SOME ERGODICITY AND TRUNCATION BOUNDS FOR A SMALL SCALE MARKOVIAN SUPERCOMPUTER MODEL

In this paper we address the transient analysis of a markovian two-server supercomputer model where customers are served by a random number of servers simultaneously. The Markov process, which described the model’s evolution, is of quasi–birth–death type. It is shown that, at least under low load conditions, the logarithmic norm method can be used to obtain ergodicity bounds for the model. This allows one to solve both the stability detection problem (i.e. determine when the computations of the time–dependent performance measures can be terminated) and the truncation problem (i.e. locate the level at which the infinite system of Kolmogorov forward equations must be truncated in order to guarantee certain accuracy). An illustrative numerical example is provided. ©ECMS Ibrahim A. Hameed, Agus Hasan, Saleh Abdel-Afou Alaliyat (Editors) 2022