We consider a class of phase-type distributions (PH-distributions), to be called the MMPP class of PH-distributions, and find bounds of their mean and squared coefficient of variation (SCV). As an application, we have shown that the SCV of the event-stationary inter-event time for Markov modulated Poisson processes (MMPPs) is greater than or equal to unity, which answers an open problem for MMPPs. The results are useful for selecting proper PH-distributions and counting processes in stochastic modeling.

A new generalised Hadjidimos preconditioner and preconditioned generalised AOR method for the solution of the linear complementarity problem are presented. The convergence and convergence rate of the new method are analysed, and numerical experiments demonstrate that it is efficient.

The absolutely continuous spectrum of a very general class of differential operators of order $2n$ is determined, for operators whose coefficients satisfy conditions that combine smoothness and decay properties. The main methods are asymptotic integration and the analysis of the associated $M$-matrix. The form of the solutions precludes the absence of a singular continuous spectrum.