Continuous-time QBD processes with continuous phase variable
In this paper, we consider a continuous-time level-dependent QBD process with a continuous phase variable. We extend the censoring technique to be able to deal with the QBD process. We define a new version for the R- and G-measures, and provide two types of RG-factorizations in terms of these measures. If the matrix of generalized density functions of the QBD process is in L-2([0, +infinity)(2)), which is a space of square integrable bivariate real functions, then we provide orthonormal representations for the R- and G-measures, which lead to the matrix structure of the RG-factorizations. Based on this, we can provide an algorithmic framework for computing main performance measures of the QBD process. Furthermore, we introduce a continuous phase type (CPH) distribution, and then analyze a CPH/CPH/1 queue as an interesting example. (c) 2006 Elsevier Ltd. All rights reserved.
qbd process the censoring technique the rg factorization orthonormal basis the stationary probability distribution the first passage time continuous phase type distribution