Analysis of Markovian queueing system with second optional service operating under the triadic policy

In this paper, we investigate an M / M /2 queueing system with a second optional service that operates under a triadic (0, Q , N , M ) policy. The stability condition and stationary probability distribution of the system size are computed by adopting the matrix-geometric method. Numerous system performance measures are also derived. The quadratic fit search method is applied to the cost optimization problem in order to optimize service rates during the first essential service and the second optional service. Finally, numerical results are presented for the illustration of the effect of model parameters.