Structured Markov chains solver

Abstract

The package SMC-Solver for solving structured Markov chains is presented. It contains the most advanced algorithms for solving QBD, M/G/1 and G/M/1 problems. The package is provided in two versions: a Matlab toolbox and a Fortran 95 version with a user-friendly graphical interface.

An advanced queueing model to analyze appointment-driven service systems

“…With respect to computational performance, the algorithms are implemented in Visual C while all other computations are performed using the Matlab software package and the structured Markov chain solver developed by [2]. The computations are performed on an doi:10.1016/j.cor.2008.12.008 • www.stefancreemers.be • info@stefancreemers.be AMD Athlon with 2.0 GHz CPU-speed and 768 MB of RAM.…”

“…Matrix analytical techniques have been studied for several decades and have attracted the attention of many researchers in the queueing field. For an overview of literature and an introduction to matrix analytical techniques, refer to [7], [12], [10] and [1] among others. In short, matrix analytical techniques allow the (numerically) exact analysis of a wide variety of queueing systems featuring some repetitive structure (more specifically, M/G/1, GI/M/1 and quasibirth-death processes).…”

“…More specifically, this involves the computation of an auxilliary matrix G j which is obtained as the solution of [1]:…”

“…Together with probabilities φ[1, t, d|j, s, c], the stationary distribution π[s, c|j] serves as the input of the algorithm outlined below. The algorithm is a simple iterative procedure that consists of two steps: (1) iteration; (2) evaluation. In what follows, we discuss these steps in detail.…”

Efficient analysis of the queue length moments of the MMAP/MAP/1 preemptive priority queue

“…The execution environment is an average PC with an Intel Core i7 processor running at 3.4 GHz and 4 GB of RAM. The matrix-quadratic equations arising at several steps are solved by logarithmic reduction, while we used the SMCSolver package ( [17]) for obtaining the fundamental matrix of the M/G/1 queue corresponding to the zero level (note that it is used only by the other methods involved in the comparison as our method does not need it).…”