Development of computational algorithm for multiserver queue with renewal input and synchronous vacation

In this paper, we develop a new computational algorithm for calculating the Markov chain stationary distribution based on a Taylor series approach, where the Taylor series coefficients are expressed in closed-form in terms of the fundamental matrix of the underlying Markov chain. Additionally, we provide an approximate expression for the remainder term of the Taylor series that can be computed in an efficient manner. Specifically, we demonstrate the application of the proposed framework in analyzing a multi-server queueing system with synchronous vacation. The only required assumption of the proposed framework is that the entries of the transition matrix are differentiable functions with respect to a control parameter. Numerical examples are sketched out to illustrate the accuracy of the proposed method.