Generalized Folding Algorithm for Transient Analysis of Finite QBD Processes and Its Queueing Applications

Abstract

In this paper we propose and implement a generalized Folding-algorithm for the transient analysis of finite QBD processes. It is a numerical method for the direct computation of xP= a where P is the QBD generator matrix in block tri-diagonal form. Define the QBD state space in two dimensions with N phases and K levels, so that $P \in {{R}^{{NK \times NK}}}andx,a \in {{R}^{{J \times NK}}},\forall J$. The time complexity of the algorithm for solving x P = a is the greater of O(N ³ log₂ K) and O(N ² KJ). The algorithm is found to be highly stable with superior error performance. In numerical studies we analyze the transient performance of MMPP/M/1 queueing system with finite buffer capacity. The MMPP arrival process is constructed to reflect the diversity of the second-order input statistics. We examine the effect of the second-order input statistics on transient queueing performance.