A multi-server with backup system employs decision strategies to enhance its service

Abstract

The queueing paradigm is frequently applied in the manufacturing, inventory, and service industries. The effectiveness of the queuing model can be greatly enhanced by specifying the real properties of queuing. This research examines impatient client behaviors that may lead to renege in a multi-server queuing system, as well as the strategic behavior of the service provider that tries to enhance the service by adding a backup server. A very intricate multi-dimensional continuous-time Markov chain that has been successfully analysed accurately describes the system's behavior. The decision rules are used to frame the value function and the iteration algorithm is used to get the total expected cost and the optimal average cost of the entire system. By enabling the numerical results for the relevant case, the sensitivity analysis is carried out.