, ensuring that customers are successfully served with a certain probability. To analyze the proposed model mathematically, Chapman-Kolmogorov (C-K) inflow-outflow balanced equations have been framed. Then, the probability generating function (PGF) method employed to explicitly derive the queue size distribution, throughput, and other performance metrics. These performance measures provide critical insights into system behavior, which are then incorporated to determine the equilibrium strategies for two types of joining strategies: (i) non-cooperative strategies and (ii) cooperative strategies. Finally, optimization approaches are employed to determine the optimum cost and make tactical decisions regarding the quality of service (QoS) in an integrated manner. The cost optimization is done using metaheuristic optimization techniques such as PSO and GWO. The analytic results established are validated by numerical simulation. The effect of various parameters on the performance indices are examined by cost optimization and sensitivity analysis. The comparison of both algorithms, including average fitness, standard deviation, and convergence analysis, were used and combined with Wilcoxon rank-sum test.