A repairable second optional service queueing system with warm and cold standbys

Throughout this paper, efforts are being made to analyse the availability of the second optional service queueing system with two kinds of servers on hold. One is warm-standby and the other is cold-standby. First essential service (FES) is provided to all arriving customers and only some of them may further demand second optional service (SOS). Both operating and standby servers provide FES and SOS to customers. Replacing the warmstandby server with the failed main operating server may not be successful. Each time an operating server or a warm-standby server fails, it is quickly sent to a repair facility. The combined approach for two models is presented through the indicator function. We derive the steady-state solution of the model using matrix geometric method. The numerical results are shown in which several features of the system are evaluated for both models. A cost model is developed to determine the optimal service rates during the first essential and second optional services using particle swarm optimisation. Copyright © 2021 Inderscience Enterprises Ltd.