Reliability and Sensitivity Analysis of Retrial Queue with Optional k-Phases Services, Vacation and Feedback

Queueing theory is implemented for modeling and analyzing actual conditions in industries and real-world problems. In many cases, the input is converted to the desired output after several successive steps. Lack of space, feedback and vacation are the main characters of these processes. This article deals with the modeling and analyzing the steady-state behavior of an M/G/1 retrial queueing system with first essential and k - 1 optional phases of service. Also, the probabilistic feedback to orbit at each phase and Bernoulli vacation at the end of k-th phase may occur in this system. If the customers find the server busy or on vacation, they join to the orbit. In this article, after finding the probability generating functions of the system and orbit sizes, some important performance measures are found. Also, the system reliability is defined. Eventually, to demonstrate the capability of the proposed model, the sensitivity analysis of cost indices and performance measures via some model parameters (arrival/retrial/vacation rate) in different reliability levels are investigated in two applicable examples. Additionally, for optimizing the performance of the system, some technical suggestions are presented.