Performance Analysis of A Queueing System with Server Arrival and Departure

In many systems, in order to fulfill demand (computing or other services) that varies over time, service capacities often change accordingly. In this paper, we analyze a simple two dimensional Markov chain model of a queueing system in which multiple servers can arrive to increase service capacity, and depart if a server has been idle for too long. It is well known that multi-dimensional Markov chains are in general difficult to analyze. Our focus is on an approximation method of stationary performance of the system via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the Poisson equation with a partial differential operator.