Methods of analysis and computation for queueing systems with phase distributions
One calls phase distribution function [\textit{M. F. Neuts}, Matrix- geometric solutions in stochastic models. (1981; Zbl 0469.60002)] a distribution function that can be represented in the form \(F(x)=1- \alpha^ Te^{Gx}I,\quad x\geq 0,\quad F(x)=0,\quad x<0\), where \(\alpha\) is an m-vector, \(\alpha_ j\geq 0\) \((j=1,...,m)\), \(\sum \alpha_ j\leq 1;\quad G\) is an \(m\times m\) matrix, \(\sum_{j}G_{ij}\leq 0,\quad G_{ij}\geq 0\) (i\(\neq j),\quad G_{ii}<0\), \((i,j=1,...,m)\), and at least for one i,\ \(\sum_{j}G_{ij}<0;\quad I\) is the m-vector with the entries 1. The paper is a survey of the properties of PH-distributions and of some relevant results regarding queueing systems with phase distributed interarrival times and service times.
queueing systems with phase distributed interarrival times
scientific article; zbMATH DE number 4007416