Some efficient computational algorithms related to phase models

Summary

This paper develops efficient computational algorithms for some models that utilize phase type distributions. As in other instances, such as matrix-geometric methods, where the PH-distribution lends itself to useful and efficient computational methods, we examine how certain probabilities based on these distributions may be efficiently computed. The examples that we consider include token ring networks, simple multiqueues, and order statistics. By exploiting the geometric nature of PH-densities, it is shown that certain exponential time computations can be reduced to linear time, if recursive algorithms are used. We demonstrate speedup with the aid of a practical example, using a recursive as well as a nonrecursive algorithm, in verifying the stability of a queue on a token ring network.