Abstract:We consider a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) {(X n , J n )} on Z 2 + × S 0 , where X n = (X 1,n , X 2,n ) is the level state, J n the phase state (background state) and S 0 a finite set, and study asymptotic properties of the stationary tail distribution. The 2d-QBD process is an extension of usual one-dimensional QBD process. By using the matrix analytic method of the queueing theory and the complex analytic method, we obtain the asymptotic decay rate of… Show more
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