Stability test in 2-D s-z domain for queue systems

Based on 2-D Laplace-z transform, this paper develops a 2-D stability test for queue systems with fixed parameters. In this paper, classical queue systems with fixed parameters are modeled into 2-D continuous-discrete systems with fixed parameters. Then taking 2-D Laplace-z transform for them, we obtain the 2-D s-z domain queue models. Applying the presented Hurwitz-Schur stability theorems, the stability of typical queue systems can be determined in 2-D s-z domain, it is not necessary to find the solutions of queue systems in time-state domain, which is difficult generally. In the 2-D stability analysis of queue systems, this paper reveals that 2-D boundary conditions of queue systems may lead to the problem of second kind nonessential singularities. The hybrid 2-D transform¿s definitions and theorems for the stability analysis of queue systems are given in the paper. Examples are given to verify the results of this paper.