The BRI Algorithm for Double-Sides QBD Process

In this paper, we study the two-dimensional tri-diagonal quasi-birth-and-death (QBD) process with infinite blocks and the blocks are infinite double sides tri-diagonal matrices, which has an important application in queue theory such as joining the shortest queue problem. Our objective is to develop an accurate and easily implementable algorithmic approach to compute the stationary probabilities of the process. We also give the computational complexity for the algorithm and some numerical examples.